Bell nonlocality and fully entangled fraction measured in an entanglement-swapping device without quantum state tomography
Open accessAbstract
We propose and experimentally implement an efficient procedure based on entanglement swapping to determine the Bell nonlocality measure of Horodecki et al. [Phys. Lett. A 200, 340 (1995)] and the fully entangled fraction of Bennett et al. [Phys. Rev. A 54, 3824 (1996)] of an arbitrary two-qubit polarization-encoded state. The nonlocality measure corresponds to the amount of the violation of the Clauser-Horne-Shimony-Holt (CHSH) optimized over all measurement settings. By using simultaneously two copies of a given state, we measure directly only six parameters. This is an experimental determination of these quantities without quantum state tomography or continuous monitoring of all measurement bases in the usual CHSH inequality tests. We analyze how well the measured degrees of Bell nonlocality and other entanglement witnesses (including the fully entangled fraction and a nonlinear entropic witness) of an arbitrary two-qubit state can estimate its entanglement. In particular, we measure these witnesses and estimate the negativity of various two-qubit Werner states. Our approach could especially be useful for quantum communication protocols based on entanglement swapping.
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The design shares the same geometry with the entanglement-swapping protocol of Ref.48.
“Moreover, our design shares the same geometry with the entanglement-swapping protocol48.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [48]
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 [48]
The setup applied in this work was also used earlier in Refs.48-51 for conceptually different tasks.
“We note that the setup applied in this work was also used earlier in Refs.48–51, but for conceptually different tasks, e.g., measuring collective nonlinear witnesses of entanglement52,53, Bell nonlocality measure54, or diagnosing an entanglement-swapping protocol.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [48]
Similar quantifiers, but describing nonlocality and entanglement, were measured in Ref.48 using the parameters M and F, which are also applied in this paper.
“Similar quantifiers, but describing nonlocality and entanglement, were measured in Ref.48 using the parameters M and F, which are also applied in this paper.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [48]
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Cites
Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels
Bennett, C. H., Brassard, G., Crépeau, C., Jozsa, R., Peres, A., & Wootters, W. K. (1993) · Physical Review Letters · doi:10.1103/physrevlett.70.1895 · Cited by 13,703 · see citing works
Measurement of subpicosecond time intervals between two photons by interference
Hong, C. K., Ou, Z. Y., & Mandel, L. (1987) · Physical Review Letters · doi:10.1103/physrevlett.59.2044 · Cited by 4,369 · see citing works
Quantum states with Einstein-Podolsky-Rosen correlations admitting a hidden-variable model
Werner, R. F. (1989) · Physical Review A · doi:10.1103/physreva.40.4277 · Cited by 4,062 · see citing works
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“tions [69], as well as to entanglement-assisted quantum error correction [70] and entanglement purification [63].”
BackgroundGottesman, D., & Chuang, I. L. (1999) · Nature · doi:10.1038/46503 · Cited by 1,860 · see citing works
Speakable and Unspeakable in Quantum Mechanics: Collected Papers on Quantum Philosophy
Bell, J. S., & Aspect, A. (2004) · doi:10.1017/cbo9780511815676 · Cited by 1,261 · see citing works
Violating Bell inequality by mixed states: necessary and sufficient condition
Horodecki, R., Horodecki, P., & Horodecki, M. (1995) · Physics Letters A · doi:10.1016/0375-9601(95)00214-n · Cited by 884 · see citing works
Method for universal detection of two-photon polarization entanglement
Bartkiewicz, K., Horodecki, P., Lemr, K., Miranowicz, A., & Życzkowski, K. (2015) · Physical Review A · doi:10.1103/physreva.91.032315 · Cited by 36 · cited 1× · see citing works
“By applying the maximum-likelihood method, we demonstrated that direct measurements of nonlinear entanglement witnesses [47,48] could be made robust to experimental errors by exploiting the correlations between them.”
MethodSelf-citationCollectibility for mixed quantum states
Rudnicki, Ł., Puchała, Z., Horodecki, P., & Życzkowski, K. (2012) · Physical Review A · doi:10.1103/physreva.86.062329 · Cited by 20 · see citing works
Flagged first, then by citations
Research works printed but not linked: 5
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Experimental hierarchy of two-qubit quantum correlations without state tomography
Abo, S., Soubusta, J., Jiráková, K., Bartkiewicz, K., Černoch, A., Lemr, K., & Miranowicz, A. (2023) · Scientific Reports · doi:10.1038/s41598-023-35015-9 · Cited by 17 · see citing works
Self-citation
- Authors
- Bartkiewicz, K., Lemr, K., Černoch, A., & Miranowicz, A.
- Affiliations
- Czech Academy of Sciences (CZ)
- FZU - Institute of Physics of the Czech Academy of Sciences (CZ)
- Adam Mickiewicz University in Poznań (PL)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2017-03-13
- Volume
- 95
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W2527963940
- Cited by
- 39
- References
- 9
- Citations by year
- 2026: 3 · 2025: 6 · 2024: 6 · 2023: 4 · 2022: 4 · 2021: 4 · 2020: 2 · 2019: 3 · 2018: 6 · 2017: 1
- FWCI
- 1.96
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- ASEP (submittedVersion, public-domain)
- arXiv (Cornell University)
- Funders
- Grantová Agentura České Republiky (16-10042Y, P205/12/0382)
- Narodowe Centrum Nauki (DEC-2013/11/D/ST2/02638)
- Ministerstvo Školství, Mládeže a Tělovýchovy
- John Templeton Foundation
- 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
- Bell nonlocality, entanglement swapping, CHSH inequality, two-qubit states, polarization encoding, entanglement witnesses, Werner states, entanglement negativity, quantum communication
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