Informational distance on quantum-state space
Abstract
By formally generalizing the classical Hellinger distance and affinity on the space of probability densities, we introduce their quantum analog on the quantum state space consisting of all density operators. We show that the infinitesimal form of the quantum Hellinger distance is the skew information introduced by Wigner and Yanase in 1963. We compare the Hellinger distance and affinity with the Bures distance and fidelity, and establish a variety of their fundamental properties. We further apply them to characterizing entanglement and to establishing some unusual uncertainty relations relating nonsimultaneous measurements of a single observable in two different quantum states.
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“We compare our bound to the most significant bounds appearing in the literature [30, 33, 48–50] which either depend on the overlap tr[ρσ] or require the evaluation of quantum fidelity F (ρ, σ) = tr[ √√ ρσ √ ρ] [65], affinity A(ρ, σ) = tr[√ρ √ σ] [66], or Fisher information [67].”
- Authors
- Luo, S., & Zhang, Q.
- Affiliations
- Chinese Academy of Sciences (CN)
- City University of Hong Kong (HK)
- Venue
- Physical Review A
- Publisher
- American Physical Society (APS)
- Published
- 2004-03-16
- Volume
- 69
- Issue
- 3
- ISSN
- 0556-2791 (ISSN-L)
- 1050-2947
- 1094-1622
- OpenAlex
- W2087844534
- Cited by
- 216
- References
- 40
- Citations by year
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- FWCI
- 2.04
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Physical Review A (publishedVersion)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum Mechanics and Applications
- Physical Sciences › Computer Science › Artificial Intelligence › Quantum Information and Cryptography
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Statistical Mechanics and Entropy
- Keywords
- density matrix, quantum state space, skew information, Bures distance, fidelity, entanglement characterization, uncertainty relations, quantum information measures
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