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
Citations
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Entanglement, quantum entropy and mutual information
TL;DR: The operational structure of quantum couplings and entanglements is studied and classified for semi–finite von Neumann algebras and it is shown that the classical–quantum correspondences can be treated as diagonal semi–classical couplings, and the entanglement, characterized by truly quantum (q–) coupling, can be regarded as truly quantum encodings.
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Lower bound for electron spin entanglement from beam splitter current correlations.
Guido Burkard,Daniel Loss +1 more
TL;DR: A lower bound for the entanglement of formation of pairs of electron spins injected into a mesoscopic conductor is determined in terms of experimentally accessible quantities, the zero-frequency current correlators after transmission through an electronic beam splitter and can be used to gain information about the entangling from experiment.
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A note on entanglement of formation and generalized concurrence
TL;DR: In this paper, a generalized concurrence for a class of high-dimensional quantum pure states such that the entanglement of formation is a monotonically increasing convex function of the concurrence is discussed.
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Constructing Smaller Pauli Twirling Sets for Arbitrary Error Channels.
Zhenyu Cai,Simon C. Benjamin +1 more
TL;DR: This article provides a theoretical background for Pauli twirling and a way to construct a twirling gate set with a number of members comparable to the size of the Pauli basis of the given error channel, usually much smaller than the full set of Pauli gates.
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Heralded entanglement concentration for photon systems with linear-optical elements
TL;DR: In this paper, two nonlocal entanglement concentration protocols (ECPs) were proposed to distill a subset of N-photon systems in a Greenberger-Horne-Zeilinger (GHZ) state or a W state from a set of photon systems in partially entangled GHZ-like pure states or a less-entangled W-like state with known parameter.
References
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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.
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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.