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Qu R, Zhang C, Chang ZH, Zhang XL, Guo Y, Hu XM, Li CF, Guo GC, Zhang P, Liu BH. Observation of Diverse Asymmetric Structures in High-Dimensional Einstein-Podolsky-Rosen Steering. PHYSICAL REVIEW LETTERS 2024; 132:210202. [PMID: 38856248 DOI: 10.1103/physrevlett.132.210202] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/28/2023] [Accepted: 04/22/2024] [Indexed: 06/11/2024]
Abstract
Einstein-Podolsky-Rosen (EPR) steering, a distinctive quantum correlation, reveals a unique and inherent asymmetry. This research delves into the multifaceted asymmetry of EPR steering within high-dimensional quantum systems, exploring both theoretical frameworks and experimental validations. We introduce the concept of genuine high-dimensional one-way steering, wherein a high Schmidt number of bipartite quantum states is demonstrable in one steering direction but not reciprocally. Additionally, we explore two criteria to certify the lower and upper bounds of the Schmidt number within a one-sided device-independent context. These criteria serve as tools for identifying potential asymmetric dimensionality of EPR steering in both directions. By preparing two-qutrit mixed states with high fidelity, we experimentally observe asymmetric structures of EPR steering in the C^{3}⊗C^{3} Hilbert space. Our Letter offers new perspectives to understand the asymmetric EPR steering beyond qubits and has potential applications in asymmetric high-dimensional quantum information tasks.
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Affiliation(s)
- Rui Qu
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Chao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Ze-Hong Chang
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Xiao-Lin Zhang
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Yu Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Xiao-Min Hu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
| | - Pei Zhang
- MOE Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, School of Physics, Xi'an Jiaotong University, Xi'an 710049, China
| | - Bi-Heng Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, China
- CAS Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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Complete classification of steerability under local filters and its relation with measurement incompatibility. Nat Commun 2022; 13:4973. [PMID: 36008389 PMCID: PMC9411635 DOI: 10.1038/s41467-022-32466-y] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/26/2022] [Accepted: 07/18/2022] [Indexed: 11/16/2022] Open
Abstract
Quantum steering is a central resource for one-sided device-independent quantum information. It is manipulated via one-way local operations and classical communication, such as local filtering on the trusted party. Here, we provide a necessary and sufficient condition for a steering assemblage to be transformable into another via local filtering. We characterize the equivalence classes with respect to filters in terms of the steering equivalent observables (SEO), first proposed to connect the problem of steerability and measurement incompatibility. We provide an efficient method to compute the extractable steerability that is maximal via local filters and show that it coincides with the incompatibility of the SEO. Moreover, we show that there always exists a bipartite state that provides an assemblage with steerability equal to the incompatibility of the measurements on the untrusted party. Finally, we investigate the optimal success probability and rates for transformation protocols (distillation and dilution) in the single-shot scenario together with examples. The study of quantum steering has both foundational and practical interest. Here, the authors show that transformability of a steerable resource into another via local filtering at the trusted party is determined by whether they have the same steering equivalent observables (SEO).
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Hao ZY, Sun K, Wang Y, Liu ZH, Yang M, Xu JS, Li CF, Guo GC. Demonstrating Shareability of Multipartite Einstein-Podolsky-Rosen Steering. PHYSICAL REVIEW LETTERS 2022; 128:120402. [PMID: 35394318 DOI: 10.1103/physrevlett.128.120402] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Revised: 04/19/2021] [Accepted: 03/03/2022] [Indexed: 06/14/2023]
Abstract
Einstein-Podolsky-Rosen (EPR) steering, a category of quantum nonlocal correlations describing the ability of one observer to influence another party's state via local measurements, is different from both entanglement and Bell nonlocality by possessing an asymmetric property. For multipartite EPR steering, the monogamous situation, where two observers cannot simultaneously steer the state of the third party, has been investigated rigorously both in theory and experiment. In contrast to the monogamous situation, the shareability of EPR steering in reduced subsystems allows the state of one party to be steered by two or more observers and thus reveals more configurations of multipartite EPR steering. However, the experimental implementation of such a kind of shareability has still been absent until now. Here, in an optical experiment, we provide a proof-of-principle demonstration of the shareability of EPR steering without the constraint of monogamy in a three-qubit system. Moreover, based on the reduced bipartite EPR steering detection results, we verify the genuine three-qubit entanglement results. This work provides a complementary viewpoint for understanding multipartite EPR steering and has potential applications in many quantum information protocols, such as multipartite entanglement detection, quantum cryptography, and the construction of quantum networks.
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Affiliation(s)
- Ze-Yan Hao
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Kai Sun
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Yan Wang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Zheng-Hao Liu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Mu Yang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei 230026, People's Republic of China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, People's Republic of China
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