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arXiv:quant-ph/0109051

A more efficient variant of the Oxford protocol

NASSER METWALLY

Published Sep 12, 2001• 1 citation
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Abstract

An alternative presentation of the Oxford purification protocol is obtained by using dynamical variables. I suggest to introduce the degree of separability as a purification parameter, where the purified state has a smaller degree of separability than the initial one. An improved version of the Oxford protocol is described, in which local unitary transformations optimize each step.

DOI
10.48550/arxiv.quant-ph/0109051

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An alternative presentation of the Oxford purification protocol is obtained by using dynamical variables. I suggest to introduce the degree of separability as a purification parameter, where the purified state has a smaller degree of separability than the initial one. An improved version of the Oxford protocol is described, in which local unitary transformations optimize each step.
Purification of mixed states in Quantum Mechanics, by which we mean the transformation into pure states, has been viewed as an {\it Operation} in the sense of Kraus et al and explicit {\it Kraus Operators} \cite{kra1,kra2,kra3} have been constructed for two seperate purification protocols. The first one, initially due to Schrodinger \cite{sch} and subsequently elaborated by Sudarshan et al \cite{sudar}, is based on the {\it preservation of probabilities}. We have constructed a second protocol here based on {\it optimization of fidelities}. Both purification protocols have been implemented on a single qubit in an attempt to improve the fidelity of the purified post measurement state of the qubit with the initial pure state. We have considered both {\it complete} and {\it partial} measurements and have established bounds and inequalities for various fidelities. We show that our purification protocol leads to better state reconstruction, most explicitly so, when partial measurements are made.
One of the fundamental concepts of quantum information theory is that of entanglement purification; that is, the transformation of a partially entangled state into a smaller-dimensional, more completely entangled state. Of particular interest are protocols for entanglement purification (EPPs) that alternate purely local operations with one- or two-way classical communication. In the present work, we consider a more general, but simpler, class of transformations, called separable superoperators. Since every EPP is a separable superoperator, bounds on separable superoperators apply as well to EPPs; we use this fact to give a new upper bound on the rate of EPPs on Bell-diagonal states, and thus on the capacity of Bell-diagonal channels.