1
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Jones JA. Controlling NMR spin systems for quantum computation. PROGRESS IN NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY 2024; 140-141:49-85. [PMID: 38705636 DOI: 10.1016/j.pnmrs.2024.02.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/02/2024] [Accepted: 02/05/2024] [Indexed: 05/07/2024]
Abstract
Nuclear magnetic resonance is arguably both the best available quantum technology for implementing simple quantum computing experiments and the worst technology for building large scale quantum computers that has ever been seriously put forward. After a few years of rapid growth, leading to an implementation of Shor's quantum factoring algorithm in a seven-spin system, the field started to reach its natural limits and further progress became challenging. Rather than pursuing more complex algorithms on larger systems, interest has now largely moved into developing techniques for the precise and efficient manipulation of spin states with the aim of developing methods that can be applied in other more scalable technologies and within conventional NMR. However, the user friendliness of NMR implementations means that they remain popular for proof-of-principle demonstrations of simple quantum information protocols.
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Affiliation(s)
- Jonathan A Jones
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
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2
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Parzygnat AJ, Fullwood J, Buscemi F, Chiribella G. Virtual Quantum Broadcasting. PHYSICAL REVIEW LETTERS 2024; 132:110203. [PMID: 38563923 DOI: 10.1103/physrevlett.132.110203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/25/2023] [Accepted: 02/02/2024] [Indexed: 04/04/2024]
Abstract
The quantum no-broadcasting theorem states that it is impossible to produce perfect copies of an arbitrary quantum state, even if the copies are allowed to be correlated. Here we show that, although quantum broadcasting cannot be achieved by any physical process, it can be achieved by a virtual process, described by a Hermitian-preserving trace-preserving map. This virtual process is canonical: it is the only map that broadcasts all quantum states, is covariant under unitary evolution, is invariant under permutations of the copies, and reduces to the classical broadcasting map when subjected to decoherence. We show that the optimal physical approximation to the canonical broadcasting map is the optimal universal quantum cloning, and we also show that virtual broadcasting can be achieved by a virtual measure-and-prepare protocol, where a virtual measurement is performed, and, depending on the outcomes, two copies of a virtual quantum state are generated. Finally, we use canonical virtual broadcasting to prove a uniqueness result for quantum states over time.
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Affiliation(s)
- Arthur J Parzygnat
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
- Experimental Study Group, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
| | - James Fullwood
- School of Mathematics and Statistics, Hainan University, Haikou, Hainan, 570228, China
- School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai, China
| | - Francesco Buscemi
- Graduate School of Informatics, Nagoya University, Chikusa-ku, 464-8601 Nagoya, Japan
| | - Giulio Chiribella
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pok Fu Lam Road, Hong Kong
- Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, Oxford, United Kingdom
- Perimeter Institute for Theoretical Physics, 31 Caroline Street North, Waterloo, Ontario, Canada
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3
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Xiao Y, Yang Y, Wang X, Liu Q, Gu M. Quantum Uncertainty Principles for Measurements with Interventions. PHYSICAL REVIEW LETTERS 2023; 130:240201. [PMID: 37390437 DOI: 10.1103/physrevlett.130.240201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/02/2022] [Revised: 01/11/2023] [Accepted: 05/10/2023] [Indexed: 07/02/2023]
Abstract
Heisenberg's uncertainty principle implies fundamental constraints on what properties of a quantum system we can simultaneously learn. However, it typically assumes that we probe these properties via measurements at a single point in time. In contrast, inferring causal dependencies in complex processes often requires interactive experimentation-multiple rounds of interventions where we adaptively probe the process with different inputs to observe how they affect outputs. Here, we demonstrate universal uncertainty principles for general interactive measurements involving arbitrary rounds of interventions. As a case study, we show that they imply an uncertainty trade-off between measurements compatible with different causal dependencies.
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Affiliation(s)
- Yunlong Xiao
- Institute of High Performance Computing (IHPC), Agency for Science Technology and Research (A*STAR), 1 Fusionopolis Way, No. 16-16 Connexis, Singapore 138632, Republic of Singapore
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Yuxiang Yang
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
- Institute for Theoretical Physics, ETH Zürich, 8093 Zürich, Switzerland
| | - Ximing Wang
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
| | - Qing Liu
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Key Laboratory for Information Science of Electromagnetic Waves (Ministry of Education), Fudan University, Shanghai 200433, China
| | - Mile Gu
- Nanyang Quantum Hub, School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore 637371, Singapore
- Centre for Quantum Technologies, National University of Singapore, Singapore 117543, Singapore
- MajuLab, CNRS-UNS-NUS-NTU International Joint Research Unit, UMI 3654, Singapore 117543, Singapore
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4
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Fullwood J, Parzygnat AJ. On quantum states over time. Proc Math Phys Eng Sci 2022. [DOI: 10.1098/rspa.2022.0104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
In 2017, D. Horsman, C. Heunen, M. Pusey, J. Barrett and R. Spekkens proved that there is no physically reasonable assignment that takes a quantum channel and an initial state and produces a joint state on the tensor product of the input and output spaces. The interpretation was that there is a clear distinction between space and time in the quantum setting that is not visible classically, where in the latter, one can freely use Bayes’ theorem to go between joint states and marginals with noisy channels. In this paper, we prove that there actually is such a physically reasonable assignment, bypassing the no-go result of Horsman
et al.
, and we illustrate that this is achievable by restricting the domain of their assignment to a domain which represents the given data more faithfully.
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Affiliation(s)
- James Fullwood
- School of Mathematical Sciences, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, People’s Republic of China
| | - Arthur J. Parzygnat
- Graduate School of Informatics, Nagoya University, Chikusa-ku, 464-8601 Nagoya, Japan
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5
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Yi B, Bose S. Quantum Liang Information Flow as Causation Quantifier. PHYSICAL REVIEW LETTERS 2022; 129:020501. [PMID: 35867429 DOI: 10.1103/physrevlett.129.020501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2022] [Accepted: 06/22/2022] [Indexed: 06/15/2023]
Abstract
Liang information flow is widely used in classical systems and network theory for causality quantification and has been applied widely, for example, to finance, neuroscience, and climate studies. The key part of the theory is to freeze a node of a network to ascertain its causal influence on other nodes. Such a theory is yet to be applied to quantum network dynamics. Here, we generalize the Liang information flow to the quantum domain with respect to von Neumann entropy and exemplify its usage by applying it to a variety of small quantum networks.
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Affiliation(s)
- Bin Yi
- Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT London, United Kingdom
| | - Sougato Bose
- Department of Physics and Astronomy, University College London, Gower Street, WC1E 6BT London, United Kingdom
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6
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Marletto C, Vedral V, Virzì S, Avella A, Piacentini F, Gramegna M, Degiovanni IP, Genovese M. Temporal teleportation with pseudo-density operators: How dynamics emerges from temporal entanglement. SCIENCE ADVANCES 2021; 7:eabe4742. [PMID: 34524847 PMCID: PMC8443168 DOI: 10.1126/sciadv.abe4742] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/25/2020] [Accepted: 07/23/2021] [Indexed: 06/13/2023]
Abstract
We show that, by using temporal quantum correlations as expressed by pseudo-density operators (PDOs), it is possible to recover formally the standard quantum dynamical evolution as a sequence of teleportations in time. We demonstrate that any completely positive evolution can be formally reconstructed by teleportation with different temporally correlated states. This provides a different interpretation of maximally correlated PDOs, as resources to induce quantum time evolution. Furthermore, we note that the possibility of this protocol stems from the strict formal correspondence between spatial and temporal entanglement in quantum theory. We proceed to demonstrate experimentally this correspondence, by showing a multipartite violation of generalized temporal and spatial Bell inequalities and verifying agreement with theoretical predictions to a high degree of accuracy, in high-quality photon qubits.
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Affiliation(s)
- Chiara Marletto
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
- ISI Foundation, Via Chisola 5, I-10126 Torino, Italy
| | - Vlatko Vedral
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543
- ISI Foundation, Via Chisola 5, I-10126 Torino, Italy
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542
| | | | | | | | | | - Ivo Pietro Degiovanni
- INRIM, Strada Delle Cacce 91, I-10135 Torino, Italy
- INFN, via P. Giuria 1, I-10125 Torino, Italy
| | - Marco Genovese
- INRIM, Strada Delle Cacce 91, I-10135 Torino, Italy
- INFN, via P. Giuria 1, I-10125 Torino, Italy
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7
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Mitra A, Chattopadhyay P, Paul G, Zarikas V. Binary Black Hole Information Loss Paradox and Future Prospects. ENTROPY (BASEL, SWITZERLAND) 2020; 22:E1387. [PMID: 33302364 PMCID: PMC7762553 DOI: 10.3390/e22121387] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 10/20/2020] [Revised: 11/08/2020] [Accepted: 11/16/2020] [Indexed: 11/17/2022]
Abstract
Various techniques to tackle the black hole information paradox have been proposed. A new way out to tackle the paradox is via the use of a pseudo-density operator. This approach has successfully dealt with the problem with a two-qubit entangle system for a single black hole. In this paper, we present the interaction with a binary black hole system by using an arrangement of the three-qubit system of Greenberger-Horne-Zeilinger (GHZ) state. We show that our results are in excellent agreement with the theoretical value. We have also studied the interaction between the two black holes by considering the correlation between the qubits in the binary black hole system. The results depict a complete agreement with the proposed model. In addition to the verification, we also propose how modern detection of gravitational waves can be used on our optical setup as an input source, thus bridging the gap with the gravitational wave's observational resources in terms of studying black hole properties with respect to quantum information and entanglement.
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Affiliation(s)
- Ayan Mitra
- Department of Mechanical and Aerospace Engineering, Nazarbayev University, Nur-Sultan 010000, Kazakhstan;
| | - Pritam Chattopadhyay
- Cryptology and Security Research Unit, R.C. Bose Center for Cryptology and Security, Indian Statistical Institute, Kolkata 700108, India; (P.C.); (G.P.)
| | - Goutam Paul
- Cryptology and Security Research Unit, R.C. Bose Center for Cryptology and Security, Indian Statistical Institute, Kolkata 700108, India; (P.C.); (G.P.)
| | - Vasilios Zarikas
- Department of Mechanical and Aerospace Engineering, Nazarbayev University, Nur-Sultan 010000, Kazakhstan;
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8
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Gachechiladze M, Miklin N, Chaves R. Quantifying Causal Influences in the Presence of a Quantum Common Cause. PHYSICAL REVIEW LETTERS 2020; 125:230401. [PMID: 33337213 DOI: 10.1103/physrevlett.125.230401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Revised: 10/18/2020] [Accepted: 10/28/2020] [Indexed: 06/12/2023]
Abstract
Quantum mechanics challenges our intuition on the cause-effect relations in nature. Some fundamental concepts, including Reichenbach's common cause principle or the notion of local realism, have to be reconsidered. Traditionally, this is witnessed by the violation of a Bell inequality. But are Bell inequalities the only signature of the incompatibility between quantum correlations and causality theory? Motivated by this question, we introduce a general framework able to estimate causal influences between two variables, without the need of interventions and irrespectively of the classical, quantum, or even postquantum nature of a common cause. In particular, by considering the simplest instrumental scenario-for which violation of Bell inequalities is not possible-we show that every pure bipartite entangled state violates the classical bounds on causal influence, thus, answering in negative to the posed question and opening a new venue to explore the role of causality within quantum theory.
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Affiliation(s)
| | - Nikolai Miklin
- International Centre for Theory of Quantum Technologies (ICTQT), University of Gdansk, 80-308 Gdańsk, Poland
| | - Rafael Chaves
- International Institute of Physics, Federal University of Rio Grande do Norte, 59070-405 Natal, Brazil
- School of Science and Technology, Federal University of Rio Grande do Norte, 59078-970 Natal, Brazil
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9
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Felce D, Vedral V. Quantum Refrigeration with Indefinite Causal Order. PHYSICAL REVIEW LETTERS 2020; 125:070603. [PMID: 32857528 DOI: 10.1103/physrevlett.125.070603] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2020] [Accepted: 06/17/2020] [Indexed: 06/11/2023]
Abstract
We propose a thermodynamic refrigeration cycle which uses indefinite causal orders to achieve nonclassical cooling. The cycle cools a cold reservoir while consuming purity in a control qubit. We first show that the application to an input state of two identical thermalizing channels of temperature T in an indefinite causal order can result in an output state with a temperature not equal to T. We investigate the properties of the refrigeration cycle and show that thermodynamically, the result is compatible with unitary quantum mechanics in the circuit model but could not be achieved classically. We believe that this cycle could be implemented experimentally using tabletop photonics. Our result suggests the development of a new class of thermodynamic resource theories in which operations are allowed to be performed in an indefinite causal order.
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Affiliation(s)
- David Felce
- Clarendon Laboratory, Department of Physics, University of Oxford, Oxford, OX1 3PU, England
| | - Vlatko Vedral
- Clarendon Laboratory, Department of Physics, University of Oxford, Oxford, OX1 3PU, England
- Centre for Quantum Technologies, National University of Singapore, Block S15, 3 Science Drive 2, 117543, Singapore
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10
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Marletto C, Vedral V, Virzì S, Rebufello E, Avella A, Piacentini F, Gramegna M, Degiovanni IP, Genovese M. Non-Monogamy of Spatio-Temporal Correlations and the Black Hole Information Loss Paradox. ENTROPY 2020; 22:e22020228. [PMID: 33286002 PMCID: PMC7516659 DOI: 10.3390/e22020228] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/10/2020] [Revised: 02/16/2020] [Accepted: 02/17/2020] [Indexed: 11/16/2022]
Abstract
Pseudo-density matrices are a generalisation of quantum states and do not obey monogamy of quantum correlations. Could this be the solution to the paradox of information loss during the evaporation of a black hole? In this paper we discuss this possibility, providing a theoretical proposal to extend quantum theory with these pseudo-states to describe the statistics arising in black-hole evaporation. We also provide an experimental demonstration of this theoretical proposal, using a simulation in optical regime, that tomographically reproduces the correlations of the pseudo-density matrix describing this physical phenomenon.
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Affiliation(s)
- Chiara Marletto
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK;
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore
- Correspondence:
| | - Vlatko Vedral
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford OX1 3PU, UK;
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore
- Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore
| | - Salvatore Virzì
- Dipartimento di Fisica, Università di Torino, via P. Giuria 1, 10125 Torino, Italy;
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy; (E.R.); (A.A.); (F.P.); (M.G.); (I.P.D.); (M.G.)
| | - Enrico Rebufello
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy; (E.R.); (A.A.); (F.P.); (M.G.); (I.P.D.); (M.G.)
- Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
| | - Alessio Avella
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy; (E.R.); (A.A.); (F.P.); (M.G.); (I.P.D.); (M.G.)
| | - Fabrizio Piacentini
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy; (E.R.); (A.A.); (F.P.); (M.G.); (I.P.D.); (M.G.)
| | - Marco Gramegna
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy; (E.R.); (A.A.); (F.P.); (M.G.); (I.P.D.); (M.G.)
| | - Ivo Pietro Degiovanni
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy; (E.R.); (A.A.); (F.P.); (M.G.); (I.P.D.); (M.G.)
| | - Marco Genovese
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135 Torino, Italy; (E.R.); (A.A.); (F.P.); (M.G.); (I.P.D.); (M.G.)
- INFN, sezione di Torino, via P. Giuria 1, 10125 Torino, Italy
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11
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Pisarczyk R, Zhao Z, Ouyang Y, Vedral V, Fitzsimons JF. Causal Limit on Quantum Communication. PHYSICAL REVIEW LETTERS 2019; 123:150502. [PMID: 31702284 DOI: 10.1103/physrevlett.123.150502] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2019] [Indexed: 06/10/2023]
Abstract
The capacity of a channel is known to be equivalent to the highest rate at which it can generate entanglement. Analogous to entanglement, the notion of a causality measure characterizes the temporal aspect of quantum correlations. Despite holding an equally fundamental role in physics, temporal quantum correlations have yet to find their operational significance in quantum communication. Here we uncover a connection between quantum causality and channel capacity. We show the amount of temporal correlations between two ends of the noisy quantum channel, as quantified by a causality measure, implies a general upper bound on its channel capacity. The expression of this new bound is simpler to evaluate than most previously known bounds. We demonstrate the utility of this bound by applying it to a class of shifted depolarizing channels, which results in improvement over previously known bounds for this class of channels.
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Affiliation(s)
- Robert Pisarczyk
- Mathematical Institute, University of Oxford, Woodstock Road, Oxford OX2 6GG, United Kingdom
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
| | - Zhikuan Zhao
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
- Department of Computer Science, ETH Zürich, Universitätstrasse 6, 8092 Zürich
- Singapore University of Technology and Design, 8 Somapah Road, 487372, Singapore
| | - Yingkai Ouyang
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
- Singapore University of Technology and Design, 8 Somapah Road, 487372, Singapore
- University of Sheffield, Department of Physics and Astronomy, 226 Hounsfield Rd, Sheffield S3 7RH, United Kingdom
| | - Vlatko Vedral
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
- Clarendon Laboratory, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
- Department of Physics, National University of Singapore, 2 Science Drive 3, 117542, Singapore
| | - Joseph F Fitzsimons
- Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, 117543, Singapore
- Singapore University of Technology and Design, 8 Somapah Road, 487372, Singapore
- Horizon Quantum Computing, 79 Ayer Rajah Crescent, Singapore 139955
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12
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Chiribella G, Ebler D. Quantum speedup in the identification of cause-effect relations. Nat Commun 2019; 10:1472. [PMID: 30931930 PMCID: PMC6443664 DOI: 10.1038/s41467-019-09383-8] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/19/2018] [Accepted: 03/08/2019] [Indexed: 11/08/2022] Open
Abstract
The ability to identify cause-effect relations is an essential component of the scientific method. The identification of causal relations is generally accomplished through statistical trials where alternative hypotheses are tested against each other. Traditionally, such trials have been based on classical statistics. However, classical statistics becomes inadequate at the quantum scale, where a richer spectrum of causal relations is accessible. Here we show that quantum strategies can greatly speed up the identification of causal relations. We analyse the task of identifying the effect of a given variable, and we show that the optimal quantum strategy beats all classical strategies by running multiple equivalent tests in a quantum superposition. The same working principle leads to advantages in the detection of a causal link between two variables, and in the identification of the cause of a given variable.
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Affiliation(s)
- Giulio Chiribella
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong.
- Department of Computer Science, University of Oxford, Oxford, OX1 3QD, UK.
- Perimeter Institute for Theoretical Physics, Waterloo, ON, N2L 2Y5, Canada.
| | - Daniel Ebler
- Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong
- Department of Physics, Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China
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13
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Marletto C, Vedral V, Virzì S, Rebufello E, Avella A, Piacentini F, Gramegna M, Degiovanni IP, Genovese M. Theoretical description and experimental simulation of quantum entanglement near open time-like curves via pseudo-density operators. Nat Commun 2019; 10:182. [PMID: 30643140 PMCID: PMC6331626 DOI: 10.1038/s41467-018-08100-1] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2018] [Accepted: 12/07/2018] [Indexed: 12/05/2022] Open
Abstract
Closed timelike curves are striking predictions of general relativity allowing for time-travel. They are afflicted by notorious causality issues (e.g. grandfather’s paradox). Quantum models where a qubit travels back in time solve these problems, at the cost of violating quantum theory’s linearity—leading e.g. to universal quantum cloning. Interestingly, linearity is violated even by open timelike curves (OTCs), where the qubit does not interact with its past copy, but is initially entangled with another qubit. Non-linear dynamics is needed to avoid violating entanglement monogamy. Here we propose an alternative approach to OTCs, allowing for monogamy violations. Specifically, we describe the qubit in the OTC via a pseudo-density operator—a unified descriptor of both temporal and spatial correlations. We also simulate the monogamy violation with polarization-entangled photons, providing a pseudo-density operator quantum tomography. Remarkably, our proposal applies to any space-time correlations violating entanglement monogamy, such as those arising in black holes. Description of a qubit following an open time-like curve usually incurs into conceptual problems such as violation of entanglement monogamy. Here, the authors show how to use the formalism of pseudo-density operators to describe such a process, showing a proof-of-principle experimental simulation.
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Affiliation(s)
- Chiara Marletto
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK. .,Fondazione ISI, Via Chisola 5, Torino, 10126, Italy. .,Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore, 117543, Singapore.
| | - Vlatko Vedral
- Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK.,Fondazione ISI, Via Chisola 5, Torino, 10126, Italy.,Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore, 117543, Singapore.,Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore, 117542, Singapore
| | - Salvatore Virzì
- Università di Torino, via P. Giuria 1, 10125, Torino, Italy.,Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Enrico Rebufello
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy.,Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino, Italy
| | - Alessio Avella
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Fabrizio Piacentini
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Marco Gramegna
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Ivo Pietro Degiovanni
- Istituto Nazionale di Ricerca Metrologica, Strada delle Cacce 91, 10135, Torino, Italy
| | - Marco Genovese
- INFN - sezione di Torino, Via P. Giuria, 110125, Torino, Italy
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14
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Abstract
We introduce the concept of spatio-temporal steering (STS), which reduces, in special cases, to Einstein-Podolsky-Rosen steering and the recently-introduced temporal steering. We describe two measures of this effect referred to as the STS weight and robustness. We suggest that these STS measures enable a new way to assess nonclassical correlations in an open quantum network, such as quantum transport through nano-structures or excitation transfer in a complex biological system. As one of our examples, we apply STS to check nonclassical correlations among sites in a photosynthetic pigment-protein complex in the Fenna-Matthews-Olson model.
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15
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MacLean JPW, Ried K, Spekkens RW, Resch KJ. Quantum-coherent mixtures of causal relations. Nat Commun 2017; 8:15149. [PMID: 28485394 PMCID: PMC5436107 DOI: 10.1038/ncomms15149] [Citation(s) in RCA: 31] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2016] [Accepted: 03/02/2017] [Indexed: 11/09/2022] Open
Abstract
Understanding the causal influences that hold among parts of a system is critical both to explaining that system's natural behaviour and to controlling it through targeted interventions. In a quantum world, understanding causal relations is equally important, but the set of possibilities is far richer. The two basic ways in which a pair of time-ordered quantum systems may be causally related are by a cause-effect mechanism or by a common-cause acting on both. Here we show a coherent mixture of these two possibilities. We realize this nonclassical causal relation in a quantum optics experiment and derive a set of criteria for witnessing the coherence based on a quantum version of Berkson's effect, whereby two independent causes can become correlated on observation of their common effect. The interplay of causality and quantum theory lies at the heart of challenging foundational puzzles, including Bell's theorem and the search for quantum gravity.
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Affiliation(s)
- Jean-Philippe W MacLean
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.,Department of Physics &Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
| | - Katja Ried
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.,Department of Physics &Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.,Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
| | - Robert W Spekkens
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada N2L 2Y5
| | - Kevin J Resch
- Institute for Quantum Computing, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1.,Department of Physics &Astronomy, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
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16
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Rubino G, Rozema LA, Feix A, Araújo M, Zeuner JM, Procopio LM, Brukner Č, Walther P. Experimental verification of an indefinite causal order. SCIENCE ADVANCES 2017; 3:e1602589. [PMID: 28378018 PMCID: PMC5365250 DOI: 10.1126/sciadv.1602589] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/20/2016] [Accepted: 02/09/2017] [Indexed: 05/27/2023]
Abstract
Investigating the role of causal order in quantum mechanics has recently revealed that the causal relations of events may not be a priori well defined in quantum theory. Although this has triggered a growing interest on the theoretical side, creating processes without a causal order is an experimental task. We report the first decisive demonstration of a process with an indefinite causal order. To do this, we quantify how incompatible our setup is with a definite causal order by measuring a "causal witness." This mathematical object incorporates a series of measurements that are designed to yield a certain outcome only if the process under examination is not consistent with any well-defined causal order. In our experiment, we perform a measurement in a superposition of causal orders-without destroying the coherence-to acquire information both inside and outside of a "causally nonordered process." Using this information, we experimentally determine a causal witness, demonstrating by almost 7 SDs that the experimentally implemented process does not have a definite causal order.
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Affiliation(s)
- Giulia Rubino
- Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
| | - Lee A. Rozema
- Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
| | - Adrien Feix
- Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria
| | - Mateus Araújo
- Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria
| | - Jonas M. Zeuner
- Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
| | - Lorenzo M. Procopio
- Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
| | - Časlav Brukner
- Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
- Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria
| | - Philip Walther
- Vienna Center for Quantum Science and Technology, Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
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17
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Procopio LM, Moqanaki A, Araújo M, Costa F, Alonso Calafell I, Dowd EG, Hamel DR, Rozema LA, Brukner Č, Walther P. Experimental superposition of orders of quantum gates. Nat Commun 2015; 6:7913. [PMID: 26250107 PMCID: PMC4918346 DOI: 10.1038/ncomms8913] [Citation(s) in RCA: 45] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/11/2015] [Accepted: 06/22/2015] [Indexed: 12/02/2022] Open
Abstract
Quantum computers achieve a speed-up by placing quantum bits (qubits) in superpositions of different states. However, it has recently been appreciated that quantum mechanics also allows one to ‘superimpose different operations'. Furthermore, it has been shown that using a qubit to coherently control the gate order allows one to accomplish a task—determining if two gates commute or anti-commute—with fewer gate uses than any known quantum algorithm. Here we experimentally demonstrate this advantage, in a photonic context, using a second qubit to control the order in which two gates are applied to a first qubit. We create the required superposition of gate orders by using additional degrees of freedom of the photons encoding our qubits. The new resource we exploit can be interpreted as a superposition of causal orders, and could allow quantum algorithms to be implemented with an efficiency unlikely to be achieved on a fixed-gate-order quantum computer. It has been conjectured that not only states but also quantum operations can be placed in a superposition of causal order. Here, the authors use a qubit superpose the order in which two photonic gates are applied, which is shown to enable a more efficient detection of their commutation relations.
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Affiliation(s)
- Lorenzo M Procopio
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
| | - Amir Moqanaki
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
| | - Mateus Araújo
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria
| | - Fabio Costa
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria
| | | | - Emma G Dowd
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
| | - Deny R Hamel
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
| | - Lee A Rozema
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
| | - Časlav Brukner
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria.,Institute for Quantum Optics and Quantum Information, Austrian Academy of Sciences, Boltzmanngasse 3, Vienna A-1090, Austria
| | - Philip Walther
- Faculty of Physics, University of Vienna, Boltzmanngasse 5, Vienna A-1090, Austria
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