Upper bounds on mixing rates

Elliott H. Lieb, Anna Vershynina

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


We prove upper bounds on the rate, called "mixing rate", at which the von Neumann entropy of the expected density operator of a given ensemble of states changes under non-local unitary evolution. For an ensemble consisting of two states, with probabil- ities of p and 1 - p, we prove that the mixing rate is bounded above by for any Hamiltonian of norm 1. For a general ensemble of states with probabilities dis- tributed according to a random variable X and individually evolving according to any set of bounded Hamiltonians, we conjecture that the mixing rate is bounded above by a Shannon entropy of a random variable X. For this general case we prove an upper bound that is independent of the dimension of the Hilbert space on which states in the ensemble act.

Original languageEnglish (US)
Pages (from-to)986-994
Number of pages9
JournalQuantum Information and Computation
Issue number11-12
StatePublished - Jul 23 2013

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Statistical and Nonlinear Physics
  • Nuclear and High Energy Physics
  • Mathematical Physics
  • General Physics and Astronomy
  • Computational Theory and Mathematics


  • Convex
  • Entanglement rate
  • Mixing rate
  • Von Neumann entropy


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