## 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

### Keywords:

preservers; quantum states; density operators; relative entropy

Zbl 1153.81407
Full Text:

### 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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