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The Resource Theory of Steering

Authors: Rodrigo Gallego and Leandro Aolita

Published in: LIPIcs, Volume 44, 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)


Abstract
We present an operational framework for Einstein-Podolsky-Rosen steering as a physical resource. To begin with, we characterize the set of steering non-increasing operations (SNIOs) – i.e., those that do not create steering– on arbitrary-dimensional bipartite systems composed of a quantum subsystem and a black-box device. Next, we introduce the notion of convex steering monotones as the fundamental axiomatic quantifiers of steering. As a convenient example thereof, we present the relative entropy of steering. In addition, we prove that two previously proposed quantifiers, the steerable weight and the robustness of steering, are also convex steering monotones. To end up with, for minimal-dimensional systems, we establish, on the one hand, necessary and sufficient conditions for pure-state steering conversions under stochastic SNIOs and prove, on the other hand, the non-existence of steering bits, i.e., measure-independent maximally steerable states from which all states can be obtained by means of the free operations. Our findings reveal unexpected aspects of steering and lay foundations for further resource-theory approaches, with potential implications in Bell non-locality.

Cite as

Rodrigo Gallego and Leandro Aolita. The Resource Theory of Steering. In 10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 44, pp. 27-38, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)


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@InProceedings{gallego_et_al:LIPIcs.TQC.2015.27,
  author =	{Gallego, Rodrigo and Aolita, Leandro},
  title =	{{The Resource Theory of Steering}},
  booktitle =	{10th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2015)},
  pages =	{27--38},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-96-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{44},
  editor =	{Beigi, Salman and K\"{o}nig, Robert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2015.27},
  URN =		{urn:nbn:de:0030-drops-55461},
  doi =		{10.4230/LIPIcs.TQC.2015.27},
  annote =	{Keywords: Entanglement, EPR-steering, nonlocality, resource theories}
}
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