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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: 0] [Impact Index Per Article: 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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Huang Z, Maccone L, Karim A, Macchiavello C, Chapman RJ, Peruzzo A. High-dimensional entanglement certification. Sci Rep 2016; 6:27637. [PMID: 27311935 PMCID: PMC4911610 DOI: 10.1038/srep27637] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2016] [Accepted: 05/23/2016] [Indexed: 11/29/2022] Open
Abstract
Quantum entanglement is the ability of joint quantum systems to possess global properties (correlation among systems) even when subsystems have no definite individual property. Whilst the 2-dimensional (qubit) case is well-understood, currently, tools to characterise entanglement in high dimensions are limited. We experimentally demonstrate a new procedure for entanglement certification that is suitable for large systems, based entirely on information-theoretics. It scales more efficiently than Bell's inequality and entanglement witness. The method we developed works for arbitrarily large system dimension d and employs only two local measurements of complementary properties. This procedure can also certify whether the system is maximally entangled. We illustrate the protocol for families of bipartite states of qudits with dimension up to 32 composed of polarisation-entangled photon pairs.
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Affiliation(s)
- Zixin Huang
- Quantum Photonics Laboratory, School of Engineering, RMIT University, Melbourne, Victoria 3000, Australia
- School of Physics, University of Sydney, NSW 2006, Australia
| | - Lorenzo Maccone
- Dip. Fisica and INFN Sez. Pavia, University of Pavia, via Bassi 6, I-27100 Pavia, Italy
| | - Akib Karim
- Quantum Photonics Laboratory, School of Engineering, RMIT University, Melbourne, Victoria 3000, Australia
- School of Physics, University of Sydney, NSW 2006, Australia
| | - Chiara Macchiavello
- Dip. Fisica and INFN Sez. Pavia, University of Pavia, via Bassi 6, I-27100 Pavia, Italy
| | - Robert J. Chapman
- Quantum Photonics Laboratory, School of Engineering, RMIT University, Melbourne, Victoria 3000, Australia
- School of Physics, University of Sydney, NSW 2006, Australia
| | - Alberto Peruzzo
- Quantum Photonics Laboratory, School of Engineering, RMIT University, Melbourne, Victoria 3000, Australia
- School of Physics, University of Sydney, NSW 2006, Australia
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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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