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DOI: 10.4230/LIPIcs.TQC.2013.178

On the Query Complexity of Perfect Gate Discrimination

Authors: Giulio Chiribella, Giacomo Mauro D'Ariano, and Martin Roetteler

Published in: LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

Abstract

We investigate the problem of finding the minimum number of queries needed to perfectly identify an unknown quantum gate within a finite set of alternatives, considering both deterministic strategies. For unambiguous gate discrimination, where errors are not tolerated but inconclusive outcomes are allowed, we prove that parallel strategies are sufficient to identify the unknown gate with minimum number of queries and we use this fact to provide upper and lower bounds on the query complexity. In addition, we introduce the notion of generalized $t$-designs, which includes unitary t-designs and group representations as special cases. For gates forming a generalized $t$-design we prove that there is no difference between perfect probabilistic and perfect deterministic gate discrimination. Hence, evaluating of the query complexity of perfect discrimination is reduced to the easier problem of evaluating the query complexity of unambiguous discrimination.

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Giulio Chiribella, Giacomo Mauro D'Ariano, and Martin Roetteler. On the Query Complexity of Perfect Gate Discrimination. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 178-191, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{chiribella_et_al:LIPIcs.TQC.2013.178,
  author =	{Chiribella, Giulio and D'Ariano, Giacomo Mauro and Roetteler, Martin},
  title =	{{On the Query Complexity of Perfect Gate Discrimination}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{178--191},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-55-2},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{22},
  editor =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.178},
  URN =		{urn:nbn:de:0030-drops-43133},
  doi =		{10.4230/LIPIcs.TQC.2013.178},
  annote =	{Keywords: quantum gate identification, unambiguous discrimination, minimum error discrimination, query complexity}
}

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DOI: 10.4230/LIPIcs.TQC.2013.220

Is Global Asymptotic Cloning State Estimation?

Authors: Yuxiang Yang and Giulio Chiribella

Published in: LIPIcs, Volume 22, 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)

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.

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Yuxiang Yang and Giulio Chiribella. Is Global Asymptotic Cloning State Estimation?. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 220-234, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{yang_et_al:LIPIcs.TQC.2013.220,
  author =	{Yang, Yuxiang and Chiribella, Giulio},
  title =	{{Is Global Asymptotic Cloning State Estimation?}},
  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 =	{Severini, Simone and Brandao, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.220},
  URN =		{urn:nbn:de:0030-drops-43100},
  doi =		{10.4230/LIPIcs.TQC.2013.220},
  annote =	{Keywords: quantum cloning, quantum estimation}
}

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Documents authored by Chiribella, Giulio

On the Query Complexity of Perfect Gate Discrimination

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Is Global Asymptotic Cloning State Estimation?

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