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Maps on states preserving the relative entropy. II. (English) Zbl 1187.47030

Summary: Let H be a finite-dimensional complex Hilbert space. The aim of this paper is to prove that every transformation on the space of all density operators on H which preserves the relative entropy is implemented by either a unitary or an antiunitary operator on H.

[For Part I, see J. Math. Phys. 49, No. 3, 032114 (2008; Zbl 1153.81407).]

MSC:
47B49Transformers, preservers (operators on spaces of operators)
47N50Applications of operator theory in quantum physics
References:
[1]Bengtsson, I.; &zdot, K.; Yczkowski: Geometry of quantum states: an introduction to quantum entanglement, (2006)
[2]Faure, C. A.: An elementary proof of the fundamental theorem of projective geometry, Geom. dedicata. 90, 145-151 (2002) · Zbl 0996.51001 · doi:10.1023/A:1014933313332
[3]Molnár, L.: Selected preserver problems on algebraic structures of linear operators and on function spaces, Lecture notes in mathematics 1895 (2007)
[4]Molnár, L.: Maps on states preserving the relative entropy, J. math. Phys. 49, 032114 (2008) · Zbl 1153.81407 · doi:10.1063/1.2898693