Article abstract

Nature Physics 4, 873 - 877 (2008)
Published online: 12 October 2008 | doi:10.1038/nphys1100

Subject Categories: Quantum physics | Statistical physics, thermodynamics and nonlinear dynamics

Entanglement theory and the second law of thermodynamics

Fernando G. S. L. Brandão1,2 & Martin B. Plenio1,2

Entanglement is central both to the foundations of quantum theory and, as a novel resource, to quantum information science. The theory of entanglement establishes basic laws that govern its manipulation, in particular the non-increase of entanglement under local operations on the constituent particles. Such laws aim to draw from them formal analogies to the second law of thermodynamics; however, whereas in the second law the entropy uniquely determines whether a state is adiabatically accessible from another, the manipulation of entanglement under local operations exhibits a fundamental irreversibility, which prevents the existence of such an order. Here, we show that a reversible theory of entanglement and a rigorous relationship with thermodynamics may be established when considering all non-entangling transformations. The role of the entropy in the second law is taken by the asymptotic relative entropy of entanglement in the basic law of entanglement. We show the usefulness of this approach to general resource theories and to quantum information theory.

  1. QOLS, Blackett Lab, Imperial College London, Prince Consort Road, London SW7 2BW, UK
  2. Institute for Mathematical Sciences, Imperial College London, 53 Exhibition Road, London SW7 2PG, UK

Correspondence to: Fernando G. S. L. Brandão1,2 e-mail:


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