Details
| Original language | English |
|---|---|
| Pages (from-to) | 1777-1788 |
| Number of pages | 12 |
| Journal | Annales Henri Poincare |
| Volume | 18 |
| Issue number | 5 |
| Publication status | Published - 1 May 2017 |
Abstract
We prove that the quantum relative entropy decreases monotonically under the application of any positive trace-preserving linear map, for underlying separable Hilbert spaces. This answers in the affirmative a natural question that has been open for a long time, as monotonicity had previously only been shown to hold under additional assumptions, such as complete positivity or Schwarz-positivity of the adjoint map. The first step in our proof is to show monotonicity of the sandwiched Renyi divergences under positive trace-preserving maps, extending a proof of the data processing inequality by Beigi (J Math Phys 54:122202, 2013) that is based on complex interpolation techniques. Our result calls into question several measures of non-Markovianity that have been proposed, as these would assess all positive trace-preserving time evolutions as Markovian.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Nuclear and High Energy Physics
- Mathematics(all)
- Mathematical Physics
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In: Annales Henri Poincare, Vol. 18, No. 5, 01.05.2017, p. 1777-1788.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Monotonicity of the Quantum Relative Entropy Under Positive Maps
AU - Müller-Hermes, Alexander
AU - Reeb, David
N1 - Publisher Copyright: © 2017, Springer International Publishing.
PY - 2017/5/1
Y1 - 2017/5/1
N2 - We prove that the quantum relative entropy decreases monotonically under the application of any positive trace-preserving linear map, for underlying separable Hilbert spaces. This answers in the affirmative a natural question that has been open for a long time, as monotonicity had previously only been shown to hold under additional assumptions, such as complete positivity or Schwarz-positivity of the adjoint map. The first step in our proof is to show monotonicity of the sandwiched Renyi divergences under positive trace-preserving maps, extending a proof of the data processing inequality by Beigi (J Math Phys 54:122202, 2013) that is based on complex interpolation techniques. Our result calls into question several measures of non-Markovianity that have been proposed, as these would assess all positive trace-preserving time evolutions as Markovian.
AB - We prove that the quantum relative entropy decreases monotonically under the application of any positive trace-preserving linear map, for underlying separable Hilbert spaces. This answers in the affirmative a natural question that has been open for a long time, as monotonicity had previously only been shown to hold under additional assumptions, such as complete positivity or Schwarz-positivity of the adjoint map. The first step in our proof is to show monotonicity of the sandwiched Renyi divergences under positive trace-preserving maps, extending a proof of the data processing inequality by Beigi (J Math Phys 54:122202, 2013) that is based on complex interpolation techniques. Our result calls into question several measures of non-Markovianity that have been proposed, as these would assess all positive trace-preserving time evolutions as Markovian.
UR - http://www.scopus.com/inward/record.url?scp=85010756775&partnerID=8YFLogxK
U2 - 10.1007/s00023-017-0550-9
DO - 10.1007/s00023-017-0550-9
M3 - Article
AN - SCOPUS:85010756775
VL - 18
SP - 1777
EP - 1788
JO - Annales Henri Poincare
JF - Annales Henri Poincare
SN - 1424-0637
IS - 5
ER -