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Rosario P, Santos AC, Piovella N, Kaiser R, Cidrim A, Bachelard R. Detecting Entanglement from Macroscopic Measurements of the Electric Field and Its Fluctuations. PHYSICAL REVIEW LETTERS 2024; 133:050203. [PMID: 39159114 DOI: 10.1103/physrevlett.133.050203] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/24/2024] [Accepted: 07/08/2024] [Indexed: 08/21/2024]
Abstract
To address the outstanding task of detecting entanglement in large quantum systems, entanglement witnesses have emerged, addressing the separable nature of a state. Yet optimizing witnesses, or accessing them experimentally, often remains a challenge. We here introduce a family of entanglement witnesses for open quantum systems. Based on the electric field, it does not require state tomography or single-site addressing, but rather macroscopic measurements of the field quadratures and of the total fluorescence. Its efficiency is demonstrated by detecting, from almost any direction, the entanglement of collective single-photon states, such as long-lived states generated by cooperative spontaneous emission. Able to detect entanglement in large open quantum systems, and through a single continuous measurement if operating in the stationary regime, these electric-field-based witnesses can be used on any set of emitters described by the Pauli group, such as atomic systems (cold atoms and trapped ions), giant atoms, color centers, and superconducting qubits.
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Affiliation(s)
| | - Alan C Santos
- Departamento de Física, Universidade Federal de São Carlos, Rodovia Washington Luís, km 235 - SP-310, 13565-905 Sáo Carlos, SP, Brazil
- Instituto de Física Fundamental (IFF), Consejo Superior de Investigaciones Científicas (CSIC), Calle Serrano 113b, 28006 Madrid, Spain
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2
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Frías-Pérez M, Tagliacozzo L, Bañuls MC. Converting Long-Range Entanglement into Mixture: Tensor-Network Approach to Local Equilibration. PHYSICAL REVIEW LETTERS 2024; 132:100402. [PMID: 38518338 DOI: 10.1103/physrevlett.132.100402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/18/2023] [Accepted: 01/30/2024] [Indexed: 03/24/2024]
Abstract
In the out-of-equilibrium evolution induced by a quench, fast degrees of freedom generate long-range entanglement that is hard to encode with standard tensor networks. However, local observables only sense such long-range correlations through their contribution to the reduced local state as a mixture. We present a tensor network method that identifies such long-range entanglement and efficiently transforms it into mixture, much easier to represent. In this way, we obtain an effective description of the time-evolved state as a density matrix that captures the long-time behavior of local operators with finite computational resources.
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Affiliation(s)
- Miguel Frías-Pérez
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
| | - Luca Tagliacozzo
- Institute of Fundamental Physics IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain
| | - Mari Carmen Bañuls
- Max-Planck-Institut für Quantenoptik, Hans-Kopfermann-Str. 1, D-85748 Garching, Germany
- Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, D-80799 München, Germany
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de Gois C, Plávala M, Schwonnek R, Gühne O. Complete Hierarchy for High-Dimensional Steering Certification. PHYSICAL REVIEW LETTERS 2023; 131:010201. [PMID: 37478449 DOI: 10.1103/physrevlett.131.010201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/06/2023] [Accepted: 06/08/2023] [Indexed: 07/23/2023]
Abstract
High-dimensional quantum steering can be seen as a test for the dimensionality of entanglement, where the devices at one side are not characterized. As such, it is an important component in quantum informational protocols that make use of high-dimensional entanglement. Although it has been recently observed experimentally, the phenomenon of high-dimensional steering is lacking a general certification procedure. We provide necessary and sufficient conditions to certify the entanglement dimension in a steering scenario. These conditions are stated in terms of a hierarchy of semidefinite programs, which can also be used to quantify the phenomenon using the steering dimension robustness. To demonstrate the practical viability of our method, we characterize the dimensionality of entanglement in steering scenarios prepared with maximally entangled states measured in mutually unbiased bases. Our methods give significantly stronger bounds on the noise robustness necessary to experimentally certify high-dimensional entanglement.
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Affiliation(s)
- Carlos de Gois
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - Martin Plávala
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
| | - René Schwonnek
- Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstraße 2, 30167, Hannover, Germany
| | - Otfried Gühne
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, 57068 Siegen, Germany
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Hrmo P, Wilhelm B, Gerster L, van Mourik MW, Huber M, Blatt R, Schindler P, Monz T, Ringbauer M. Native qudit entanglement in a trapped ion quantum processor. Nat Commun 2023; 14:2242. [PMID: 37076475 PMCID: PMC10115791 DOI: 10.1038/s41467-023-37375-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2023] [Accepted: 03/15/2023] [Indexed: 04/21/2023] Open
Abstract
Quantum information carriers, just like most physical systems, naturally occupy high-dimensional Hilbert spaces. Instead of restricting them to a two-level subspace, these high-dimensional (qudit) quantum systems are emerging as a powerful resource for the next generation of quantum processors. Yet harnessing the potential of these systems requires efficient ways of generating the desired interaction between them. Here, we experimentally demonstrate an implementation of a native two-qudit entangling gate up to dimension 5 in a trapped-ion system. This is achieved by generalizing a recently proposed light-shift gate mechanism to generate genuine qudit entanglement in a single application of the gate. The gate seamlessly adapts to the local dimension of the system with a calibration overhead that is independent of the dimension.
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Affiliation(s)
- Pavel Hrmo
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria.
| | - Benjamin Wilhelm
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
| | - Lukas Gerster
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
| | - Martin W van Mourik
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
| | - Marcus Huber
- Atominstitut, Technische Universität Wien, 1020, Vienna, Austria
- Institute for Quantum Optics and Quantum Information-IQOQI Vienna, Austrian Academy of Sciences, Boltzmanngasse 3, 1090, Vienna, Austria
| | - Rainer Blatt
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
- Institut für Quantenoptik und Quanteninformation, Österreichische Akademie der Wissenschaften, Technikerstraße 21a, 6020, Innsbruck, Austria
- AQT, Technikerstraße 17, 6020, Innsbruck, Austria
| | - Philipp Schindler
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
| | - Thomas Monz
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
- AQT, Technikerstraße 17, 6020, Innsbruck, Austria
| | - Martin Ringbauer
- Institut für Experimentalphysik, Universität Innsbruck, Technikerstraße 25/4, 6020, Innsbruck, Austria
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Imai S, Wyderka N, Ketterer A, Gühne O. Bound Entanglement from Randomized Measurements. PHYSICAL REVIEW LETTERS 2021; 126:150501. [PMID: 33929215 DOI: 10.1103/physrevlett.126.150501] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/04/2020] [Accepted: 03/03/2021] [Indexed: 06/12/2023]
Abstract
If only limited control over a multiparticle quantum system is available, a viable method to characterize correlations is to perform random measurements and consider the moments of the resulting probability distribution. We present systematic methods to analyze the different forms of entanglement with these moments in an optimized manner. First, we find the optimal criteria for different forms of multiparticle entanglement in three-qubit systems using the second moments of randomized measurements. Second, we present the optimal inequalities if entanglement in a bipartition of a multiqubit system shall be analyzed in terms of these moments. Finally, for higher-dimensional two-particle systems and higher moments, we provide criteria that are able to characterize various examples of bound entangled states, showing that detection of such states is possible in this framework.
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Affiliation(s)
- Satoya Imai
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany
| | - Nikolai Wyderka
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany
- Institut für Theoretische Physik III, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, D-40225 Düsseldorf, Germany
| | - Andreas Ketterer
- Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3, D-79104 Freiburg, Germany
- EUCOR Centre for Quantum Science and Quantum Computing, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Straße 3,D-79104 Freiburg, Germany
| | - Otfried Gühne
- Naturwissenschaftlich-Technische Fakultät, Universität Siegen, Walter-Flex-Straße 3, D-57068 Siegen, Germany
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Zhang WH, Chen G, Peng XX, Ye XJ, Yin P, Xu XY, Xu JS, Li CF, Guo GC. Experimental Realization of Robust Self-Testing of Bell State Measurements. PHYSICAL REVIEW LETTERS 2019; 122:090402. [PMID: 30932519 DOI: 10.1103/physrevlett.122.090402] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2019] [Indexed: 06/09/2023]
Abstract
Bell state measurements, of which the eigenvectors are in an entangled form, are crucial resources in the construction of quantum networks. Therefore, device-independent certification of a Bell state measurement has significance in the quantum information process because it satisfies the exact demand on security. In this study, we implement a proof-of-concept experiment to certify a Bell state measurement device independently in an entanglement swapping process, namely, self-testing. Instead of preparing a tensor product of two singlets with four photons, multiplex encoding in polarization and spatial modes is utilized to produce two pairs of entangled qubits. As a result, we implement a full Bell state measurement and achieve a high degree of Bell violation on the remaining two qubits, which are required for nontrivial self-testing of a Bell state measurement. Furthermore, our results combine the correlations before and after the swapping; thus, the quality of the performed Bell state measurement can be precisely inferred.
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Affiliation(s)
- Wen-Hao Zhang
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Geng Chen
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xing-Xiang Peng
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiang-Jun Ye
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Peng Yin
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Xiao-Ye Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Jin-Shi Xu
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Chuan-Feng Li
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
| | - Guang-Can Guo
- CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, Anhui 230026, China and CAS Center For Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
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