1
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Mao YL, Chen H, Guo B, Liu S, Li ZD, Luo MX, Fan J. Certifying Network Topologies and Nonlocalities of Triangle Quantum Networks. PHYSICAL REVIEW LETTERS 2024; 132:240801. [PMID: 38949366 DOI: 10.1103/physrevlett.132.240801] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/06/2023] [Accepted: 04/09/2024] [Indexed: 07/02/2024]
Abstract
Quantum networks promise unprecedented advantages in information processing and open up intriguing new opportunities in fundamental research, where network topology and network nonlocality fundamentally underlie these applications. Hence, the detections of network topology and nonlocality are crucial, which, however, remain an open problem. Here, we conceive and experimentally demonstrate to determine the network topology and network nonlocality hosted by a triangle quantum network comprising three parties, within and beyond Bell theorem, with a general witness operator for the first time. We anticipate that this unique approach may stimulate further studies toward the efficient characterization of large complex quantum networks so as to better harness the advantage of quantum networks for quantum information applications.
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Affiliation(s)
- Ya-Li Mao
- Department of Physics and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Hu Chen
- Department of Physics and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Bixiang Guo
- Department of Physics and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Shiting Liu
- Department of Physics and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Zheng-Da Li
- Department of Physics and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Ming-Xing Luo
- School of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, Hefei, 230026, China
| | - Jingyun Fan
- Department of Physics and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
- Center for Advanced Light Source, Southern University of Science and Technology, Shenzhen, 518055, China
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2
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Böttcher L, Porter MA. Complex networks with complex weights. Phys Rev E 2024; 109:024314. [PMID: 38491610 DOI: 10.1103/physreve.109.024314] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/15/2022] [Accepted: 12/20/2023] [Indexed: 03/18/2024]
Abstract
In many studies, it is common to use binary (i.e., unweighted) edges to examine networks of entities that are either adjacent or not adjacent. Researchers have generalized such binary networks to incorporate edge weights, which allow one to encode node-node interactions with heterogeneous intensities or frequencies (e.g., in transportation networks, supply chains, and social networks). Most such studies have considered real-valued weights, despite the fact that networks with complex weights arise in fields as diverse as quantum information, quantum chemistry, electrodynamics, rheology, and machine learning. Many of the standard network-science approaches in the study of classical systems rely on the real-valued nature of edge weights, so it is necessary to generalize them if one seeks to use them to analyze networks with complex edge weights. In this paper, we examine how standard network-analysis methods fail to capture structural features of networks with complex edge weights. We then generalize several network measures to the complex domain and show that random-walk centralities provide a useful approach to examine node importances in networks with complex weights.
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Affiliation(s)
- Lucas Böttcher
- Department of Computational Science and Philosophy, Frankfurt School of Finance and Management, 60322 Frankfurt am Main, Germany
- Department of Medicine, University of Florida, Gainesville, Florida, 32610, USA
| | - Mason A Porter
- Department of Mathematics, University of California, Los Angeles, California 90095, USA
- Department of Sociology, University of California, Los Angeles, California 90095, USA
- Santa Fe Institute, Santa Fe, New Mexico 87501, USA
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3
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Makris N. Revisiting Schrödinger's fourth-order, real-valued wave equation and the implication from the resulting energy levels. ROYAL SOCIETY OPEN SCIENCE 2023; 10:230793. [PMID: 38126064 PMCID: PMC10731319 DOI: 10.1098/rsos.230793] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/12/2023] [Accepted: 11/22/2023] [Indexed: 12/23/2023]
Abstract
In his seminal part IV, Annalen der Physik vol. 81, 1926 paper, Schrödinger has developed a clear understanding about the wave equation that produces the correct quadratic dispersion relation for matter-waves and he first presents a real-valued wave equation that is fourth-order in space and second-order in time. In the view of the mathematical difficulties associated with the eigenvalue analysis of a fourth-order, differential equation in association with the structure of the Hamilton-Jacobi equation, Schrödinger splits the fourth-order real operator into the product of two, second-order, conjugate complex operators and retains only one of the two complex operators to construct his iconic second-order, complex-valued wave equation. In this paper, we show that Schrödinger's original fourth-order, real-valued wave equation is a stiffer equation that produces higher energy levels than his second-order, complex-valued wave equation that predicts with remarkable accuracy the energy levels observed in the atomic line spectra of the chemical elements. Accordingly, the fourth-order, real-valued wave equation is too stiff to predict the emitted energy levels from the electrons of the chemical elements; therefore, the paper concludes that quantum mechanics can only be described with the less stiff, second-order, complex-valued wave equation.
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Affiliation(s)
- Nicos Makris
- Department of Civil and Environmental Engineering, Southern Methodist University, Dallas, TX 75276, USA
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4
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Mao YL, Chen H, Niu C, Li ZD, Yu S, Fan J. Testing Heisenberg-Type Measurement Uncertainty Relations of Three Observables. PHYSICAL REVIEW LETTERS 2023; 131:150203. [PMID: 37897772 DOI: 10.1103/physrevlett.131.150203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/29/2022] [Revised: 04/18/2023] [Accepted: 09/15/2023] [Indexed: 10/30/2023]
Abstract
Heisenberg-type measurement uncertainty relations (MURs) of two quantum observables are essential for contemporary research in quantum foundations and quantum information science. Going beyond, here we report the first experimental study of MUR of three quantum observables. We establish rigorously MURs for triplets of unbiased qubit observables as combined approximation errors lower bounded by an incompatibility measure, inspired by the proposal of Busch et al. [Phys. Rev. A 89, 012129 (2014)PLRAAN1050-294710.1103/PhysRevA.89.012129]. We develop a convex programming protocol to numerically find the exact value of the incompatibility measure and the optimal measurements. We propose a novel implementation of the optimal joint measurements and present several experimental demonstrations with a single-photon qubit. We stress that our method is universally applicable to the study of many qubit observables. Besides, we theoretically show that MURs for joint measurement can be attained by sequential measurements in two of our explored cases. We anticipate that this work may stimulate broad interests associated with Heisenberg's uncertainty principle in the case of multiple observables, enriching our understanding of quantum mechanics and inspiring innovative applications in quantum information science.
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Affiliation(s)
- Ya-Li Mao
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Hu Chen
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Chang Niu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Zheng-Da Li
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Sixia Yu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jingyun Fan
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
- Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
- Center for Advanced Light Source, Southern University of Science and Technology, Shenzhen, 518055, China
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5
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Wootters WK. Optimal Information Transfer and the Uniform Measure over Probability Space. ENTROPY (BASEL, SWITZERLAND) 2023; 25:875. [PMID: 37372219 DOI: 10.3390/e25060875] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2023] [Revised: 05/29/2023] [Accepted: 05/29/2023] [Indexed: 06/29/2023]
Abstract
For a quantum system with a d-dimensional Hilbert space, suppose a pure state |ψ⟩ is subjected to a complete orthogonal measurement. The measurement effectively maps |ψ⟩ to a point (p1,…,pd) in the appropriate probability simplex. It is a known fact-which depends crucially on the complex nature of the system's Hilbert space-that if |ψ⟩ is distributed uniformly over the unit sphere, then the resulting ordered set (p1,…,pd) is distributed uniformly over the probability simplex; that is, the resulting measure on the simplex is proportional to dp1⋯dpd-1. In this paper we ask whether there is some foundational significance to this uniform measure. In particular, we ask whether it is the optimal measure for the transmission of information from a preparation to a measurement in some suitably defined scenario. We identify a scenario in which this is indeed the case, but our results suggest that an underlying real-Hilbert-space structure would be needed to realize the optimization in a natural way.
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6
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Wang NN, Pozas-Kerstjens A, Zhang C, Liu BH, Huang YF, Li CF, Guo GC, Gisin N, Tavakoli A. Certification of non-classicality in all links of a photonic star network without assuming quantum mechanics. Nat Commun 2023; 14:2153. [PMID: 37059704 PMCID: PMC10104853 DOI: 10.1038/s41467-023-37842-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2022] [Accepted: 04/03/2023] [Indexed: 04/16/2023] Open
Abstract
Networks composed of independent sources of entangled particles that connect distant users are a rapidly developing quantum technology and an increasingly promising test-bed for fundamental physics. Here we address the certification of their post-classical properties through demonstrations of full network nonlocality. Full network nonlocality goes beyond standard nonlocality in networks by falsifying any model in which at least one source is classical, even if all the other sources are limited only by the no-signaling principle. We report on the observation of full network nonlocality in a star-shaped network featuring three independent sources of photonic qubits and joint three-qubit entanglement-swapping measurements. Our results demonstrate that experimental observation of full network nonlocality beyond the bilocal scenario is possible with current technology.
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Affiliation(s)
- Ning-Ning Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, China
- Hefei National Laboratory, University of Science and Technology of China, 230088, Hefei, China
| | | | - Chao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China.
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, China.
- Hefei National Laboratory, University of Science and Technology of China, 230088, Hefei, China.
| | - Bi-Heng Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, China
- Hefei National Laboratory, University of Science and Technology of China, 230088, Hefei, China
| | - Yun-Feng Huang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China.
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, China.
- Hefei National Laboratory, University of Science and Technology of China, 230088, Hefei, China.
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China.
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, China.
- Hefei National Laboratory, University of Science and Technology of China, 230088, Hefei, China.
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, 230026, Hefei, China
- CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, 230026, Hefei, China
- Hefei National Laboratory, University of Science and Technology of China, 230088, Hefei, China
| | - Nicolas Gisin
- Group of Applied Physics, University of Geneva, 1211, Geneva 4, Switzerland
- Constructor University, Geneva, Switzerland
| | - Armin Tavakoli
- Physics Department, Lund University, Box 118, 22100, Lund, Sweden.
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna Austrian Academy of Sciences, Boltzmanngasse 3, 1090, Vienna, Austria.
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7
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Polino E, Poderini D, Rodari G, Agresti I, Suprano A, Carvacho G, Wolfe E, Canabarro A, Moreno G, Milani G, Spekkens RW, Chaves R, Sciarrino F. Experimental nonclassicality in a causal network without assuming freedom of choice. Nat Commun 2023; 14:909. [PMID: 36808157 PMCID: PMC9938195 DOI: 10.1038/s41467-023-36428-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2021] [Accepted: 01/31/2023] [Indexed: 02/19/2023] Open
Abstract
In a Bell experiment, it is natural to seek a causal account of correlations wherein only a common cause acts on the outcomes. For this causal structure, Bell inequality violations can be explained only if causal dependencies are modeled as intrinsically quantum. There also exists a vast landscape of causal structures beyond Bell that can witness nonclassicality, in some cases without even requiring free external inputs. Here, we undertake a photonic experiment realizing one such example: the triangle causal network, consisting of three measurement stations pairwise connected by common causes and no external inputs. To demonstrate the nonclassicality of the data, we adapt and improve three known techniques: (i) a machine-learning-based heuristic test, (ii) a data-seeded inflation technique generating polynomial Bell-type inequalities and (iii) entropic inequalities. The demonstrated experimental and data analysis tools are broadly applicable paving the way for future networks of growing complexity.
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Affiliation(s)
- Emanuele Polino
- grid.7841.aDipartimento di Fisica-Sapienza Università di Roma, P.le Aldo Moro 5, I-00185 Roma, Italy
| | - Davide Poderini
- grid.7841.aDipartimento di Fisica-Sapienza Università di Roma, P.le Aldo Moro 5, I-00185 Roma, Italy ,grid.411233.60000 0000 9687 399XInternational Institute of Physics, Federal University of Rio Grande do Norte, 59078-970, P. O. Box 1613 Natal, Brazil
| | - Giovanni Rodari
- grid.7841.aDipartimento di Fisica-Sapienza Università di Roma, P.le Aldo Moro 5, I-00185 Roma, Italy
| | - Iris Agresti
- grid.7841.aDipartimento di Fisica-Sapienza Università di Roma, P.le Aldo Moro 5, I-00185 Roma, Italy
| | - Alessia Suprano
- grid.7841.aDipartimento di Fisica-Sapienza Università di Roma, P.le Aldo Moro 5, I-00185 Roma, Italy
| | - Gonzalo Carvacho
- grid.7841.aDipartimento di Fisica-Sapienza Università di Roma, P.le Aldo Moro 5, I-00185 Roma, Italy
| | - Elie Wolfe
- Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, ON, N2L 2Y5, Canada.
| | - Askery Canabarro
- grid.411233.60000 0000 9687 399XInternational Institute of Physics, Federal University of Rio Grande do Norte, 59078-970, P. O. Box 1613 Natal, Brazil ,grid.411179.b0000 0001 2154 120XGrupo de Física da Matéria Condensada, Núcleo de Ciências Exatas-NCEx, Campus Arapiraca, Universidade Federal de ALagoas, 57309-005 Arapiraca, Alagoas Brazil
| | - George Moreno
- grid.411233.60000 0000 9687 399XInternational Institute of Physics, Federal University of Rio Grande do Norte, 59078-970, P. O. Box 1613 Natal, Brazil ,grid.411177.50000 0001 2111 0565Departamento de Computação, Universidade Federal Rural de Pernambuco, 52171-900 Recife, Pernambuco Brazil
| | - Giorgio Milani
- grid.7841.aDipartimento di Fisica-Sapienza Università di Roma, P.le Aldo Moro 5, I-00185 Roma, Italy
| | - Robert W. Spekkens
- grid.420198.60000 0000 8658 0851Perimeter Institute for Theoretical Physics, 31 Caroline St. N, Waterloo, ON N2L 2Y5 Canada
| | - Rafael Chaves
- International Institute of Physics, Federal University of Rio Grande do Norte, 59078-970, P. O. Box 1613, Natal, Brazil. .,School of Science and Technology, Federal University of Rio Grande do Norte, Natal, Brazil.
| | - Fabio Sciarrino
- Dipartimento di Fisica-Sapienza Università di Roma, P.le Aldo Moro 5, I-00185, Roma, Italy.
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8
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Schuch D, Bonilla-Licea M. Uncertainty Relations in the Madelung Picture Including a Dissipative Environment. ENTROPY (BASEL, SWITZERLAND) 2023; 25:312. [PMID: 36832678 PMCID: PMC9955996 DOI: 10.3390/e25020312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/24/2022] [Revised: 01/31/2023] [Accepted: 02/02/2023] [Indexed: 06/18/2023]
Abstract
In a recent paper, we have shown how in Madelung's hydrodynamic formulation of quantum mechanics, the uncertainties are related to the phase and amplitude of the complex wave function. Now we include a dissipative environment via a nonlinear modified Schrödinger equation. The effect of the environment is described by a complex logarithmic nonlinearity that vanishes on average. Nevertheless, there are various changes in the dynamics of the uncertainties originating from the nonlinear term. Again, this is illustrated explicitly using generalized coherent states as examples. With particular focus on the quantum mechanical contribution to the energy and the uncertainty product, connections can be made with the thermodynamic properties of the environment.
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Affiliation(s)
- Dieter Schuch
- Institute of Theoretical Physics, Goethe-University Frankfurt, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany
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9
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Soleimani P, Khoshsima H, Yeganeh M. Optical vortex beam controlling based on fork grating stored in a dye-doped liquid crystal cell. Sci Rep 2022; 12:21271. [PMID: 36481872 PMCID: PMC9732362 DOI: 10.1038/s41598-022-25779-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 12/05/2022] [Indexed: 12/13/2022] Open
Abstract
In this paper, we investigate the generation and controlling of the optical vortex beam using a dye-doped liquid crystal (DDLC) cell. The spatial distribution of the quasi-sinusoidal orientation of the liquid crystal molecules creates a quasi-sinusoidal phase grating (PG) in the DDLC cell. Depending on the incident light pattern, Trans to Cis photoisomerization of the dye molecules affects the orientation of the liquid crystal molecules. To do so, an amplitude fork grating (FG) is used as a mask, and its pattern is stored in the cell by a pattern printing method as the PG. One of the particular features of the stored grating in the cell is its capability in the diffraction efficiency controlled by the applied electric field. The results show, based on the central defect in the FG pattern, the diffracted probe beam in different orders is optical vortices. As a new technique, this type of stored pattern acts like an amplitude grating but according to the results, its structure is in fact a PG. This technique leads to the vortex beam switching capability by applying an electric field to the cell. The results show that by applying 22 V, all the diffraction orders vanish. Meanwhile, the vortex beams reappear by removing the applied voltage. The diffraction efficiency of the vortex beams as well as its generation dependency on the polarization of the incident beam studied. The maximum efficiency of the first diffraction order for linear polarized incident beam was obtained at 0 V, about 8%. Based on the presented theory, a simulation has been done which shows the Cis form of the dye molecules has been able to change the angle of LC molecules on average about 12.7°. The study of diffracted beam profiles proves that they are electrically controllable vortex beams.
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Affiliation(s)
- P. Soleimani
- grid.412831.d0000 0001 1172 3536Faculty of Physics, University of Tabriz, Tabriz, Iran
| | - H. Khoshsima
- grid.412831.d0000 0001 1172 3536Faculty of Physics, University of Tabriz, Tabriz, Iran
| | - M. Yeganeh
- grid.412831.d0000 0001 1172 3536Faculty of Physics, University of Tabriz, Tabriz, Iran
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10
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Mohageg M, Mazzarella L, Anastopoulos C, Gallicchio J, Hu BL, Jennewein T, Johnson S, Lin SY, Ling A, Marquardt C, Meister M, Newell R, Roura A, Schleich WP, Schubert C, Strekalov DV, Vallone G, Villoresi P, Wörner L, Yu N, Zhai A, Kwiat P. The deep space quantum link: prospective fundamental physics experiments using long-baseline quantum optics. EPJ QUANTUM TECHNOLOGY 2022; 9:25. [PMID: 36227029 PMCID: PMC9547810 DOI: 10.1140/epjqt/s40507-022-00143-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/09/2021] [Accepted: 09/15/2022] [Indexed: 06/16/2023]
Abstract
The National Aeronautics and Space Administration's Deep Space Quantum Link mission concept enables a unique set of science experiments by establishing robust quantum optical links across extremely long baselines. Potential mission configurations include establishing a quantum link between the Lunar Gateway moon-orbiting space station and nodes on or near the Earth. This publication summarizes the principal experimental goals of the Deep Space Quantum Link. These goals, identified through a multi-year design study conducted by the authors, include long-range teleportation, tests of gravitational coupling to quantum states, and advanced tests of quantum nonlocality.
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Affiliation(s)
- Makan Mohageg
- Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California USA
| | - Luca Mazzarella
- Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California USA
| | | | - Jason Gallicchio
- Department of Physics, Harvey Mudd College, Claremont, California USA
| | - Bei-Lok Hu
- Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, Maryland USA
| | - Thomas Jennewein
- Institute for Quantum Computing and Dep. of Physics and Astronomy, University of Waterloo, Waterloo, Canada
| | - Spencer Johnson
- Department of Physics, Illinois Quantum Information Science & Technology Center, University of Illinois at Urbana-Champaign, Urbana, Illinois USA
| | - Shih-Yuin Lin
- Department of Physics, National Changhua University of Education, Changhua, Taiwan
| | - Alexander Ling
- Centre for Quantum Technologies and Department of Physics, National University of Singapore, Singapore, Singapore
| | | | - Matthias Meister
- Institute of Quantum Technologies, German Aerospace Center (DLR), Ulm, Germany
| | - Raymond Newell
- Los Alamos National Laboratory, Los Alamos, New Mexico USA
| | - Albert Roura
- Institute of Quantum Technologies, German Aerospace Center (DLR), Ulm, Germany
| | - Wolfgang P. Schleich
- Institute of Quantum Technologies, German Aerospace Center (DLR), Ulm, Germany
- Institut für Quantenphysik and Center for Integrated Quantum Science and Technology (IQst), Universität Ulm, Ulm, Germany
- Hagler Institute for Advanced Study, AgriLife Research, Institute for Quantum Science and Engineering (IQSE), and Department of Physics and Astronomy, Texas A& M University, College Station, Texas USA
| | - Christian Schubert
- Institute for Satellite Geodesy and Inertial Sensing, German Aerospace Center (DLR), Hanover, Germany
- Institute for Quantum Optics, Germany Leibniz University Hannover, Hanover, Germany
| | - Dmitry V. Strekalov
- Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California USA
| | - Giuseppe Vallone
- Dipartimento di Ingegneria dell’Informazione, Universitá degli Studi di Padova, Padova, Italy
- Padua Quantum Technologies Research Center, Universitá degli Studi di Padova, Padova, Italy
- Dipartimento di Fisica e Astronomia, Universitá degli Studi di Padova, Padova, Italy
| | - Paolo Villoresi
- Dipartimento di Ingegneria dell’Informazione, Universitá degli Studi di Padova, Padova, Italy
- Padua Quantum Technologies Research Center, Universitá degli Studi di Padova, Padova, Italy
| | - Lisa Wörner
- Institute of Quantum Technologies, German Aerospace Center (DLR), Ulm, Germany
| | - Nan Yu
- Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California USA
| | - Aileen Zhai
- Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California USA
| | - Paul Kwiat
- Department of Physics, University of Patras, Patras, Greece
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11
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Mao YL, Li ZD, Yu S, Fan J. Test of Genuine Multipartite Nonlocality. PHYSICAL REVIEW LETTERS 2022; 129:150401. [PMID: 36269952 DOI: 10.1103/physrevlett.129.150401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2022] [Accepted: 08/31/2022] [Indexed: 06/16/2023]
Abstract
While Bell nonlocality of a bipartite system is counterintuitive, multipartite nonlocality in our many-body world turns out to be even more so. Recent theoretical study reveals in a theory-agnostic manner that genuine multipartite nonlocal correlations cannot be explained by any causal theory involving fewer-partite nonclassical resources and global shared randomness. Here, we provide a Bell-type inequality as a test for genuine multipartite nonlocality in network by exploiting a matrix representation of the causal structure of a multipartite system. We further present experimental demonstrations that both four-photon GHZ state and generalized four-photon GHZ state significantly violate the inequality, i.e., the observed four-partite correlations resist explanations involving three-way nonlocal resources subject to local operations and common shared randomness, hence confirming that nature is boundless multipartite nonlocal.
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Affiliation(s)
- Ya-Li Mao
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
- Center for Advanced Light Source, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Zheng-Da Li
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
| | - Sixia Yu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jingyun Fan
- Shenzhen Institute for Quantum Science and Engineering and Department of Physics, Southern University of Science and Technology, Shenzhen, 518055, China
- Center for Advanced Light Source, Southern University of Science and Technology, Shenzhen, 518055, China
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12
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Wu D, Jiang YF, Gu XM, Huang L, Bai B, Sun QC, Zhang X, Gong SQ, Mao Y, Zhong HS, Chen MC, Zhang J, Zhang Q, Lu CY, Pan JW. Experimental Refutation of Real-Valued Quantum Mechanics under Strict Locality Conditions. PHYSICAL REVIEW LETTERS 2022; 129:140401. [PMID: 36240393 DOI: 10.1103/physrevlett.129.140401] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/11/2022] [Revised: 06/29/2022] [Accepted: 08/08/2022] [Indexed: 06/16/2023]
Abstract
Quantum mechanics is commonly formulated in a complex, rather than real, Hilbert space. However, whether quantum theory really needs the participation of complex numbers has been debated ever since its birth. Recently, a Bell-like test in an entanglement-swapping scenario has been proposed to distinguish standard quantum mechanics from its real-valued analog. Previous experiments have conceptually demonstrated, yet not satisfied, the central requirement of independent state preparation and measurements and leave several loopholes. Here, we implement such a Bell-like test with two separated independent sources delivering entangled photons to three separated parties under strict locality conditions that are enforced by spacelike separation of the relevant events, rapid random setting generation, and fast measurement. With the fair-sampling assumption and closed loopholes of independent source, locality, and measurement independence simultaneously, we violate the constraints of real-valued quantum mechanics by 5.30 standard deviations. Our results disprove the real-valued quantum theory to describe nature and ensure the indispensable role of complex numbers in quantum mechanics.
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Affiliation(s)
- Dian Wu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Yang-Fan Jiang
- Jinan Institute of Quantum Technology, Jinan 250101, China
| | - Xue-Mei Gu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Liang Huang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Bing Bai
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Qi-Chao Sun
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Xingjian Zhang
- Center for Quantum Information, Institute for Interdisciplinary Information Sciences, Tsinghua University, Beijing 100084, China
| | - Si-Qiu Gong
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Yingqiu Mao
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Han-Sen Zhong
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Ming-Cheng Chen
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jun Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Qiang Zhang
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Chao-Yang Lu
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jian-Wei Pan
- Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- Shanghai Research Center for Quantum Science and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
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13
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Tavakoli A, Pozas-Kerstjens A, Luo MX, Renou MO. Bell nonlocality in networks. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2022; 85:056001. [PMID: 34883470 DOI: 10.1088/1361-6633/ac41bb] [Citation(s) in RCA: 17] [Impact Index Per Article: 8.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2021] [Accepted: 12/09/2021] [Indexed: 06/13/2023]
Abstract
Bell's theorem proves that quantum theory is inconsistent with local physical models. It has propelled research in the foundations of quantum theory and quantum information science. As a fundamental feature of quantum theory, it impacts predictions far beyond the traditional scenario of the Einstein-Podolsky-Rosen paradox. In the last decade, the investigation of nonlocality has moved beyond Bell's theorem to consider more sophisticated experiments that involve several independent sources which distribute shares of physical systems among many parties in a network. Network scenarios, and the nonlocal correlations that they give rise to, lead to phenomena that have no counterpart in traditional Bell experiments, thus presenting a formidable conceptual and practical challenge. This review discusses the main concepts, methods, results and future challenges in the emerging topic of Bell nonlocality in networks.
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Affiliation(s)
- Armin Tavakoli
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Institute for Atomic and Subatomic Physics, Vienna University of Technology, 1020 Vienna, Austria
| | - Alejandro Pozas-Kerstjens
- Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain
- Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM), Madrid, Spain
| | - Ming-Xing Luo
- Information Coding & Transmission Key Laboratory of Sichuan Province, School of Information Science & Technology, Southwest Jiaotong University, Chengdu 610031, People's Republic of China
- Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, China
| | - Marc-Olivier Renou
- ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, 08860 Castelldefels (Barcelona), Spain
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14
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Linear Superposition as a Core Theorem of Quantum Empiricism. UNIVERSE 2022. [DOI: 10.3390/universe8040217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Clarifying the nature of the quantum state |Ψ⟩ is at the root of the problems with insight into counter-intuitive quantum postulates. We provide a direct—and math-axiom free—empirical derivation of this object as an element of a vector space. Establishing the linearity of this structure—quantum superposition—is based on a set-theoretic creation of ensemble formations and invokes the following three principia: (I) quantum statics, (II) doctrine of the number in the physical theory, and (III) mathematization of matching the two observations with each other (quantum covariance). All of the constructs rest upon a formalization of the minimal experimental entity—the registered micro-event, detector click. This is sufficient for producing the C-numbers, axioms of linear vector space (superposition principle), statistical mixtures of states, eigenstates and their spectra, and non-commutativity of observables. No use is required of the spatio-temporal concepts. As a result, the foundations of theory are liberated to a significant extent from the issues associated with physical interpretations, philosophical exegeses, and mathematical reconstruction of the entire quantum edifice.
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15
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Chen MC, Wang C, Liu FM, Wang JW, Ying C, Shang ZX, Wu Y, Gong M, Deng H, Liang FT, Zhang Q, Peng CZ, Zhu X, Cabello A, Lu CY, Pan JW. Ruling Out Real-Valued Standard Formalism of Quantum Theory. PHYSICAL REVIEW LETTERS 2022; 128:040403. [PMID: 35148136 DOI: 10.1103/physrevlett.128.040403] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2021] [Accepted: 12/07/2021] [Indexed: 06/14/2023]
Abstract
Standard quantum theory was formulated with complex-valued Schrödinger equations, wave functions, operators, and Hilbert spaces. Previous work attempted to simulate quantum systems using only real numbers by exploiting an enlarged Hilbert space. A fundamental question arises: are the complex numbers really necessary in the standard formalism of quantum theory? To answer this question, a quantum game has been developed to distinguish standard quantum theory from its real-number analog, by revealing a contradiction between a high-fidelity multiqubit quantum experiment and players using only real-number quantum theory. Here, using superconducting qubits, we faithfully realize the quantum game based on deterministic entanglement swapping with a state-of-the-art fidelity of 0.952. Our experimental results violate the real-number bound of 7.66 by 43 standard deviations. Our results disprove the real-number formulation and establish the indispensable role of complex numbers in the standard quantum theory.
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Affiliation(s)
- Ming-Cheng Chen
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Can Wang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Feng-Ming Liu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jian-Wen Wang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Chong Ying
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Zhong-Xia Shang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Yulin Wu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - M Gong
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - H Deng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - F-T Liang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Qiang Zhang
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Cheng-Zhi Peng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Xiaobo Zhu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, E-41012 Sevilla, Spain
| | - Chao-Yang Lu
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
| | - Jian-Wei Pan
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
- CAS Centre for Excellence and Synergetic Innovation Centre in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China
- Shanghai Research Center for Quantum Sciences, Shanghai 201315, China
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16
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Avella A. Quantum Mechanics Must Be Complex. PHYSICS 2022. [DOI: 10.1103/physics.15.7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
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