Purification of Noisy Entanglement and Faithful Teleportation via Noisy Channels
Charles H. Bennett,Gilles Brassard,Sandu Popescu,Benjamin Schumacher,John A. Smolin,William K. Wootters +5 more
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TLDR
Upper and lower bounds on the yield of pure singlets ($\ket{\Psi^-}$) distillable from mixed states $M$ are given, showing $D(M)>0$ if $\bra{Psi-}M\ket-}>\half$.Abstract:
Two separated observers, by applying local operations to a supply of not-too-impure entangled states (e.g., singlets shared through a noisy channel), can prepare a smaller number of entangled pairs of arbitrarily high purity (e.g., near-perfect singlets). These can then be used to faithfully teleport unknown quantum states from one observer to the other, thereby achieving faithful transmission of quantum information through a noisy channel. We give upper and lower bounds on the yield $D\left(M\right)$ of pure singlets $(|{\ensuremath{\Psi}}^{\ensuremath{-}}〉)$ distillable from mixed states $M$, showing $D\left(M\right)g0$ if $〈{\ensuremath{\Psi}}^{\ensuremath{-}}|M|{\ensuremath{\Psi}}^{\ensuremath{-}}〉g\frac{1}{2}$.read more
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Low rank positive partial transpose states and their relation to product vectors
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Bounds on mixedness and entanglement of quantum teleportation resources
TL;DR: In this article, rank dependent upper bounds on Von Neumann entropy and linear entropy beyond which the states of respective ranks cease to be useful for quantum teleportation are derived analytically for a general d × d bipartite system.
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Entanglement purification via controlled–controlled-NOT operations
TL;DR: In this article, an entanglement purification protocol based on controlled-controlled-NOT operations and Bell state measurements was proposed, which is more efficient than the standard protocol of Bennett et al.
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Optimal verification of general bipartite pure states
TL;DR: In this paper, the authors considered the task of verifying entangled states using one-way and two-way classical communication and characterized the optimal strategies via convex optimization, which can be constructed for any bipartite pure state.
References
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Journal ArticleDOI
Concentrating partial entanglement by local operations
TL;DR: 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.
Journal ArticleDOI
Generalized privacy amplification
TL;DR: This paper provides a general treatment of privacy amplification by public discussion, a concept introduced by Bennett, Brassard, and Robert for a special scenario, and yields results on wiretap and broadcast channels for a considerably strengthened definition of secrecy capacity.