Information-theoretic limitations on approximate quantum cloning and broadcasting

Information-theoretic limitations on approximate quantum cloning and broadcasting We prove quantitative limitations on any approximate simultaneous cloning or broadcasting of mixed states. The results are based on information-theoretic (entropic) considerations and generalize the well-known no-cloning and no-broadcasting theorems. We also observe and exploit the fact that the universal cloning machine on the symmetric subspace of n qudits and symmetrized partial trace channels are dual to each other. This duality manifests itself both in the algebraic sense of adjointness of quantum channels and in the operational sense that a universal cloning machine can be used as an approximate recovery channel for a symmetrized partial trace channel and vice versa. The duality extends to give control of the performance of generalized universal quantum cloning machines (UQCMs) on subspaces more general than the symmetric subspace. This gives a way to quantify the usefulness of a priori information in the context of cloning. For example, we can control the performance of an antisymmetric analog of the UQCM in recovering from the loss of n−k fermionic particles. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review A American Physical Society (APS)

Information-theoretic limitations on approximate quantum cloning and broadcasting

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Information-theoretic limitations on approximate quantum cloning and broadcasting

Abstract

We prove quantitative limitations on any approximate simultaneous cloning or broadcasting of mixed states. The results are based on information-theoretic (entropic) considerations and generalize the well-known no-cloning and no-broadcasting theorems. We also observe and exploit the fact that the universal cloning machine on the symmetric subspace of n qudits and symmetrized partial trace channels are dual to each other. This duality manifests itself both in the algebraic sense of adjointness of quantum channels and in the operational sense that a universal cloning machine can be used as an approximate recovery channel for a symmetrized partial trace channel and vice versa. The duality extends to give control of the performance of generalized universal quantum cloning machines (UQCMs) on subspaces more general than the symmetric subspace. This gives a way to quantify the usefulness of a priori information in the context of cloning. For example, we can control the performance of an antisymmetric analog of the UQCM in recovering from the loss of n−k fermionic particles.
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Publisher
American Physical Society (APS)
Copyright
Copyright © ©2017 American Physical Society
ISSN
1050-2947
eISSN
1094-1622
D.O.I.
10.1103/PhysRevA.96.012304
Publisher site
See Article on Publisher Site

Abstract

We prove quantitative limitations on any approximate simultaneous cloning or broadcasting of mixed states. The results are based on information-theoretic (entropic) considerations and generalize the well-known no-cloning and no-broadcasting theorems. We also observe and exploit the fact that the universal cloning machine on the symmetric subspace of n qudits and symmetrized partial trace channels are dual to each other. This duality manifests itself both in the algebraic sense of adjointness of quantum channels and in the operational sense that a universal cloning machine can be used as an approximate recovery channel for a symmetrized partial trace channel and vice versa. The duality extends to give control of the performance of generalized universal quantum cloning machines (UQCMs) on subspaces more general than the symmetric subspace. This gives a way to quantify the usefulness of a priori information in the context of cloning. For example, we can control the performance of an antisymmetric analog of the UQCM in recovering from the loss of n−k fermionic particles.

Journal

Physical Review AAmerican Physical Society (APS)

Published: Jul 5, 2017

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