On an extension problem for density matrices

Journal Article · Sat Jun 15 04:00:00 EDT 2013 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.4808218· OSTI ID:22163079

Carlen, Eric A. ^[1]; Lebowitz, Joel L. ^[2]; Lieb, Elliott H. ^[3]

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1. Department of Mathematics, Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019 (United States)
2. Departments of Mathematics and Physics, Hill Center, Rutgers University, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019 (United States)
3. Departments of Mathematics and Physics, Jadwin Hall, Princeton University, Washington Road, Princeton, New Jersey 08544-0001 (United States)

We investigate the problem of the existence of a density matrix {rho}{sub 123} on a Hilbert space H{sub 1} Circled-Times H{sub 2} Circled-Times H{sub 3} with given partial traces {rho}{sub 12}= Tr{sub 3} {rho}{sub 123} and {rho}{sub 23}= Tr{sub 1} {rho}{sub 123}. While we do not solve this problem completely, we offer partial results in the form of some necessary and some sufficient conditions on {rho}{sub 12} and {rho}{sub 23}. The quantum case differs markedly from the classical (commutative) case, where the obvious necessary compatibility condition suffices, namely, Tr{sub 1} {rho}{sub 12}= Tr{sub 3}{rho}{sub 23}.

• OSTI ID: 22163079
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 6 Vol. 54; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
COMPATIBILITY
DENSITY MATRIX
HILBERT SPACE