Direct Measurement of Nonlinear Properties of Bipartite Quantum States
Open accessAbstract
Nonlinear properties of quantum states, such as entropy or entanglement, quantify important physical resources and are frequently used in quantum-information science. They are usually calculated from a full description of a quantum state, even though they depend only on a small number of parameters that specify the state. Here we extract a nonlocal and a nonlinear quantity, namely, the Renyi entropy, from local measurements on two pairs of polarization-entangled photons. We also introduce a "phase marking" technique which allows the selection of uncorrupted outcomes even with nondeterministic sources of entangled photons. We use our experimental data to demonstrate the violation of entropic inequalities. They are examples of nonlinear entanglement witnesses and their power exceeds all linear tests for quantum entanglement based on all possible Bell-Clauser-Horne-Shimony-Holt inequalities.
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The experimental setup requires only a single Hong-Ou-Mandel interferometer instead of two, compared with the method of Ref.56.
“Namely from the experimental point of view, it only requires a single Hong–Ou–Mandel interferometer instead of two.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [56]
The experimental method of measuring R for general two-qubit states is conceptually similar to that reported in Ref.56 for measuring a nonlinear entropic witness.
“Our experimental method of measuring R for general two qubit states is conceptually similar to that reported in Ref.56 for measuring a nonlinear entropic witness.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [56]
The setup enables entanglement swapping and measuring multicopy entanglement witnesses.
“Moreover, the setup enables entanglement swapping and measuring multicopy entanglement witnesses as inspired by Refs.55,56.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [56]
The setup bears some similarities with a previously proposed and implemented scheme by Bovino et al.56.
“The setup also bears some similarities with a previously proposed and implemented scheme by Bovino et al.56.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [56]
The method can perform full tomography of all elements of the R matrix rather than only determining its trace, so from the six numbers one can learn much more about quantum correlations compared to the original method of Ref.56.
“As shown in Ref.48, one can perform a full tomography of all the elements of the R matrix rather than only determining its trace. Thus, from the set of six numbers (determining a correlation matrix R) we can learn much more about quantum correlations compared to the original method of Ref.56.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [56]
Our copy describes direct measurements of Rényi entropy and purity, and gives equations for traces of the bipartite state and its subsystems (Abstract; page unavailable). Searches for full tomography, an R matrix, and six numbers found no passage addressing whether the method determines every element of an R matrix. (LLM, conf=0.72)
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Cites
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Gühne, O., & Tóth, G. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.02.004 · Cited by 2,401 · see citing works
Measuring Entanglement Growth in Quench Dynamics of Bosons in an Optical Lattice
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Self-citationExperimental hierarchy of two-qubit quantum correlations without state tomography
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“[55] for measuring a nonlinear entropic witness.”
- Authors
- Bovino, F. A., Castagnoli, G., Ekert, A., Horodecki, P., Alves, C. M., & Sergienko, A. V.
- Affiliations
- National University of Singapore (SG)
- Gdańsk University of Technology (PL)
- University of Cambridge (GB)
- Boston University (US)
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2005-12-09
- Volume
- 95
- Issue
- 24
- Pages
- 240407-240407
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2964280276
- Cited by
- 168
- References
- 1
- Citations by year
- 2026: 2 · 2025: 9 · 2024: 7 · 2023: 11 · 2022: 11 · 2021: 7 · 2020: 7 · 2019: 7 · 2018: 8 · 2017: 8 · 2016: 10 · 2015: 7 · 2014: 4 · 2013: 3 · 2012: 9
- FWCI
- 12.34
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- National University of Singapore (submittedVersion)
- arXiv (Cornell University)
- Funders
- National Science Foundation
- Ministero dell’Istruzione, dell’Università e della Ricerca
- Defense Advanced Research Projects Agency
- Topics
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Semiconductor Quantum Structures and Devices
- Keywords
- Rényi entropy, polarization-entangled photons, bipartite quantum states, entanglement witnesses, entropy inequality, Bell inequalities, local measurements, quantum entanglement
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