Experimental hierarchy and optimal robustness of quantum correlations of two-qubit states with controllable white noise
Open accessAbstract
We demonstrate a hierarchy of various classes of quantum correlations on experimentally prepared two-qubit Werner-like states with controllable white noise. Werner states, which are white-noise-affected Bell states, are prototypal examples for studying such a hierarchy as a function of the amount of white noise. We experimentally generate Werner states and their generalizations, i.e., partially entangled pure states affected by white noise. These states enable us to study the hierarchy of the following classes of correlations: separability, entanglement, steering in three- and two-measurement scenarios, and Bell nonlocality. We show that the generalized Werner states (GWSs) reveal fundamentally different aspects of the hierarchy compared to the Werner states. In particular, we find five different parameter regimes of the GWSs, including those steerable in a two-measurement scenario but not violating Bell inequalities. This regime cannot be observed for the usual Werner states. Moreover, we find threshold curves separating different regimes of the quantum correlations and find the optimal states which allow for the largest amount of white noise which does not destroy their specific quantum correlations (e.g., unsteerable entanglement). Thus, we could identify the optimal Bell-nondiagonal GWSs which are, for this specific meaning, more robust against the white noise compared to the Bell-diagonal GWSs (i.e., Werner states).
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The steering measure S2 in the two-measurement scenario is equivalent to the Bell nonlocality measure B, but is fundamentally different from the steering measure S1 studied in Ref.9 because it corresponds to Alice (Bob) performing two (three) measurements.
“However, the steering measure , as defined in Eq. (13) in the 2MS, although it is equivalent to the Bell nonlocality measure B, but it is fundamentally different from another steering measure (for clarity denoted here as ) studied by us in Ref.9, because it corresponds to the case when Alice (Bob) performs two (three) measurements on her (his) qubit.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [9]
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Experimental — accuracy not yet measuredA QST-based approach to study a hierarchy of quantum correlations was applied in the authors' former related study9, based on measuring 16 real parameters for two-qubit Werner states.
“Thus, a QST-based approach to study a hierarchy of quantum correlations was applied in our former related study9, which was based on measuring 16 real parameters for two-qubit Werner states.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [9]
Section II (p. 3) says the study used full quantum state tomography to investigate a hierarchy of correlations, and the experimental setup (pp. 7–8) includes Werner states. But the setup describes measurements under 36 two-photon projection combinations, not measurement of 16 real parameters; our copy does not substantiate that numerical detail. (LLM, conf=0.88)
Experimental — accuracy not yet measuredThe maximum steering difference for the experimental states of Ref.9 is practically negligible and much less than the corresponding error bars.
“Thus, the maximum steering difference for the experimental states of Ref.9 can be found to be , which is practically negligible and much less than the corresponding error bars.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [9]
S2=0 does not imply S1=0, as shown experimentally in Ref.9.
“Thus, (corresponding to vanishing Bell nonlocality of a given state ) does not imply that also , which was shown experimentally in Ref.9).”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [9]
Experimental QST-based hierarchies of quantum entanglement, steering, and Bell nonlocality for specific classes of two-qubit states were reported, including experiments with mixtures of partially entangled two-qubit pure states and GWSs based on full QST or full quantum process tomography.
“Experimental QST-based hierarchies of quantum entanglement, steering, and Bell nonlocality for specific classes of two-qubit states in relation to the above-mentioned estimations were also reported, which include experiments with mixtures of partially entangled two-qubit pure states41 and GWSs based on full QST9 or full quantum process tomography24.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [9]
None of the experimental states of Ref.9 exhibited one-way steering.
“More importantly, none of those experimental states exhibited one-way steering.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [9]
The steerable-weight discussion (p. 5) and Appendix B (p. 16) assess steering from Alice to Bob. I searched for one-way and asymmetric steering, including steering from Bob to Alice, but found no passage comparing both directions for the experimental states. Our copy therefore does not establish that none exhibited one-way steering. (LLM, conf=0.76)
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Cites
James, D. F. V., Kwiat, P. G., Munro, W. J., & White, A. G. (2001) · Physical Review A · doi:10.1103/physreva.64.052312 · Cited by 2,176 · 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
Detection-Loophole-Free Test of Quantum Nonlocality, and Applications
Christensen, B. G., McCusker, K. T., Altepeter, J. B., Calkins, B., Gerrits, T., Lita, A. E., Miller, A., Shalm, L. K., Zhang, Y., Nam, S. W., et al. (2013) · Physical Review Letters · doi:10.1103/physrevlett.111.130406 · Cited by 477 · see citing works
Method for universal detection of two-photon polarization entanglement
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“[17] (see also [18, 19]) based on the universal witness of Ref.”
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Research works printed but not linked: 2
- [85]Z. Hradil, J. Řeháček, J. Fiurášek, and M. Ježek, in (eds) Quantum State Estimation. Lecture Notes in Physics, vol 649 , edited by P. M. and Řeháček J. (Springer, Berlin, Heidelberg, Oxford, 2004) Chap. 3, pp. 266-290.
- [87]C. Sanderson and R. Curtin, in Mathematical Software - ICMS 2018 , Lecture Notes in Computer Science, Vol. 10931 (Springer Int. Pub., 2018) pp. 422-430.
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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
“[9], because it corresponds to the case when Alice (Bob) performs two (three) measurements on her (his) qubit.”
BackgroundMethodResultInfluentialSelf-citation
- Authors
- Jiráková, K., Černoch, A., Lemr, K., Bartkiewicz, K., & 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
- 2021-12-21
- Volume
- 104
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 2469-9926
- 2469-9934
- OpenAlex
- W3133711965
- Cited by
- 24
- References
- 4
- Citations by year
- 2026: 4 · 2025: 6 · 2024: 6 · 2023: 4 · 2022: 3 · 2021: 1
- FWCI
- 1.24
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Grantová Agentura České Republiky (20-17765S, CZ.02.1.01/0.0/0.0/16_019/0000754)
- Ministerstvo Školství, Mládeže a Tělovýchovy
- Univerzita Palackého v Olomouci (IGA-PrF-2021-004)
- Narodowe Centrum Nauki (DEC-2019/34/A/ST2/00081)
- 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 › Quantum optics and atomic interactions
- Keywords
- quantum correlations, two-qubit states, Werner states, white noise, entanglement, quantum steering, Bell nonlocality, separability, Bell-diagonal states, ideal state
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