Heisenberg uncertainty relation for mixed states

Journal Article · Sat Oct 15 04:00:00 EDT 2005 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.72.042110· OSTI ID:20718690

Shunlong, Luo ^[1]

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1. Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, 100080 Beijing (China)

The Heisenberg uncertainty relation sets a fundamental limit for quantum measurement of incompatible observables. Its standard form derived by Weyl and Robertson is of purely quantum nature when the state is pure. However, for mixed states, because the variance involving a mixed state is a hybrid of classical and quantum uncertainty, the conventional uncertainty relation is of a 'mixed' flavor. It is desirable to seek some decomposition of variance into classical and quantum parts and to cast the Heisenberg uncertainty relation for mixed states in a more quantum form. By use of the skew information introduced by Wigner and Yanase in 1963, we make such an attempt and establish a different uncertainty relation which is stronger than the conventional one.

• OSTI ID: 20718690
• Journal Information: Physical Review. A, Journal Name: Physical Review. A Journal Issue: 4 Vol. 72; ISSN 1050-2947; ISSN PLRAAN
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
ENERGY LEVELS
MIXED STATE
QUANTUM MECHANICS
UNCERTAINTY PRINCIPLE