Quantum conditional relative entropy and quasi-factorization of the relative entropy

  title={Quantum conditional relative entropy and quasi-factorization of the relative entropy},
  author={{\'A}. Capel and A. Lucia and D. P{\'e}rez-Garc{\'i}a},
  • Á. Capel, A. Lucia, D. Pérez-García
  • Published 2018
  • Computer Science, Physics, Mathematics
  • ArXiv
  • The existence of a positive log-Sobolev constant implies a bound on the mixing time of a quantum dissipative evolution under the Markov approximation. For classical spin systems, such constant was proven to exist, under the assumption of a mixing condition in the Gibbs measure associated to their dynamics, via a quasi-factorization of the entropy in terms of the conditional entropy in some sub-σ-algebras. In this work we analyze analogous quasi-factorization results in the quantum case. For… CONTINUE READING

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