Abstract
In a certain sense we generalize the recently introduced and extensively studied notion called quantum Rényi divergence (also called ”sandwiched Rényi relative entropy”) and describe the structures of corresponding symmetries. More precisely, we characterize all transformations on the set of density operators which leave our new general quantity invariant and also determine the structure of all bijective transformations on the cone of positive definite operators which preserve the quantum Rényi divergence.
| Original language | English |
|---|---|
| Pages (from-to) | 88-107 |
| Number of pages | 20 |
| Journal | Periodica Mathematica Hungarica |
| Volume | 74 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Mar 1 2017 |
Fingerprint
Keywords
- Density operators
- Positive definite operators
- Preservers
- Quantum Rényi divergence
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Transformations on density operators and on positive definite operators preserving the quantum Rényi divergence. / Gaál, Marcell; Molnár, L.
In: Periodica Mathematica Hungarica, Vol. 74, No. 1, 01.03.2017, p. 88-107.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Transformations on density operators and on positive definite operators preserving the quantum Rényi divergence
AU - Gaál, Marcell
AU - Molnár, L.
PY - 2017/3/1
Y1 - 2017/3/1
N2 - In a certain sense we generalize the recently introduced and extensively studied notion called quantum Rényi divergence (also called ”sandwiched Rényi relative entropy”) and describe the structures of corresponding symmetries. More precisely, we characterize all transformations on the set of density operators which leave our new general quantity invariant and also determine the structure of all bijective transformations on the cone of positive definite operators which preserve the quantum Rényi divergence.
AB - In a certain sense we generalize the recently introduced and extensively studied notion called quantum Rényi divergence (also called ”sandwiched Rényi relative entropy”) and describe the structures of corresponding symmetries. More precisely, we characterize all transformations on the set of density operators which leave our new general quantity invariant and also determine the structure of all bijective transformations on the cone of positive definite operators which preserve the quantum Rényi divergence.
KW - Density operators
KW - Positive definite operators
KW - Preservers
KW - Quantum Rényi divergence
UR - http://www.scopus.com/inward/record.url?scp=84994692125&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84994692125&partnerID=8YFLogxK
U2 - 10.1007/s10998-016-0174-8
DO - 10.1007/s10998-016-0174-8
M3 - Article
AN - SCOPUS:84994692125
VL - 74
SP - 88
EP - 107
JO - Periodica Mathematica Hungarica
JF - Periodica Mathematica Hungarica
SN - 0031-5303
IS - 1
ER -