Checking 2xM quantum separability via semidefinite programming

Journal Article · Wed Jan 01 00:00:00 EST 2003 · Physical Review. A

DOI:https://doi.org/10.1103/PhysRevA.67.010303· OSTI ID:20634056

Woerdeman, Hugo J ^[1]

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1. Department of Mathematics, The College of William and Mary, Williamsburg, Virginia 23187-8795 (United States)

In this paper, we propose a sequence of tests which give a definitive test for checking 2xM separability. The test is definitive in the sense that each test corresponds to checking membership in a cone, and that the closure of the union of all these cones consists exactly of all 2xM separable states. Membership in each single cone may be checked via semidefinite programming, and is thus a tractable problem. This sequential test comes about by considering the dual problem, the characterization of all positive maps acting C{sup 2x2}{yields}C{sup MxM}. The latter in turn is solved by characterizing all positive quadratic matrix polynomials in a complex variable.

• OSTI ID: 20634056
• Journal Information: Physical Review. A, Vol. 67, Issue 1; Other Information: DOI: 10.1103/PhysRevA.67.010303; (c) 2003 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

74 ATOMIC AND MOLECULAR PHYSICS
CONES
CORRELATIONS
DATA TRANSMISSION
ENERGY LEVELS
INFORMATION THEORY
MATRICES
POLYNOMIALS
QUANTUM MECHANICS