1
|
Xu ZP, Saha D, Bharti K, Cabello A. Certifying Sets of Quantum Observables with Any Full-Rank State. PHYSICAL REVIEW LETTERS 2024; 132:140201. [PMID: 38640382 DOI: 10.1103/physrevlett.132.140201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/15/2023] [Revised: 02/10/2024] [Accepted: 03/01/2024] [Indexed: 04/21/2024]
Abstract
We show that some sets of quantum observables are unique up to an isometry and have a contextuality witness that attains the same value for any initial state. We prove that these two properties make it possible to certify any of these sets by looking at the statistics of experiments with sequential measurements and using any initial state of full rank, including thermal and maximally mixed states. We prove that this "certification with any full-rank state" (CFR) is possible for any quantum system of finite dimension d≥3 and is robust and experimentally useful in dimensions 3 and 4. In addition, we prove that complete Kochen-Specker sets can be Bell self-tested if and only if they enable CFR. This establishes a fundamental connection between these two methods of certification, shows that both methods can be combined in the same experiment, and opens new possibilities for certifying quantum devices.
Collapse
Affiliation(s)
- Zhen-Peng Xu
- School of Physics and Optoelectronics Engineering, Anhui University, 230601 Hefei, People's Republic of China
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Debashis Saha
- School of Physics, Indian Institute of Science Education and Research Thiruvananthapuram, Kerala 695551, India
| | - Kishor Bharti
- Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Republic of Singapore
| | - Adán Cabello
- Departamento de Física Aplicada II, Universidad de Sevilla, E-41012 Sevilla, Spain
- Instituto Carlos I de Física Teórica y Computacional, Universidad de Sevilla, E-41012 Sevilla, Spain
| |
Collapse
|
2
|
Vallée K, Emeriau PE, Bourdoncle B, Sohbi A, Mansfield S, Markham D. Corrected Bell and non-contextuality inequalities for realistic experiments. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2024; 382:20230011. [PMID: 38281716 DOI: 10.1098/rsta.2023.0011] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 10/20/2023] [Indexed: 01/30/2024]
Abstract
Contextuality is a feature of quantum correlations. It is crucial from a foundational perspective as a non-classical phenomenon, and from an applied perspective as a resource for quantum advantage. It is commonly defined in terms of hidden variables, for which it forces a contradiction with the assumptions of parameter-independence and determinism. The former can be justified by the empirical property of non-signalling or non-disturbance, and the latter by the empirical property of measurement sharpness. However, in realistic experiments neither empirical property holds exactly, which leads to possible objections to contextuality as a form of non-classicality, and potential vulnerabilities for supposed quantum advantages. We introduce measures to quantify both properties, and introduce quantified relaxations of the corresponding assumptions. We prove the continuity of a known measure of contextuality, the contextual fraction, which ensures its robustness to noise. We then bound the extent to which these relaxations can account for contextuality, via corrections terms to the contextual fraction (or to any non-contextuality inequality), culminating in a notion of genuine contextuality, which is robust to experimental imperfections. We then show that our result is general enough to apply or relate to a variety of established results and experimental set-ups. This article is part of the theme issue 'Quantum contextuality, causality and freedom of choice'.
Collapse
Affiliation(s)
- Kim Vallée
- Sorbonne Université, CNRS, LIP6, Paris 75005, France
| | | | | | | | | | | |
Collapse
|
3
|
Guo Y, Ji W, Kong X, Wang M, Sun H, Zhou J, Chai Z, Rong X, Shi F, Wang Y, Du J. Single-Shot Readout of a Solid-State Electron Spin Qutrit. PHYSICAL REVIEW LETTERS 2024; 132:060601. [PMID: 38394571 DOI: 10.1103/physrevlett.132.060601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2023] [Accepted: 01/09/2024] [Indexed: 02/25/2024]
Abstract
Quantum systems usually feature a rich multilevel structure with promising resources for developing superior quantum technologies compared with their binary counterpart. Single-shot readout of these high-dimensional quantum systems is essential for exploiting their potential. Although there have been various high-spin systems, the single-shot readout of the overall state of high-spin systems remains a challenging issue. Here we demonstrate a reliable single-shot readout of spin qutrit state in a low-temperature solid-state system utilizing a binary readout scheme. We achieve a single-shot readout of an electron spin qutrit associated with a single nitrogen-vacancy center in diamond with an average fidelity of 87.80%. We use this spin qutrit system to verify quantum contextuality, a fundamental test of quantum mechanics. We observe a violation of the noncontextual hidden variable inequality with the developed single-shot readout in contrast to the conventional binary readout. These results pave the way for developing quantum information processing based on spin qutrits.
Collapse
Affiliation(s)
- Yuhang Guo
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Wentao Ji
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Xi Kong
- The State Key Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing 210093, China
| | - Mengqi Wang
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Haoyu Sun
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Jingyang Zhou
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Zihua Chai
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xing Rong
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Fazhan Shi
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Ya Wang
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
| | - Jiangfeng Du
- CAS Key Laboratory of Microscale Magnetic Resonance and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China
- CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
- Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China
- School of Physics, Zhejiang University, Hangzhou 310027, China
| |
Collapse
|
4
|
Dzhafarov EN, Kujala JV. Contextuality with Disturbance and without: Neither Can Violate Substantive Requirements the Other Satisfies. ENTROPY (BASEL, SWITZERLAND) 2023; 25:581. [PMID: 37190369 PMCID: PMC10137645 DOI: 10.3390/e25040581] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/23/2023] [Revised: 03/15/2023] [Accepted: 03/23/2023] [Indexed: 05/17/2023]
Abstract
Contextuality was originally defined only for consistently connected systems of random variables (those without disturbance/signaling). Contextuality-by-Default theory (CbD) offers an extension of the notion of contextuality to inconsistently connected systems (those with disturbance) by defining it in terms of the systems' couplings subject to certain constraints. Such extensions are sometimes met with skepticism. We pose the question of whether it is possible to develop a set of substantive requirements (i.e., those addressing a notion itself rather than its presentation form) such that (1) for any consistently connected system, these requirements are satisfied, but (2) they are violated for some inconsistently connected systems. We show that no such set of requirements is possible, not only for CbD but for all possible CbD-like extensions of contextuality. This follows from the fact that any extended contextuality theory T is contextually equivalent to a theory T' in which all systems are consistently connected. The contextual equivalence means the following: there is a bijective correspondence between the systems in T and T' such that the corresponding systems in T and T' are, in a well-defined sense, mere reformulations of each other, and they are contextual or noncontextual together.
Collapse
Affiliation(s)
- Ehtibar N. Dzhafarov
- Department of Psychological Sciences, Purdue University, West Lafayette, IN 47907, USA
| | - Janne V. Kujala
- Department of Mathematics and Statistics, University of Turku, FI-20014 Turun yliopisto, Finland
| |
Collapse
|
5
|
Holik FH. Non-Kolmogorovian Probabilities and Quantum Technologies. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1666. [PMID: 36421520 PMCID: PMC9689320 DOI: 10.3390/e24111666] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 10/01/2022] [Revised: 10/29/2022] [Accepted: 11/07/2022] [Indexed: 06/16/2023]
Abstract
In this work, we focus on the philosophical aspects and technical challenges that underlie the axiomatization of the non-Kolmogorovian probability framework, in connection with the problem of quantum contextuality. This fundamental feature of quantum theory has received a lot of attention recently, given that it might be connected to the speed-up of quantum computers-a phenomenon that is not fully understood. Although this problem has been extensively studied in the physics community, there are still many philosophical questions that should be properly formulated. We analyzed different problems from a conceptual standpoint using the non-Kolmogorovian probability approach as a technical tool.
Collapse
Affiliation(s)
- Federico Hernán Holik
- Instituto de Física La Plata, CONICET-UNLP, Diagonal 113 e/63 y 64, La Plata 1900, Argentina
| |
Collapse
|