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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 (linear operators on spaces of linear operators)
47N50 Applications of operator theory in the physical sciences

Citations:

Zbl 1153.81407
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References:

[1] Bengtsson, I.; Życzkowski, K., Geometry of quantum states: an introduction to quantum entanglement, (2006), Cambridge University Press Cambridge · Zbl 1146.81004
[2] Faure, C.A., An elementary proof of the fundamental theorem of projective geometry, Geom. dedicata., 90, 145-151, (2002) · Zbl 0996.51001
[3] Molnár, L., Selected preserver problems on algebraic structures of linear operators and on function spaces, Lecture notes in mathematics, vol. 1895, (2007), Springer, p. 236
[4] Molnár, L., Maps on states preserving the relative entropy, J. math. phys., 49, 032114, (2008) · Zbl 1153.81407
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