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Palma Torres L, Solís-Prosser MÁ, Jiménez O, Gómez ES, Delgado A. Optimal High-Dimensional Entanglement Concentration for Pure Bipartite Systems. MICROMACHINES 2023; 14:1207. [PMID: 37374791 DOI: 10.3390/mi14061207] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/10/2023] [Revised: 05/15/2023] [Accepted: 05/19/2023] [Indexed: 06/29/2023]
Abstract
Considering pure quantum states, entanglement concentration is the procedure where, from N copies of a partially entangled state, a single state with higher entanglement can be obtained. Obtaining a maximally entangled state is possible for N=1. However, the associated success probability can be extremely low when increasing the system's dimensionality. In this work, we study two methods to achieve a probabilistic entanglement concentration for bipartite quantum systems with a large dimensionality for N=1, regarding a reasonably good probability of success at the expense of having a non-maximal entanglement. Firstly, we define an efficiency function Q considering a tradeoff between the amount of entanglement (quantified by the I-Concurrence) of the final state after the concentration procedure and its success probability, which leads to solving a quadratic optimization problem. We found an analytical solution, ensuring that an optimal scheme for entanglement concentration can always be found in terms of Q. Finally, a second method was explored, which is based on fixing the success probability and searching for the maximum amount of entanglement attainable. Both ways resemble the Procrustean method applied to a subset of the most significant Schmidt coefficients but obtaining non-maximally entangled states.
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Affiliation(s)
- Lukas Palma Torres
- Departamento de Ciencias Físicas, Facultad de Ingeniería y Ciencias, Universidad de La Frontera, Avenida Francisco Salazar 01145, Temuco 4811230, Chile
| | - Miguel Ángel Solís-Prosser
- Departamento de Ciencias Físicas, Facultad de Ingeniería y Ciencias, Universidad de La Frontera, Avenida Francisco Salazar 01145, Temuco 4811230, Chile
| | - Omar Jiménez
- Centro de Óptica e Información Cuántica, Facultad de Ciencias, Universidad Mayor, Camino La Pirámide 5750, Huechuraba, Santiago 8580745, Chile
| | - Esteban S Gómez
- Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción 4070043, Chile
- Millennium Institute for Research in Optics, Universidad de Concepción, Casilla 160-C, Concepción 4070043, Chile
| | - Aldo Delgado
- Departamento de Física, Universidad de Concepción, Casilla 160-C, Concepción 4070043, Chile
- Millennium Institute for Research in Optics, Universidad de Concepción, Casilla 160-C, Concepción 4070043, Chile
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Jiang GL, Liu WQ, Wei HR. Heralded and high-efficient entanglement concentrations based on linear optics assisted by time-delay degree of freedom. OPTICS EXPRESS 2022; 30:47836-47846. [PMID: 36558702 DOI: 10.1364/oe.476342] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/23/2022] [Accepted: 11/30/2022] [Indexed: 06/17/2023]
Abstract
Entanglement concentration is a critical technique to prevent degraded fidelity and security in long-distance quantum communication. We propose novel practical entanglement concentration protocols (ECPs) for less-entangled Bell and Greenberger-Horne-Zeilinger states with unknown parameters by solely using simple linear optics. We avoid the need for the post-selection principles or photon-number-resolving detectors to identify the parity-check measurement completely by orchestrating auxiliary time degree of freedom, and the success of ECPs is exactly heralded by the detection signatures without destroying the incident qubits. Additionally, the outting incident photons kept are in the maximally entangled or the less-entangled state, and the success probability can be increased by recycling the latter. The heralded and the basic linear optical elements make our practical ECPs are accessible to experimental investigation with current technology.
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Protecting nonlocal quantum correlations in correlated squeezed generalized amplitude damping channel. Sci Rep 2022; 12:20481. [DOI: 10.1038/s41598-022-24789-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/28/2022] [Accepted: 11/21/2022] [Indexed: 11/29/2022] Open
Abstract
AbstractNonlocal quantum correlations, such as quantum entanglement, quantum steering, and Bell nonlocality, are crucial resources for quantum information tasks. How to protect these quantum resources from decoherence is one of the most urgent problems to be solved. Here, we investigate the evolution of these correlations in the correlated squeezed generalized amplitude damping (SGAD) channel and propose a scheme to protect them with weak measurement (WM) and quantum measurement reversal (QMR). Compared with the results of the uncorrelated SGAD channel, we find that when $$n=1$$
n
=
1
, correlation and squeezing effects can prolong the survival time of quantum entanglement, Bell nonlocality, and quantum steering by about 152 times, 207 times, and 10 times, respectively. In addition, local WM and QMR can effectively recover the disappeared nonlocal quantum correlations either in uncorrelated or completely correlated SGAD channels. Moreover, we find that these initial nonlocal quantum correlations could be drastically amplified under the correlated channel. And the steering direction can be flexibly manipulated either by changing the channel parameters or the strength of WM and QMR. These results not only make a step forward in suppressing decoherence and enhancing quantum correlation in noise channels, but also help to develop relevant practical applications.
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Huang CX, Hu XM, Guo Y, Zhang C, Liu BH, Huang YF, Li CF, Guo GC, Gisin N, Branciard C, Tavakoli A. Entanglement Swapping and Quantum Correlations via Symmetric Joint Measurements. PHYSICAL REVIEW LETTERS 2022; 129:030502. [PMID: 35905332 DOI: 10.1103/physrevlett.129.030502] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Accepted: 06/17/2022] [Indexed: 06/15/2023]
Abstract
We use hyperentanglement to experimentally realize deterministic entanglement swapping based on quantum elegant joint measurements. These are joint projections of two qubits onto highly symmetric, isoentangled bases. We report measurement fidelities no smaller than 97.4%. We showcase the applications of these measurements by using the entanglement swapping procedure to demonstrate quantum correlations in the form of proof-of-principle violations of both bilocal Bell inequalities and more stringent correlation criteria corresponding to full network nonlocality. Our results are a foray into entangled measurements and nonlocality beyond the paradigmatic Bell state measurement and they show the relevance of more general measurements in entanglement swapping scenarios.
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Affiliation(s)
- Cen-Xiao Huang
- CAS Key Laboratory of Quantum Information, 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
| | - Xiao-Min Hu
- CAS Key Laboratory of Quantum Information, 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
| | - Yu Guo
- CAS Key Laboratory of Quantum Information, 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
| | - Chao Zhang
- CAS Key Laboratory of Quantum Information, 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
| | - Bi-Heng Liu
- CAS Key Laboratory of Quantum Information, 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
| | - Yun-Feng Huang
- CAS Key Laboratory of Quantum Information, 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
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, 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
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, 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
| | - Nicolas Gisin
- Group of Applied Physics, University of Geneva, 1211 Geneva 4, Switzerland
- Schaffhausen Institute of Technology-SIT, 1211 Geneva, Switzerland
| | - Cyril Branciard
- Université Grenoble Alpes, CNRS, Grenoble INP, Institut Néel, 38000 Grenoble, France
| | - Armin Tavakoli
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090 Vienna, Austria
- Atominstitut, Technische Universität Wien, Stadionallee 2, 1020 Vienna, Austria
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Sun K, Hao ZY, Wang Y, Li JK, Xu XY, Xu JS, Han YJ, Li CF, Guo GC. Optical demonstration of quantum fault-tolerant threshold. LIGHT, SCIENCE & APPLICATIONS 2022; 11:203. [PMID: 35790719 PMCID: PMC9256730 DOI: 10.1038/s41377-022-00891-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/30/2022] [Revised: 06/08/2022] [Accepted: 06/10/2022] [Indexed: 06/15/2023]
Abstract
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable to the output of a higher probability of correct logical qubits under the presence of errors. However, strict requirements to encode qubits and operators render the implementation of a full fault-tolerant computation challenging even for the achievable noisy intermediate-scale quantum technology. Especially the threshold for fault-tolerant computation still lacks experimental verification. Here, based on an all-optical setup, we experimentally demonstrate the existence of the threshold for the fault-tolerant protocol. Four physical qubits are represented as the spatial modes of two entangled photons, which are used to encode two logical qubits. The experimental results clearly show that when the error rate is below the threshold, the probability of correct output in the circuit, formed with fault-tolerant gates, is higher than that in the corresponding non-encoded circuit. In contrast, when the error rate is above the threshold, no advantage is observed in the fault-tolerant implementation. The developed high-accuracy optical system may provide a reliable platform to investigate error propagation in more complex circuits with fault-tolerant gates.
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Affiliation(s)
- Kai Sun
- CAS Key Laboratory of Quantum Information, 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
| | - Ze-Yan Hao
- CAS Key Laboratory of Quantum Information, 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
| | - Yan Wang
- CAS Key Laboratory of Quantum Information, 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
| | - Jia-Kun Li
- CAS Key Laboratory of Quantum Information, 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
| | - Xiao-Ye Xu
- CAS Key Laboratory of Quantum Information, 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
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, 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.
| | - Yong-Jian Han
- CAS Key Laboratory of Quantum Information, 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.
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, 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.
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, 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
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