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DOI: 10.4230/LIPIcs.TQC.2013.220
URN: urn:nbn:de:0030-drops-43100
URL: http://drops.dagstuhl.de/opus/volltexte/2013/4310/
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Yang, Yuxiang ; Chiribella, Giulio

Is Global Asymptotic Cloning State Estimation?

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Abstract

We investigate the asymptotic relationship between quantum cloning and quantum estimation from the global point of view where all the copies produced by the cloner are considered jointly. For an N-to-M cloner, we consider the overall fidelity between the state of the M output systems and the state of M ideal copies, and we ask whether the optimal fidelity is attained by a measure and-prepare protocol in the limit M -> \infty. In order to gain intuition into the general problem, we analyze two concrete examples: i) cloning qubit states on the equator of the Bloch sphere and ii) cloning two-qubit maximally entangled states. In the first case, we show that the optimal measure-and-prepare fidelity converges to the fidelity of the optimal cloner in the limit M -> \infty. In the second case, we restrict our attention to economical covariant cloners, and again, we exhibit a measure-and-prepare protocol that achieves asymptotically the optimal fidelity. Quite counterintuitively, in both cases the optimal states that have to be prepared in order to maximize the overall fidelity are not product states corresponding to M identical copies, but instead suitable M-partite entangled states.

BibTeX - Entry

@InProceedings{yang_et_al:LIPIcs:2013:4310,
  author =	{Yuxiang Yang and Giulio Chiribella},
  title =	{{Is Global Asymptotic Cloning State Estimationl}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{220--234},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Simone Severini and Fernando Brandao},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2013/4310},
  URN =		{urn:nbn:de:0030-drops-43100},
  doi =		{10.4230/LIPIcs.TQC.2013.220},
  annote =	{Keywords: quantum cloning, quantum estimation}
}

Keywords: quantum cloning, quantum estimation
Seminar: 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)
Issue Date: 2013
Date of publication: 05.11.2013


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