1
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Jiráková K, Černoch A, Barasiński A, Lemr K. Enhancing collective entanglement witnesses through correlation with state purity. Sci Rep 2024; 14:16374. [PMID: 39013996 PMCID: PMC11252302 DOI: 10.1038/s41598-024-65385-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2024] [Accepted: 06/19/2024] [Indexed: 07/18/2024] Open
Abstract
This research analyzes the adverse impact of white noise on collective quantum measurements and argues that such noise poses a significant obstacle for the otherwise straightforward deployment of collective measurements in quantum communications. Our findings then suggests addressing this issue by correlating outcomes of these measurements with quantum state purity. To test the concept, a support vector machine is employed to boost the performance of several collective entanglement witnesses by incorporating state purity into the classification task of distinguishing entangled states from separable ones. Furthermore, the application of machine learning allows to optimize specificity of entanglement detection given a target value of sensitivity. A response operating characteristic curve is reconstructed based on this optimization and the area under curve calculated to assess the efficacy of the proposed model. Finally, we test the presented approach on an experimental dataset of Werner states.
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Affiliation(s)
- Kateřina Jiráková
- Institute of Physics of the Academy of Sciences of the Czech Republic, Joint Laboratory of Optics of Palacký University and Institute of Physics AS CR, 17. listopadu 50a, 772 07, Olomouc, Czech Republic
| | - Antonín Černoch
- Institute of Physics of the Academy of Sciences of the Czech Republic, Joint Laboratory of Optics of Palacký University and Institute of Physics AS CR, 17. listopadu 50a, 772 07, Olomouc, Czech Republic
| | - Artur Barasiński
- Institute of Theoretical Physics, University of Wroclaw, Plac Maxa Borna 9, 50-204, Wroclaw, Poland
| | - Karel Lemr
- Joint Laboratory of Optics of Palacký University, Institute of Physics AS CR, Faculty of Science, Palacký University in Olomouc, 17. listopadu 12, 771 46, Olomouc, Czech Republic.
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2
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Abo S, Soubusta J, Jiráková K, Bartkiewicz K, Černoch A, Lemr K, Miranowicz A. Experimental hierarchy of two-qubit quantum correlations without state tomography. Sci Rep 2023; 13:8564. [PMID: 37237018 DOI: 10.1038/s41598-023-35015-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/22/2023] [Accepted: 05/11/2023] [Indexed: 05/28/2023] Open
Abstract
A Werner state, which is the singlet Bell state affected by white noise, is a prototype example of states, which can reveal a hierarchy of quantum entanglement, steering, and Bell nonlocality by controlling the amount of noise. However, experimental demonstrations of this hierarchy in a sufficient and necessary way (i.e., by applying measures or universal witnesses of these quantum correlations) have been mainly based on full quantum state tomography, corresponding to measuring at least 15 real parameters of two-qubit states. Here we report an experimental demonstration of this hierarchy by measuring only six elements of a correlation matrix depending on linear combinations of two-qubit Stokes parameters. We show that our experimental setup can also reveal the hierarchy of these quantum correlations of generalized Werner states, which are any two-qubit pure states affected by white noise.
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Affiliation(s)
- Shilan Abo
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614, Poznań, Poland
| | - Jan Soubusta
- Palacký University Olomouc, Faculty of Science, Joint Laboratory of Optics of PU and IP CAS, 17. listopadu 1192/12, 779 00, Olomouc, Czech Republic.
| | - Kateřina Jiráková
- Palacký University Olomouc, Faculty of Science, Joint Laboratory of Optics of PU and IP CAS, 17. listopadu 1192/12, 779 00, Olomouc, Czech Republic
| | - Karol Bartkiewicz
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614, Poznań, Poland
- Palacký University Olomouc, Faculty of Science, Joint Laboratory of Optics of PU and IP CAS, 17. listopadu 1192/12, 779 00, Olomouc, Czech Republic
| | - Antonín Černoch
- Institute of Physics of the Czech Academy of Sciences, Joint Laboratory of Optics of PU and IP CAS, 17. listopadu 1154/50a, 779 00, Olomouc, Czech Republic
| | - Karel Lemr
- Palacký University Olomouc, Faculty of Science, Joint Laboratory of Optics of PU and IP CAS, 17. listopadu 1192/12, 779 00, Olomouc, Czech Republic
| | - Adam Miranowicz
- Institute of Spintronics and Quantum Information, Faculty of Physics, Adam Mickiewicz University, 61-614, Poznań, Poland.
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3
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Schneeloch J, Tison CC, Jacinto HS, Alsing PM. Negativity vs. purity and entropy in witnessing entanglement. Sci Rep 2023; 13:4601. [PMID: 36944676 PMCID: PMC10030834 DOI: 10.1038/s41598-023-31273-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2022] [Accepted: 03/09/2023] [Indexed: 03/23/2023] Open
Abstract
In this paper, we explore the value of measures of mixedness in witnessing entanglement. While all measures of mixedness may be used to witness entanglement, we show that all such entangled states must have a negative partial transpose (NPT). Where the experimental resources needed to determine this negativity scale poorly at high dimension, we compare different measures of mixedness over both Haar-uniform and uniform-purity ensembles of joint quantum states at varying dimension to gauge their relative success at witnessing entanglement. In doing so, we find that comparing joint and marginal purities is overwhelmingly (albeit not exclusively) more successful at identifying entanglement than comparing joint and marginal von Neumann entropies, in spite of requiring fewer resources. We conclude by showing how our results impact the fundamental relationship between correlation and entanglement and related witnesses.
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Affiliation(s)
- James Schneeloch
- Air Force Research Laboratory, Information Directorate, Rome, NY, 13441, USA.
| | - Christopher C Tison
- Air Force Research Laboratory, Information Directorate, Rome, NY, 13441, USA
| | - H Shelton Jacinto
- Air Force Research Laboratory, Information Directorate, Rome, NY, 13441, USA
| | - Paul M Alsing
- Air Force Research Laboratory, Information Directorate, Rome, NY, 13441, USA
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4
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Dehesa JS. Rényi Entropies of Multidimensional Oscillator and Hydrogenic Systems with Applications to Highly Excited Rydberg States. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1590. [PMID: 36359680 PMCID: PMC9689141 DOI: 10.3390/e24111590] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/18/2022] [Revised: 10/29/2022] [Accepted: 10/31/2022] [Indexed: 06/16/2023]
Abstract
The various facets of the internal disorder of quantum systems can be described by means of the Rényi entropies of their single-particle probability density according to modern density functional theory and quantum information techniques. In this work, we first show the lower and upper bounds for the Rényi entropies of general and central-potential quantum systems, as well as the associated entropic uncertainty relations. Then, the Rényi entropies of multidimensional oscillator and hydrogenic-like systems are reviewed and explicitly determined for all bound stationary position and momentum states from first principles (i.e., in terms of the potential strength, the space dimensionality and the states's hyperquantum numbers). This is possible because the associated wavefunctions can be expressed by means of hypergeometric orthogonal polynomials. Emphasis is placed on the most extreme, non-trivial cases corresponding to the highly excited Rydberg states, where the Rényi entropies can be amazingly obtained in a simple, compact, and transparent form. Powerful asymptotic approaches of approximation theory have been used when the polynomial's degree or the weight-function parameter(s) of the Hermite, Laguerre, and Gegenbauer polynomials have large values. At present, these special states are being shown of increasing potential interest in quantum information and the associated quantum technologies, such as e.g., quantum key distribution, quantum computation, and quantum metrology.
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Affiliation(s)
- Jesús S. Dehesa
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain;
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain
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5
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Dehesa JS. Spherical-Symmetry and Spin Effects on the Uncertainty Measures of Multidimensional Quantum Systems with Central Potentials. ENTROPY (BASEL, SWITZERLAND) 2021; 23:607. [PMID: 34068983 PMCID: PMC8156006 DOI: 10.3390/e23050607] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 04/18/2021] [Revised: 05/10/2021] [Accepted: 05/11/2021] [Indexed: 01/06/2023]
Abstract
The spreading of the stationary states of the multidimensional single-particle systems with a central potential is quantified by means of Heisenberg-like measures (radial and logarithmic expectation values) and entropy-like quantities (Fisher, Shannon, Rényi) of position and momentum probability densities. Since the potential is assumed to be analytically unknown, these dispersion and information-theoretical measures are given by means of inequality-type relations which are explicitly shown to depend on dimensionality and state's angular hyperquantum numbers. The spherical-symmetry and spin effects on these spreading properties are obtained by use of various integral inequalities (Daubechies-Thakkar, Lieb-Thirring, Redheffer-Weyl, ...) and a variational approach based on the extremization of entropy-like measures. Emphasis is placed on the uncertainty relations, upon which the essential reason of the probabilistic theory of quantum systems relies.
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Affiliation(s)
- Jesús S. Dehesa
- Departamento de Física Atómica, Molecular y Nuclear, Universidad de Granada, 18071 Granada, Spain;
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, 18071 Granada, Spain
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6
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Wang DZ, Gauthier AQ, Siegmund AE, Hunt KLC. Bell inequalities for entangled qubits: quantitative tests of quantum character and nonlocality on quantum computers. Phys Chem Chem Phys 2021; 23:6370-6387. [PMID: 33538732 DOI: 10.1039/d0cp05444e] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
This work provides quantitative tests of the extent of violation of two inequalities applicable to qubits coupled into Bell states, using IBM's publicly accessible quantum computers. Violations of the inequalities are well established. Our purpose is not to test the inequalities, but rather to determine how well quantum mechanical predictions can be reproduced on quantum computers, given their current fault rates. We present results for the spin projections of two entangled qubits, along three axes A, B, and C, with a fixed angle θ between A and B and a range of angles θ' between B and C. For any classical object that can be characterized by three observables with two possible values, inequalities govern relationships among the probabilities of outcomes for the observables, taken pairwise. From set theory, these inequalities must be satisfied by all such classical objects; but quantum systems may violate the inequalities. We have detected clear-cut violations of one inequality in runs on IBM's publicly accessible quantum computers. The Clauser-Horne-Shimony-Holt (CHSH) inequality governs a linear combination S of expectation values of products of spin projections, taken pairwise. Finding S > 2 rules out local, hidden variable theories for entangled quantum systems. We obtained values of S greater than 2 in our runs prior to error mitigation. To reduce the quantitative errors, we used a modification of the error-mitigation procedure in the IBM documentation. We prepared a pair of qubits in the state |00〉, found the probabilities to observe the states |00〉, |01〉, |10〉, and |11〉 in multiple runs, and used that information to construct the first column of an error matrix M. We repeated this procedure for states prepared as |01〉, |10〉, and |11〉 to construct the full matrix M, whose inverse is the filtering matrix. After applying filtering matrices to our averaged outcomes, we have found good quantitative agreement between the quantum computer output and the quantum mechanical predictions for the extent of violation of both inequalities as functions of θ'.
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Affiliation(s)
- David Z Wang
- Department of Chemistry, Michigan State University, East Lansing, MI 48824, USA.
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Styliaris G, Anand N, Zanardi P. Information Scrambling over Bipartitions: Equilibration, Entropy Production, and Typicality. PHYSICAL REVIEW LETTERS 2021; 126:030601. [PMID: 33543955 DOI: 10.1103/physrevlett.126.030601] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/29/2020] [Revised: 12/02/2020] [Accepted: 12/07/2020] [Indexed: 06/12/2023]
Abstract
In recent years, the out-of-time-order correlator (OTOC) has emerged as a diagnostic tool for information scrambling in quantum many-body systems. Here, we present exact analytical results for the OTOC for a typical pair of random local operators supported over two regions of a bipartition. Quite remarkably, we show that this "bipartite OTOC" is equal to the operator entanglement of the evolution, and we determine its interplay with entangling power. Furthermore, we compute long-time averages of the OTOC and reveal their connection with eigenstate entanglement. For Hamiltonian systems, we uncover a hierarchy of constraints over the structure of the spectrum and elucidate how this affects the equilibration value of the OTOC. Finally, we provide operational significance to this bipartite OTOC by unraveling intimate connections with average entropy production and scrambling of information at the level of quantum channels.
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Affiliation(s)
- Georgios Styliaris
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
- Munich Center for Quantum Science and Technology, Schellingstrasse 4, 80799 München, Germany
- Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA
| | - Namit Anand
- Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA
| | - Paolo Zanardi
- Department of Physics and Astronomy, and Center for Quantum Information Science and Technology, University of Southern California, Los Angeles, California 90089, USA
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8
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Trávníček V, Bartkiewicz K, Černoch A, Lemr K. Experimental Measurement of the Hilbert-Schmidt Distance between Two-Qubit States as a Means for Reducing the Complexity of Machine Learning. PHYSICAL REVIEW LETTERS 2019; 123:260501. [PMID: 31951446 DOI: 10.1103/physrevlett.123.260501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/03/2019] [Indexed: 06/10/2023]
Abstract
We report on the experimental measurement of the Hilbert-Schmidt distance between two two-qubit states by many-particle interference. We demonstrate that our three-step method for measuring distances in the Hilbert space is far less complex than reconstructing density matrices and that it can be applied in quantum-enhanced machine learning to reduce the complexity of calculating Euclidean distances between multidimensional points, which can be especially interesting for near term quantum technologies and quantum artificial intelligence research. Our results are also a novel example of applying mixed states in quantum information processing. Usually working with mixed states is undesired, but here it gives the possibility of encoding extra information as the degree of coherence between the given two dimensions of the density matrix.
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Affiliation(s)
- Vojtěch Trávníček
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences, 17. listopadu 12, 771 46 Olomouc, Czech Republic
| | - Karol Bartkiewicz
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences, 17. listopadu 12, 771 46 Olomouc, Czech Republic
- Faculty of Physics, Adam Mickiewicz University, PL-61-614 Poznań, Poland
| | - Antonín Černoch
- Institute of Physics of the Czech Academy of Sciences, Joint Laboratory of Optics of PU and IP AS CR, 17. listopadu 50A, 772 07 Olomouc, Czech Republic
| | - Karel Lemr
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of Czech Academy of Sciences, 17. listopadu 12, 771 46 Olomouc, Czech Republic
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9
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Time-Energy and Time-Entropy Uncertainty Relations in Nonequilibrium Quantum Thermodynamics under Steepest-Entropy-Ascent Nonlinear Master Equations. ENTROPY 2019; 21:e21070679. [PMID: 33267393 PMCID: PMC7515176 DOI: 10.3390/e21070679] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/13/2019] [Revised: 07/07/2019] [Accepted: 07/08/2019] [Indexed: 11/29/2022]
Abstract
In the domain of nondissipative unitary Hamiltonian dynamics, the well-known Mandelstam–Tamm–Messiah time–energy uncertainty relation τFΔH≥ℏ/2 provides a general lower bound to the characteristic time τF=ΔF/|d〈F〉/dt| with which the mean value of a generic quantum observable F can change with respect to the width ΔF of its uncertainty distribution (square root of F fluctuations). A useful practical consequence is that in unitary dynamics the states with longer lifetimes are those with smaller energy uncertainty ΔH (square root of energy fluctuations). Here we show that when unitary evolution is complemented with a steepest-entropy-ascent model of dissipation, the resulting nonlinear master equation entails that these lower bounds get modified and depend also on the entropy uncertainty ΔS (square root of entropy fluctuations). For example, we obtain the time–energy-and–time–entropy uncertainty relation (2τFΔH/ℏ)2+(τFΔS/kBτ)2≥1 where τ is a characteristic dissipation time functional that for each given state defines the strength of the nonunitary, steepest-entropy-ascent part of the assumed master equation. For purely dissipative dynamics this reduces to the time–entropy uncertainty relation τFΔS≥kBτ, meaning that the nonequilibrium dissipative states with longer lifetime are those with smaller entropy uncertainty ΔS.
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10
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Barasiński A, Černoch A, Lemr K. Demonstration of Controlled Quantum Teleportation for Discrete Variables on Linear Optical Devices. PHYSICAL REVIEW LETTERS 2019; 122:170501. [PMID: 31107073 DOI: 10.1103/physrevlett.122.170501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2018] [Indexed: 06/09/2023]
Abstract
We report an experimental implementation of tripartite controlled quantum teleportation on quantum optical devices. The protocol is performed through bi- and tripartite entangled channels of discrete variables and qubits encoded in the polarization of individual photons. The experimental results demonstrate successful controlled quantum teleportation with a fidelity around 83%, well above the classical limit. By realizing the controlled quantum teleportation through a biseparable state, we show that tripartite entanglement is not a necessary resource for controlled quantum teleportation, and the controller's capability to allow or prohibit the teleportation cannot be considered to be a manifestation of tripartite entanglement. These results open new possibilities for further application of controlled quantum teleportation by lowering the teleportation channel's requirements.
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Affiliation(s)
- Artur Barasiński
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
- Institute of Physics, University of Zielona Góra, Z. Szafrana 4a, 65-516 Zielona Góra, Poland
| | - Antonín Černoch
- Institute of Physics of the Czech Academy of Sciences, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, 17. listopadu 50A, 772 07 Olomouc, Czech Republic
| | - Karel Lemr
- RCPTM, Joint Laboratory of Optics of Palacký University and Institute of Physics of CAS, Faculty of Science, Palacký University, 17. listopadu 12, 771 46 Olomouc, Czech Republic
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11
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Gong H, Ullah A, Ye L, Zheng X, Yan Y. Quantum entanglement of parallel-coupled double quantum dots: A theoretical study using the hierarchical equations of motion approach. CHINESE J CHEM PHYS 2018. [DOI: 10.1063/1674-0068/31/cjcp1806138] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Affiliation(s)
- Hong Gong
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Arif Ullah
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - LvZhou Ye
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xiao Zheng
- Hefei National Laboratory for Physical Sciences at the Microscale & Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - YiJing Yan
- Hefei National Laboratory for Physical Sciences at the Microscale & iChEM, University of Science and Technology of China, Hefei 230026, China
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12
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Lu D, Xin T, Yu N, Ji Z, Chen J, Long G, Baugh J, Peng X, Zeng B, Laflamme R. Tomography is Necessary for Universal Entanglement Detection with Single-Copy Observables. PHYSICAL REVIEW LETTERS 2016; 116:230501. [PMID: 27341217 DOI: 10.1103/physrevlett.116.230501] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/24/2016] [Indexed: 06/06/2023]
Abstract
Entanglement, one of the central mysteries of quantum mechanics, plays an essential role in numerous tasks of quantum information science. A natural question of both theoretical and experimental importance is whether universal entanglement detection can be accomplished without full state tomography. In this Letter, we prove a no-go theorem that rules out this possibility for nonadaptive schemes that employ single-copy measurements only. We also examine a previously implemented experiment [H. Park et al., Phys. Rev. Lett. 105, 230404 (2010)], which claimed to detect entanglement of two-qubit states via adaptive single-copy measurements without full state tomography. In contrast, our simulation and experiment both support the opposite conclusion that the protocol, indeed, leads to full state tomography, which supplements our no-go theorem. These results reveal a fundamental limit of single-copy measurements in entanglement detection and provide a general framework of the detection of other interesting properties of quantum states, such as the positivity of partial transpose and the k-symmetric extendibility.
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Affiliation(s)
- Dawei Lu
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
| | - Tao Xin
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Nengkun Yu
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- Centre for Quantum Computation and Intelligent Systems, Faculty of Engineering and Information Technology, University of Technology Sydney, NSW 2007, Australia
- Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
| | - Zhengfeng Ji
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, China
| | - Jianxin Chen
- Joint Center for Quantum Information and Computer Science, University of Maryland, College Park, Maryland 20742, USA
| | - Guilu Long
- State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China
| | - Jonathan Baugh
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
| | - Xinhua Peng
- Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230036, China
| | - Bei Zeng
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario N1G 2W1, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
| | - Raymond Laflamme
- Institute for Quantum Computing, University of Waterloo, Waterloo N2L 3G1, Ontario, Canada
- Canadian Institute for Advanced Research, Toronto, Ontario M5G 1Z8, Canada
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada
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13
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Experimental verification of genuine multipartite entanglement without shared reference frames. Sci Bull (Beijing) 2016. [DOI: 10.1007/s11434-016-1063-5] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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14
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Islam R, Ma R, Preiss PM, Tai ME, Lukin A, Rispoli M, Greiner M. Measuring entanglement entropy in a quantum many-body system. Nature 2016; 528:77-83. [PMID: 26632587 DOI: 10.1038/nature15750] [Citation(s) in RCA: 194] [Impact Index Per Article: 24.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2015] [Accepted: 09/16/2015] [Indexed: 12/28/2022]
Abstract
Entanglement is one of the most intriguing features of quantum mechanics. It describes non-local correlations between quantum objects, and is at the heart of quantum information sciences. Entanglement is now being studied in diverse fields ranging from condensed matter to quantum gravity. However, measuring entanglement remains a challenge. This is especially so in systems of interacting delocalized particles, for which a direct experimental measurement of spatial entanglement has been elusive. Here, we measure entanglement in such a system of itinerant particles using quantum interference of many-body twins. Making use of our single-site-resolved control of ultracold bosonic atoms in optical lattices, we prepare two identical copies of a many-body state and interfere them. This enables us to directly measure quantum purity, Rényi entanglement entropy, and mutual information. These experiments pave the way for using entanglement to characterize quantum phases and dynamics of strongly correlated many-body systems.
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Affiliation(s)
- Rajibul Islam
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Ruichao Ma
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Philipp M Preiss
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - M Eric Tai
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Alexander Lukin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Matthew Rispoli
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Markus Greiner
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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15
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Aolita L, de Melo F, Davidovich L. Open-system dynamics of entanglement: a key issues review. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2015; 78:042001. [PMID: 25811809 DOI: 10.1088/0034-4885/78/4/042001] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
One of the greatest challenges in the fields of quantum information processing and quantum technologies is the detailed coherent control over each and every constituent of quantum systems with an ever increasing number of particles. Within this endeavor, harnessing of many-body entanglement against the detrimental effects of the environment is a major pressing issue. Besides being an important concept from a fundamental standpoint, entanglement has been recognized as a crucial resource for quantum speed-ups or performance enhancements over classical methods. Understanding and controlling many-body entanglement in open systems may have strong implications in quantum computing, quantum simulations of many-body systems, secure quantum communication or cryptography, quantum metrology, our understanding of the quantum-to-classical transition, and other important questions of quantum foundations.In this paper we present an overview of recent theoretical and experimental efforts to underpin the dynamics of entanglement under the influence of noise. Entanglement is thus taken as a dynamic quantity on its own, and we survey how it evolves due to the unavoidable interaction of the entangled system with its surroundings. We analyze several scenarios, corresponding to different families of states and environments, which render a very rich diversity of dynamical behaviors.In contrast to single-particle quantities, like populations and coherences, which typically vanish only asymptotically in time, entanglement may disappear at a finite time. In addition, important classes of entanglement display an exponential decay with the number of particles when subject to local noise, which poses yet another threat to the already-challenging scaling of quantum technologies. Other classes, however, turn out to be extremely robust against local noise. Theoretical results and recent experiments regarding the difference between local and global decoherence are summarized. Control and robustness-enhancement techniques, scaling laws, statistical and geometrical aspects of multipartite-entanglement decay are also reviewed; all in order to give a broad picture of entanglement dynamics in open quantum systems addressed to both theorists and experimentalists inside and outside the field of quantum information.
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Affiliation(s)
- Leandro Aolita
- Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany
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16
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Agnew M, Salvail JZ, Leach J, Boyd RW. Generation of orbital angular momentum Bell states and their verification via accessible nonlinear witnesses. PHYSICAL REVIEW LETTERS 2013; 111:030402. [PMID: 23909296 DOI: 10.1103/physrevlett.111.030402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/20/2013] [Indexed: 06/02/2023]
Abstract
The controlled generation of entangled states and their subsequent detection are integral aspects of quantum information science. In this Letter, we implement a simple and precise technique that produces any of the four Bell states in the orbital angular momentum degree of freedom. We then use these states to perform the first experimental demonstration of an accessible nonlinear entanglement witness. Such a witness determines entanglement by using the same measurements as required for a linear witness but can detect, in this case, twice as many states as a single linear witness can. We anticipate that our method of state preparation and nonlinear witnesses will have further uses in areas of quantum science, such as superdense coding and quantum key distribution.
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Affiliation(s)
- Megan Agnew
- Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, K1N 6N5 Canada
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17
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Silva IA, Girolami D, Auccaise R, Sarthour RS, Oliveira IS, Bonagamba TJ, deAzevedo ER, Soares-Pinto DO, Adesso G. Measuring bipartite quantum correlations of an unknown state. PHYSICAL REVIEW LETTERS 2013; 110:140501. [PMID: 25166969 DOI: 10.1103/physrevlett.110.140501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/18/2012] [Indexed: 06/03/2023]
Abstract
We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance setup and employing geometric discord, we evaluate the quantum correlations of a state without resorting to prior knowledge of its density matrix. The method is applicable to any 2 ⊗ d system and provides, in terms of number of measurements required, an advantage over full state tomography scaling with the dimension d of the unmeasured subsystem. The negativity of quantumness is measured as well for reference. We also observe the phenomenon of sudden transition of quantum correlations when local phase and amplitude damping channels are applied to the state.
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Affiliation(s)
- I A Silva
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
| | - D Girolami
- School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
| | - R Auccaise
- Empresa Brasileira de Pesquisa Agropecuária, Rua Jardim Botânico 1024, 22460-000 Rio de Janeiro, Brazil
| | - R S Sarthour
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil
| | - I S Oliveira
- Centro Brasileiro de Pesquisas Físicas, Rua Dr. Xavier Sigaud 150, 22290-180 Rio de Janeiro, Brazil
| | - T J Bonagamba
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
| | - E R deAzevedo
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
| | - D O Soares-Pinto
- Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-970 São Carlos, São Paulo, Brazil
| | - G Adesso
- School of Mathematical Sciences, The University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom
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18
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Daley AJ, Pichler H, Schachenmayer J, Zoller P. Measuring entanglement growth in quench dynamics of bosons in an optical lattice. PHYSICAL REVIEW LETTERS 2012; 109:020505. [PMID: 23030143 DOI: 10.1103/physrevlett.109.020505] [Citation(s) in RCA: 64] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2012] [Indexed: 06/01/2023]
Abstract
We discuss a scheme to measure the many-body entanglement growth during quench dynamics with bosonic atoms in optical lattices. By making use of a 1D or 2D setup in which two copies of the same state are prepared, we show how arbitrary order Rényi entropies can be extracted by using tunnel coupling between the copies and measurement of the parity of on-site occupation numbers, as has been performed in recent experiments. We illustrate these ideas for a superfluid-Mott insulator quench in the Bose-Hubbard model, and also for hard-core bosons, and show that the scheme is robust against imperfections in the measurements.
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Affiliation(s)
- A J Daley
- Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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19
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Girolami D, Adesso G. Observable measure of bipartite quantum correlations. PHYSICAL REVIEW LETTERS 2012; 108:150403. [PMID: 22587235 DOI: 10.1103/physrevlett.108.150403] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/23/2011] [Indexed: 05/31/2023]
Abstract
We introduce a measure Q of bipartite quantum correlations for arbitrary two-qubit states, expressed as a state-independent function of the density matrix elements. The amount of quantum correlations can be quantified experimentally by measuring the expectation value of a small set of observables on up to four copies of the state, without the need for a full tomography. We extend the measure to 2×d systems, providing its explicit form in terms of observables and applying it to the relevant class of multiqubit states employed in the deterministic quantum computation with one quantum bit model. The number of required measurements to determine Q in our scheme does not increase with d. Our results provide an experimentally friendly framework to estimate quantitatively the degree of general quantum correlations in composite systems.
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Affiliation(s)
- Davide Girolami
- School of Mathematical Sciences, University of Nottingham, University Park, Nottingham NG7 2RD, United Kingdom.
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20
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Aguilar GH, Farías OJ, Maziero J, Serra RM, Ribeiro PHS, Walborn SP. Experimental estimate of a classicality witness via a single measurement. PHYSICAL REVIEW LETTERS 2012; 108:063601. [PMID: 22401071 DOI: 10.1103/physrevlett.108.063601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2011] [Indexed: 05/31/2023]
Abstract
The perception that quantum correlations can still appear in separable states has opened exciting new possibilities regarding their use as a resource in quantum information science. Quantifying such quantum correlations involves the complete knowledge of the system's state and numerical optimization procedures. Thus, it is natural to seek methods involving fewer measurements that indicate the nature of the correlations in a system. Here we propose a classicality witness that can be accurately estimated via statistics from a single measurement and perform an experiment to explore the utility of this witness for quantum states with different types of correlations.
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Affiliation(s)
- G H Aguilar
- Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro, RJ, Brazil.
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21
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Rudnicki Ł, Horodecki P, Zyczkowski K. Collective uncertainty entanglement test. PHYSICAL REVIEW LETTERS 2011; 107:150502. [PMID: 22107275 DOI: 10.1103/physrevlett.107.150502] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/17/2011] [Indexed: 05/31/2023]
Abstract
For a given pure state of a composite quantum system we analyze the product of its projections onto a set of locally orthogonal separable pure states. We derive a bound for this product analogous to the entropic uncertainty relations. For bipartite systems the bound is saturated for maximally entangled states and it allows us to construct a family of entanglement measures, we shall call collectibility. As these quantities are experimentally accessible, the approach advocated contributes to the task of experimental quantification of quantum entanglement, while for a three-qubit system it is capable to identify the genuine three-party entanglement.
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Affiliation(s)
- Łukasz Rudnicki
- Center for Theoretical Physics, Polish Academy of Sciences, Aleja Lotników 32/46, PL-02-668 Warsaw, Poland.
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22
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Schmid C, Kiesel N, Wieczorek W, Weinfurter H, Mintert F, Buchleitner A. Experimental direct observation of mixed state entanglement. PHYSICAL REVIEW LETTERS 2008; 101:260505. [PMID: 19437629 DOI: 10.1103/physrevlett.101.260505] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/27/2023]
Abstract
We report on the direct estimation of concurrence for mixed quantum states. The used method relies on joint measurements on two copies of an entangled state. In the experimental demonstration two polarization-entangled photon pairs emitted from spontaneous parametric down-conversion are analyzed together using a linear optics controlled phase gate. We demonstrate that the measured data, without need for further numerical processing, directly yield reliable estimates, despite experimental imperfections.
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Affiliation(s)
- Christian Schmid
- Max-Planck-Institute of Quantum Optics, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
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23
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Branderhorst MPA, Londero P, Wasylczyk P, Brif C, Kosut RL, Rabitz H, Walmsley IA. Coherent Control of Decoherence. Science 2008; 320:638-43. [DOI: 10.1126/science.1154576] [Citation(s) in RCA: 93] [Impact Index Per Article: 5.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
Affiliation(s)
- Matthijs P. A. Branderhorst
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
- SCSolutions, 1261 Oakmead Parkway, Sunnyvale, CA 94085, USA
| | - Pablo Londero
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
- SCSolutions, 1261 Oakmead Parkway, Sunnyvale, CA 94085, USA
| | - Piotr Wasylczyk
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
- SCSolutions, 1261 Oakmead Parkway, Sunnyvale, CA 94085, USA
| | - Constantin Brif
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
- SCSolutions, 1261 Oakmead Parkway, Sunnyvale, CA 94085, USA
| | - Robert L. Kosut
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
- SCSolutions, 1261 Oakmead Parkway, Sunnyvale, CA 94085, USA
| | - Herschel Rabitz
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
- SCSolutions, 1261 Oakmead Parkway, Sunnyvale, CA 94085, USA
| | - Ian A. Walmsley
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Department of Chemistry, Princeton University, Princeton, NJ 08544, USA
- SCSolutions, 1261 Oakmead Parkway, Sunnyvale, CA 94085, USA
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24
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Mosley PJ, Lundeen JS, Smith BJ, Wasylczyk P, U'Ren AB, Silberhorn C, Walmsley IA. Heralded generation of ultrafast single photons in pure quantum States. PHYSICAL REVIEW LETTERS 2008; 100:133601. [PMID: 18517952 DOI: 10.1103/physrevlett.100.133601] [Citation(s) in RCA: 36] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/30/2007] [Indexed: 05/26/2023]
Abstract
We present an experimental demonstration of heralded single photons prepared in pure quantum states from a parametric down-conversion source. It is shown that, through controlling the modal structure of the photon pair emission, one can generate pairs in factorable states and thence eliminate the need for spectral filters in multiple-source interference schemes. Indistinguishable heralded photons were generated in two independent spectrally engineered sources and Hong-Ou-Mandel interference observed between them without spectral filters. The measured visibility of 94.4% sets a minimum bound on the mean photon purity.
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Affiliation(s)
- Peter J Mosley
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, United Kingdom.
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25
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Carvalho ARR, Busse M, Brodier O, Viviescas C, Buchleitner A. Optimal dynamical characterization of entanglement. PHYSICAL REVIEW LETTERS 2007; 98:190501. [PMID: 17677610 DOI: 10.1103/physrevlett.98.190501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/02/2006] [Indexed: 05/16/2023]
Abstract
We show that, for experimentally relevant systems, there is an optimal measurement strategy to monitor the time evolution of entanglement under open system dynamics. This suggests an efficient, dynamical characterization of the entanglement of composite, open quantum systems.
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Affiliation(s)
- André R R Carvalho
- Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, 01187 Dresden, Germany
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26
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Mintert F, Buchleitner A. Observable entanglement measure for mixed quantum States. PHYSICAL REVIEW LETTERS 2007; 98:140505. [PMID: 17501257 DOI: 10.1103/physrevlett.98.140505] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/30/2006] [Indexed: 05/15/2023]
Abstract
We quantify an unknown mixed quantum state's entanglement by suitable, local parity measurements on its twofold copy. The associated observable qualifies as a generalized entanglement witness.
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Affiliation(s)
- Florian Mintert
- Department of Physics, Harvard University, 17 Oxford Street, Cambridge Massachusetts, USA
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27
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Gühne O, Lütkenhaus N. Nonlinear entanglement witnesses. PHYSICAL REVIEW LETTERS 2006; 96:170502. [PMID: 16712282 DOI: 10.1103/physrevlett.96.170502] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2006] [Indexed: 05/09/2023]
Abstract
Entanglement detection typically relies on linear inequalities for mean values of certain observables (entanglement witnesses), where violation indicates entanglement. We provide a general method to improve any of these inequalities for bipartite systems via nonlinear expressions. The nonlinearities are of different orders and can be directly measured in experiments, often without any extra effort.
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Affiliation(s)
- Otfried Gühne
- Institut für Quantenoptik und Quanteninformation, Osterreichische Akademie der Wissenschaften, Innsbruck, Austria
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