Quantum mutual information along unitary orbits

Sania Jevtic, David Jennings, and Terry Rudolph
Phys. Rev. A 85, 052121 – Published 23 May 2012

Abstract

Motivated by thermodynamic considerations, we analyze the variation of the quantum mutual information on a unitary orbit of a bipartite system's state with and without global constraints such as energy conservation. We solve the full optimization problem for the smallest system of two qubits and explore thoroughly the effect of unitary operations on the space of reduced-state spectra. We then provide applications of these ideas to physical processes within closed quantum systems such as a generalized collision model approach to thermal equilibrium and a global Maxwell demon playing tricks on local observers. For higher dimensions, the maximization of correlations is relatively straightforward for equal-sized subsystems, however their minimization displays nontrivial structures. We characterize a set of separable states in which the minimally correlated state resides: a collection of classically correlated states admitting a particular “Young tableau” form. Furthermore, a partial order exists on this set with respect to individual marginal entropies, and the presence of a “see-saw effect” for these entropies forces a finer analysis to determine the optimal tableau.

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  • Received 2 February 2012

DOI:https://doi.org/10.1103/PhysRevA.85.052121

©2012 American Physical Society

Authors & Affiliations

Sania Jevtic, David Jennings, and Terry Rudolph

  • Controlled Quantum Dynamics Theory, Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom

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Issue

Vol. 85, Iss. 5 — May 2012

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