Benjamin Schumacher

Concentrating partial entanglement by local operations

If two separated observers are supplied with entanglement, in the form of n pairs of particles in identical partly entangled pure states, one member of each pair being given to each observer, they can, by local actions of each observer, concentrate this entanglement into a smaller number of maximally entangled pairs of particles, for example, Einstein-Podolsky-Rosen singlets, similarly shared between the two observers. The concentration process asymptotically conserves entropy of entanglement---the von Neumann entropy of the partial density matrix seen by either observer---with the yield of singlets approaching, for large n, the base-2 entropy of entanglement of the initial partly entangled pure state. Conversely, 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. \textcopyright{} 1996 The American Physical Society.

Purification of noisy entanglement and faithful teleportation via noisy channels

Two separated observers, by applying local operations to a supply of not-too-impure entangled states ({\em e.g.} singlets shared through a noisy channel), can prepare a smaller number of entangled pairs of arbitrarily high purity ({\em 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 transfrom 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

Noncommuting Mixed States Cannot Be Broadcast

D(M)

QUANTUM DATA PROCESSING AND ERROR CORRECTION

of pure singlets (

A New Proof of the Quantum Noiseless Coding Theorem

\ket{\Psi^-}

Information transmission through a noisy quantum channel

) distillable from mixed states

Approximate Quantum Error Correction

M

Quantum Privacy and Quantum Coherence

, showing

Quantum mutual information and the one-time pad

D(M)>0

General fidelity limit for quantum channels

if