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An analysis of completelypositive tracepreserving maps on 2x2 matrices
"... We give a useful new characterization of the set of all completely positive, tracepreserving maps Φ: M2 → M2 from which one can easily check any tracepreserving map for complete positivity. We also determine explicitly all extreme points of this set, and give a useful parameterization after reduct ..."
Abstract

Cited by 43 (5 self)
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We give a useful new characterization of the set of all completely positive, tracepreserving maps Φ: M2 → M2 from which one can easily check any tracepreserving map for complete positivity. We also determine explicitly all extreme points of this set, and give a useful parameterization after reduction to a certain canonical form. This allows a detailed examination of an important class of nonunital extreme points which can be characterized as having exactly two images on the Bloch sphere. We also discuss a number of related issues about the images and the geometry of the set of stochastic maps, and show that any stochastic map on M2 can be written as a convex combination of two “generalized ” extreme points.
A Graphic Representation of States for Quantum Copying Machines
, 2006
"... The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear and detailed visualization of quantum information’s flow du ..."
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Cited by 3 (3 self)
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The aim of this paper is to introduce a new graphic representation of quantum states by means of a specific application: the analysis of two models of quantum copying machines. The graphic representation by diagrams of states offers a clear and detailed visualization of quantum information’s flow during the unitary evolution of not too complex systems. The diagrams of states are exponentially more complex in respect to the standard representation and this clearly illustrates the discrepancy of computational power between quantum and classical systems. After a brief introductive exposure of the general theory, we present a constructive procedure to illustrate the new representation by means of concrete examples. Elementary diagrams of states for singlequbit and twoqubit systems and a simple scheme to represent entangled states are presented. Quantum copying machines as imperfect cloners of quantum states are introduced and the quantum copying machines of Griffiths and Niu and of Buˇzek and Hillery are analyzed, determining quantum circuits of easier interpretation. The method has indeed shown itself to be extremely successful for the representation of the involved quantum operations and it has allowed to point out the characteristic aspects of the quantum computations examined. 1
unknown title
, 2005
"... Channel kets, entangled states, and the location of quantum information ..."
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unknown title
, 2004
"... Channel kets, entangled states, and the location of quantum information ..."
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unknown title
, 2004
"... Channel kets, entangled states, and the location of quantum information ..."
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Publisher SPIE Version Final published version
, 2014
"... individual attack on BB84 quantum key ..."