A Reversible Theory of Entanglement and its Relation to the Second Law

@article{Brando2010ART,
  title={A Reversible Theory of Entanglement and its Relation to the Second Law},
  author={Fernando G. S. L. Brand{\~a}o and Martin Bodo Plenio},
  journal={Communications in Mathematical Physics},
  year={2010},
  volume={295},
  pages={829-851}
}
We consider the manipulation of multipartite entangled states in the limit of many copies under quantum operations that asymptotically cannot generate entanglement. In stark contrast to the manipulation of entanglement under local operations and classical communication, the entanglement shared by two or more parties can be reversibly interconverted in this setting. The unique entanglement measure is identified as the regularized relative entropy of entanglement, which is shown to be equal to a… 
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References

SHOWING 1-10 OF 54 REFERENCES
Entanglement theory and the second law of thermodynamics
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
Quantifying entanglement with witness operators
TLDR
An infinite family of new entanglement quantifiers is introduced, having as its limits the best separable approximation measure and the generalized robustness, and provides sharper bounds to d_(min) and E_D than the negativity in most the states.
Entanglement and thermodynamical analogies
TLDR
A scheme of the search of representative state for given entanglement which can be viewed as an analogue of the Jaynes maximum entropy principle is proposed and proposes a concept of local orthogonality of ensembles which leads to the mixed states with distillableEntanglement equal to entanglements of formation.
Robustness of entanglement
In the quest to completely describe entanglement in the general case of a finite number of parties sharing a physical system of finite-dimensional Hilbert space an entanglement magnitude is
Entanglement measures and purification procedures
TLDR
It is argued that the statistical basis of the measure of entanglement determines an upper bound to the number of singlets that can be obtained by any purification procedure.
Entanglement purification via separable superoperators
TLDR
This work uses the fact that every EPP is a separable superoperator to give a new upper bound on the rate of EPPs on Bell- diagonal states, and thus on the capacity of Bell-diagonal channels.
Max- Relative Entropy of Entanglement, alias Log Robustness
Properties of the max-relative entropy of entanglement, defined in Ref. 10, are investigated, and its significance as an upper bound to the one-shot rate for perfect entanglement dilution, under a
Teleportation, entanglement and thermodynamics in the quantum world
Quantum mechanics has many counter-intuitive consequences which contradict our intuition which is based on classical physics. Here we discuss a special aspect of quantum mechanics, namely the
Concentrating partial entanglement by local operations.
TLDR
Any pure or mixed entangled state of two systems can be produced by two classically communicating separated observers, drawing on a supply of singlets as their sole source of entanglement.
Entanglement measures under symmetry
We show how to simplify the computation of the entanglement of formation and the relative entropy of entanglement for states, which are invariant under a group of local symmetries. For several
...
...