The automorphism group of separable states in quantum information theory

Journal Article · Fri Apr 15 00:00:00 EDT 2011 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.3578015· OSTI ID:21501303

Friedland, Shmuel ^[1]; Li, Chi-Kwong ^[2]; Poon, Yiu-Tung ^[3]; Sze, Nung-Sing ^[4]

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1. Department of Mathematics, Statistics and Computer Science, University of Illinois at Chicago, Chicago, Illinois 60607-7045 (United States)
2. Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795 (United States)
3. Department of Mathematics, Iowa State University, Ames, Iowa 50011 (United States)
4. Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Kowloon (Hong Kong)

We show that the linear group of automorphism of Hermitian matrices which preserves the set of separable states is generated by natural automorphisms: change of an orthonormal basis in each tensor factor, partial transpose in each tensor factor, and interchanging two tensor factors of the same dimension. We apply our results to the preservers of the product numerical range.

• OSTI ID: 21501303
• Journal Information: Journal of Mathematical Physics, Vol. 52, Issue 4; Other Information: DOI: 10.1063/1.3578015; (c) 2011 American Institute of Physics; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
GROUP THEORY
HERMITIAN MATRIX
INFORMATION THEORY
QUANTUM ENTANGLEMENT
QUANTUM INFORMATION
QUANTUM MECHANICS
TENSORS
INFORMATION
MATHEMATICS
MATRICES
MECHANICS