Collective Randomized Measurements in Quantum Information Processing

Year: 2024

Authors: Imai S., Tòth G., Guhne O.

Autors Affiliation: Univ Siegen, Nat wissensch Tech Fak, Walter-Flex-Str 3, D-57068 Siegen, Germany; QSTAR, INO CNR, Largo Enr Fermi 2, I-50125 Florence, Italy; LENS, Largo Enr Fermi 2, I-50125 Florence, Italy; Univ Basque Country UPV EHU, Dept Theoret Phys, POB 644, E-48080 Bilbao, Spain; Univ Basque Country UPV EHU, EHU Quantum Ctr, Barrio Sarriena S N, ES-48940 Leioa, Biscay, Spain; Donostia Int Phys Ctr DIPC, POB 1072, E-20018 San Sebastian, Spain; Basque Fdn Sci, IKERBASQUE, E-48009 Bilbao, Spain; HUN REN Wigner Res Ctr Phys, POB 49, H-1525 Budapest, Hungary.

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-frameindependent 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.

Journal/Review: PHYSICAL REVIEW LETTERS

Volume: 133 (6)      Pages from: 60203-1  to: 60203-8

More Information: We would like to thank Iagoba Apellaniz, Jan Lennart Boensel, Sophia Denker, Kiara Hansenne, Andreas Ketterer, Matthias Kleinmann, Yi Li, Zhenhuan Liu, H. Chau Nguyen, Stefan Nimmrichter, Martin Plavala, Robert Trenyi, Giuseppe Vitagliano, Nikolai Wyderka, Zhen-Peng Xu, Benjamin Yadin, and Xiao-Dong Yu for discussions. This work was supported by the DAAD, the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, Projects No. 447948357 and No. 440958198) , the Sino-German Center for Research Promotion (Project No. M-0294) , the ERC (Consolidator Grant 683107/TempoQ) , the German Ministry of Education and Research (Project QuKuK, BMBF Grant No. 16KIS1618K) , the Hungarian Scientific Research Fund (Grant No. 2019-2.1.7-ERA-NET-2021-00036) , and the National Research, Development and Innovation Office of Hungary (NKFIH) within the Quantum Information National Laboratory of Hungary. We acknowledge the support of the EU (QuantERA MENTA, QuantERA QuSiED) , the Spanish MCIU (No. PCI2022-132947) , and the Basque Government (No. IT1470-22) . We acknowledge the support of Grant No. PID2021-126273NB-I00 funded by MCIN/AEI and by ERDF A way of making Europe. We thank the Frontline Research Excellence Programme of the NKFIH (Grant No. KKP133827) . G. T. acknowledges a Bessel Research Award of the Humboldt Foundation. We acknowledge Project No. TKP2021-NVA-04, which has been implemented with the support provided by the Ministry of Innovation and Technology of Hungary from the National Research, Development and Innovation Office (NKFIH) , financed under the TKP2021-NVA funding scheme.
KeyWords: Multipartite Entanglement; Separability; Nonlocality; Systems; States; Noise
DOI: 10.1103/PhysRevLett.133.060203