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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:
 47B49 Transformers, preservers (operators on spaces of operators) 47N50 Applications of operator theory in quantum physics
##### Keywords:
preservers; quantum states; density operators; relative entropy
Full Text:
##### 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) · Zbl 1119.47001 [4] Molnár, L.: Maps on states preserving the relative entropy, J. math. Phys. 49, 032114 (2008) · Zbl 1153.81407 · doi:10.1063/1.2898693