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Imai S, Tóth G, Gühne O. Collective Randomized Measurements in Quantum Information Processing. PHYSICAL REVIEW LETTERS 2024; 133:060203. [PMID: 39178439 DOI: 10.1103/physrevlett.133.060203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2023] [Revised: 05/08/2024] [Accepted: 07/09/2024] [Indexed: 08/25/2024]
Abstract
The concept of randomized measurements on individual particles has proven to be useful for analyzing quantum systems and is central for methods like shadow tomography of quantum states. We introduce collective randomized measurements as a tool in quantum information processing. Our idea is to perform measurements of collective angular momentum on a quantum system and actively rotate the directions using simultaneous multilateral unitaries. Based on the moments of the resulting probability distribution, we propose systematic approaches to characterize quantum entanglement in a collective-reference-frame-independent manner. First, we show that existing spin-squeezing inequalities can be accessible in this scenario. Next, we present an entanglement criterion based on three-body correlations, going beyond spin-squeezing inequalities with two-body correlations. Finally, we apply our method to characterize entanglement between spatially separated two ensembles.
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Affiliation(s)
- Satoya Imai
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
- QSTAR, INO-CNR, and LENS, Largo Enrico Fermi, 2, 50125 Firenze, Italy
| | - Géza Tóth
- Department of Theoretical Physics, University of the Basque Country UPV/EHU, P.O. Box 644, E-48080 Bilbao, Spain
- EHU Quantum Center, University of the Basque Country UPV/EHU, Barrio Sarriena s/n, ES-48940 Leioa, Biscay, Spain
- Donostia International Physics Center (DIPC), P.O. Box 1072, E-20080 San Sebastián, Spain
- IKERBASQUE, Basque Foundation for Science, E-48009 Bilbao, Spain
- HUN-REN Wigner Research Centre for Physics, P.O. Box 49, H-1525 Budapest, Hungary
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Weinbrenner LT, Prasannan N, Hansenne K, Denker S, Sperling J, Brecht B, Silberhorn C, Gühne O. Certifying the Topology of Quantum Networks: Theory and Experiment. PHYSICAL REVIEW LETTERS 2024; 132:240802. [PMID: 38949362 DOI: 10.1103/physrevlett.132.240802] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2023] [Accepted: 05/13/2024] [Indexed: 07/02/2024]
Abstract
Distributed quantum information in networks is paramount for global secure quantum communication. Moreover, it finds applications as a resource for relevant tasks, such as clock synchronization, magnetic field sensing, and blind quantum computation. For quantum network analysis and benchmarking of implementations, however, it is crucial to characterize the topology of networks in a way that reveals the nodes between which entanglement can be reliably distributed. Here, we demonstrate an efficient scheme for this topology certification. Our scheme allows for distinguishing, in a scalable manner, different networks consisting of bipartite and multipartite entanglement sources. It can be applied to semi-device-independent scenarios also, where the measurement devices and network nodes are not well characterized and trusted. We experimentally demonstrate our approach by certifying the topology of different six-qubit networks generated with polarized photons, employing active feed-forward and time multiplexing. Our methods can be used for general simultaneous tests of multiple hypotheses with few measurements, being useful for other certification scenarios in quantum technologies.
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Yang Y, Yadin B, Xu ZP. Quantum-Enhanced Metrology with Network States. PHYSICAL REVIEW LETTERS 2024; 132:210801. [PMID: 38856242 DOI: 10.1103/physrevlett.132.210801] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/27/2023] [Revised: 12/12/2023] [Accepted: 04/15/2024] [Indexed: 06/11/2024]
Abstract
Armed with quantum correlations, quantum sensors in a network have shown the potential to outclass their classical counterparts in distributed sensing tasks such as clock synchronization and reference frame alignment. On the other hand, this analysis was done for simple and idealized networks, whereas the correlation shared within a practical quantum network, captured by the notion of network states, is much more complex. Here, we prove a general bound that limits the performance of using quantum network states to estimate a global parameter, establishing the necessity of genuine multipartite entanglement for achieving a quantum advantage. The bound can also serve as an entanglement witness in networks and can be generalized to states generated by shallow circuits. Moreover, while our bound prohibits local network states from achieving the Heisenberg limit, we design a probabilistic protocol that, once successful, attains this ultimate limit of quantum metrology and preserves the privacy of involved parties. Our work establishes both the limitation and the possibility of quantum metrology within quantum networks.
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Affiliation(s)
- Yuxiang Yang
- QICI Quantum Information and Computation Initiative, Department of Computer Science, The University of Hong Kong, Pokfulam Road, Hong Kong, China
| | - Benjamin Yadin
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Zhen-Peng Xu
- School of Physics and Optoelectronics Engineering, Anhui University, Hefei 230601, People's Republic of China
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Hansenne K, Gühne O. Covariance-Matrix-Based Criteria for Network Entanglement. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1260. [PMID: 37761559 PMCID: PMC10528436 DOI: 10.3390/e25091260] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/19/2023] [Revised: 08/14/2023] [Accepted: 08/20/2023] [Indexed: 09/29/2023]
Abstract
Quantum networks offer a realistic and practical scheme for generating multiparticle entanglement and implementing multiparticle quantum communication protocols. However, the correlations that can be generated in networks with quantum sources and local operations are not yet well understood. Covariance matrices, which are powerful tools in entanglement theory, have been also applied to the network scenario. We present simple proofs for the decomposition of such matrices into the sum of positive semi-definite block matrices and, based on that, develop analytical and computable necessary criteria for preparing states in quantum networks. These criteria can be applied to networks where nodes share at most one source, such as all bipartite networks.
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Affiliation(s)
- Kiara Hansenne
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
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