Fidelity and concurrence of conjugated states
Open accessAbstract
We prove some properties of fidelity (transition probability) and concurrence, the latter defined by a straightforward extension of Wootters' notation. Choose a conjugation and consider the dependence of fidelity or of concurrence on conjugated pairs of density operator. These functions turn out to be concave or convex roofs. Optimal decompositions are constructed. Some applications to two and tripartite systems illustrate the general theorems.
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In two-level systems, for Θ = σy ⊗ σy C*, cΘ(ψ) is non-vanishing if and only if |ψ> is entangled.
“For Θ = σ y ⊗ σ y C ∗ [49,66], with the second Pauli matrix σ y and C ∗ the complex conjugation in the standard basis (defined after Eq. (34)), c Θ ( ψ ) is non-vanishing if and only if | ψ 〉 is entangled.”
From Measures and dynamics of entangled states (2005) · cites this paper as [49]
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- Authors
- Uhlmann, A.
- Affiliations
- Leipzig University (DE)
- Corresponding author
- Uhlmann, Armin
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2000-08-16
- Volume
- 62
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2120002077
- Cited by
- 421
- References
- 19
- Citations by year
- 2026: 7 · 2025: 15 · 2024: 16 · 2023: 18 · 2022: 14 · 2021: 14 · 2020: 19 · 2019: 25 · 2018: 16 · 2017: 9 · 2016: 9 · 2015: 17 · 2014: 19 · 2013: 20 · 2012: 17
- FWCI
- 5.38
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- CERN Document Server (European Organization for Nuclear Research) (submittedVersion)
- arXiv (Cornell University)
- 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 › Computer Science › Artificial Intelligence › Quantum Computing Algorithms and Architecture
- Keywords
- quantum fidelity, concurrence, density matrix, optimal decomposition, two-qubit systems, tripartite system, quantum entanglement
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