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
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
More filters
Journal ArticleDOI
Entanglement purification for high-dimensional multipartite systems
TL;DR: In this article, an entanglement purification protocol for high-dimensional multipartite systems is proposed, which selects a sub-ensemble in a pure generalized Greenberger-Horne-Zeilinger (GHZ) state by detecting the noise which contaminated the initial pure ensemble when the systems passed through a noisy environment.
Book ChapterDOI
Approximate quantum error-correcting codes and secret sharing schemes
TL;DR: In this paper, it was shown that error-tolerant secret sharing schemes can be constructed in the quantum model with fidelity exponentially close to 1, at the price of increasing the size of the register.
Journal ArticleDOI
Entanglement and secret-key-agreement capacities of bipartite quantum interactions and read-only memory devices
TL;DR: This work derives both lower and upper bounds on the private reading capacities of a wiretap memory cell, and extends these results to determine achievable rates for the generation of entanglement between two distant parties who have coherent access to a controlled point-to-point channel.
Journal ArticleDOI
Dynamical Entanglement
Gilad Gour,Carlo Maria Scandolo +1 more
TL;DR: This work works with the partial transpose of a superchannel, and shows that a version of it, the max-logarithmic negativity, represents the exact asymptotic dynamical entanglement cost.
Journal ArticleDOI
Entanglement Sharing in Real-Vector-Space Quantum Theory
TL;DR: In this article, it was shown that the limitation on the sharing of entanglement is lost when one replaces the usual complex vector space of quantum states with a real vector space, and the difference between the two theories is extreme: in the real-vector-space theory, there exist states of arbitrarily many binary objects, called rebits, in which every rebit in the system is maximally entangled with each of the other rebits.
References
More filters
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.