Informational distance on quantum-state space

Journal Article · Mon Mar 01 04:00:00 EST 2004 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.69.032106· OSTI ID:20640819

Shunlong, Luo ^[1]; Qiang, Zhang ^[2]

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1. Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, 100080 Beijing (China)
2. Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong (China)

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.

• OSTI ID: 20640819
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 3 Vol. 69; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
AFFINITY
COMPARATIVE EVALUATIONS
CORRELATIONS
DENSITY
DISTANCE
ENERGY LEVELS
INFORMATION
INFORMATION THEORY
PROBABILITY
QUANTUM MECHANICS
SPACE