Quantum discord for two-qubit systems
Abstract
Quantum discord, as introduced by Olliver and Zurek [Phys. Rev. Lett. 88, 017901 (2001)], is a measure of the discrepancy between two natural yet different quantum analogs of the classical mutual information. This notion characterizes and quantifies quantumness of correlations in bipartite states from a measurement perspective, and is fundamentally different from the various entanglement measures in the entanglement vs separability paradigm. The phenomenon of nonzero quantum discord is a manifestation of quantum correlations due to noncommutativity rather than due to entanglement, and has interesting and significant applications in revealing the advantage of certain quantum tasks. We will evaluate analytically the quantum discord for a large family of two-qubit states, and make a comparative study of the relationships between classical and quantum correlations in terms of the quantum discord. We furthermore compare the quantum discord with the entanglement of formation, and illustrate that the latter may be larger than the former, although for separable states, the entanglement of formation always vanishes and thus is less than the quantum discord.
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
As shown in Ref.59, an arbitrary state described by a nondiagonal T can be transformed via singular-value decomposition into a state with a diagonal T by local unitary operations, without changing its quantum correlations.
“Anyway, as shown in Ref.59, an arbitrary state described by a nondiagonal T, can be transformed (via a singular-value decomposition) into a state with a diagonal T by local unitary operations, thus, without changing its quantum correlations, including those studied below.”
From Experimental hierarchy of two-qubit quantum correlations without state tomography (2023) · cites this paper as [59]
Cites
Entanglement of Formation of an Arbitrary State of Two Qubits
Wootters, W. K. (1998) · Physical Review Letters · doi:10.1103/physrevlett.80.2245 · Cited by 8,290 · 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
Flagged first, then by citations
Cited by
Sorted by citations
The classical-quantum boundary for correlations: Discord and related measures
Modi, K., Brodutch, A., Cable, H., Paterek, T., & Vedral, V. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.1655 · Cited by 1,600 · see citing works
Chen, Q., Zhang, C., Yu, S., Yi, X. X., & Oh, C. H. (2011) · Physical Review A · doi:10.1103/physreva.84.042313 · Cited by 300 · see citing works
Revival of quantum correlations without system-environment back-action
Lo Franco, R., Bellomo, B., Andersson, E., & Compagno, G. (2012) · Physical Review A · doi:10.1103/physreva.85.032318 · Cited by 188 · see citing works
Non-Markovianity of local dephasing channels and time-invariant discord
Haikka, P., Johnson, T. H., & Maniscalco, S. (2013) · Physical Review A · doi:10.1103/physreva.87.010103 · Cited by 172 · see citing works
Speed limits in Liouville space for open quantum systems
Uzdin, R., & Kosloff, R. (2016) · EPL (Europhysics Letters) · doi:10.1209/0295-5075/115/40003 · Cited by 52 · see citing works
Frozen Gaussian quantum discord in photonic crystal cavity array system
Lü, Y.-Q., An, J.-H., Chen, X.-M., Luo, H.-G., & Oh, C. H. (2013) · Physical Review A · doi:10.1103/physreva.88.012129 · Cited by 20 · see citing works
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
“[58], an arbitrary state ρ described by a nondiagonal T , can be transformed (via a singular-value decomposition) into a state with a diagonal T by local unitary operations, thus, without changing its quantum correlations, including those studied below.”
Background
- Authors
- Luo, S.
- Affiliations
- Chinese Academy of Sciences (CN)
- Corresponding author
- Luo, Shunlong
- ORCID
- Luo, Shunlong
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2008-04-03
- Volume
- 77
- Issue
- 4
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2038645424
- Cited by
- 1,060
- References
- 2
- Citations by year
- 2026: 27 · 2025: 35 · 2024: 44 · 2023: 44 · 2022: 53 · 2021: 49 · 2020: 36 · 2019: 49 · 2018: 46 · 2017: 55 · 2016: 66 · 2015: 82 · 2014: 104 · 2013: 106 · 2012: 120
- FWCI
- 76.11
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- Funders
- National Natural Science Foundation of China
- Science Fund for Creative Research Groups
- 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 many-body systems
- Keywords
- quantum discord, two-qubit systems, quantum correlations, classical correlations, entanglement of formation, separable states, bipartite quantum states, non-commutativity
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
