Characterization of the positivity of the density matrix in terms of the coherence vector representation
Open accessAbstract
A parametrization of the density operator, a coherence vector representation, which uses a basis of orthogonal, traceless, Hermitian matrices is discussed. Using this parametrization we find the region of permissible vectors which represent a density operator. The inequalities which specify the region are shown to involve the Casimir invariants of the group. In particular cases, this allows the determination of degeneracies in the spectrum of the operator. The identification of the Casimir invariants also provides a method of constructing quantities which are invariant under local unitary operations. Several examples are given which illustrate the constraints provided by the positivity requirements and the utility of the coherence vector parametrization.
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The angle between generalized Bloch vectors is a distance for unitarily connectable elements of state space and induces an attainable bound for unitary evolution of mixed qubits.
“We propose the use of the angle between generalized Bloch vectors [45,46] as a distance for those elements of the state space that can be unitarily connected, and show that it induces an attainable bound for the unitary evolution of mixed qubits.”
From Tightening Quantum Speed Limits for Almost All States (2018) · cites this paper as [46]
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Sorted by citations
Adiabatic approximation in open quantum systems
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Tightening Quantum Speed Limits for Almost All States
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“The generalized Bloch vector r is a vector in a (d2 − 1)dimensional real vector space, equipped with the standard Euclidean norm ‖r‖2 = √∑ i r 2 i [56].”
BackgroundMethodInfluential
- Authors
- Byrd, M. S., & Khaneja, N.
- Affiliations
- Harvard University (US)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2003-12-31
- Volume
- 68
- Issue
- 6
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2089110262
- Cited by
- 268
- References
- 20
- Citations by year
- 2026: 3 · 2025: 10 · 2024: 13 · 2023: 13 · 2022: 21 · 2021: 24 · 2020: 10 · 2019: 13 · 2018: 5 · 2017: 9 · 2016: 13 · 2015: 11 · 2014: 9 · 2013: 12 · 2012: 14
- FWCI
- 10.64
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review A (publishedVersion)
- arXiv (Cornell University) (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
- Casimir operators, local unitary invariance, quantum coherence
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