Details

Autor(en) / Beteiligte

• Müller-Hermes, Alexander
• Reeb, David

Titel

Monotonicity of the Quantum Relative Entropy Under Positive Maps

Ist Teil von

• Annales Henri Poincaré, 2017-05, Vol.18 (5), p.1777-1788

Ort / Verlag

Cham: Springer International Publishing

Erscheinungsjahr

2017

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• 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.