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Documents authored by Wilde, Mark M.

Document
Complete Volume
DOI: 10.4230/LIPIcs.TQC.2017
LIPIcs, Volume 73, TQC'17, Complete Volume

Authors: Mark M. Wilde

Published in: LIPIcs, Volume 73, 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)

Abstract
LIPIcs, Volume 73, TQC'17, Complete Volume
Cite as

12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 73, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@Proceedings{wilde:LIPIcs.TQC.2017,
  title =	{{LIPIcs, Volume 73, TQC'17, Complete Volume}},
  booktitle =	{12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-034-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{73},
  editor =	{Wilde, Mark M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2017},
  URN =		{urn:nbn:de:0030-drops-86203},
  doi =		{10.4230/LIPIcs.TQC.2017},
  annote =	{Keywords: Data Encryption, Coding and Information Theory, Theory of Computation}
}
Document
Front Matter
DOI: 10.4230/LIPIcs.TQC.2017.0
Front Matter, Table of Contents, Preface, Conference Organization

Authors: Mark M. Wilde

Published in: LIPIcs, Volume 73, 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)

Abstract
Front Matter, Table of Contents, Preface, Conference Organization
Cite as

12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 73, pp. 0:i-0:x, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{wilde:LIPIcs.TQC.2017.0,
  author =	{Wilde, Mark M.},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization}},
  booktitle =	{12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)},
  pages =	{0:i--0:x},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-034-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{73},
  editor =	{Wilde, Mark M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2017.0},
  URN =		{urn:nbn:de:0030-drops-85742},
  doi =		{10.4230/LIPIcs.TQC.2017.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization}
}
Document
DOI: 10.4230/LIPIcs.TQC.2017.10
Approximate Reversal of Quantum Gaussian Dynamics

Authors: Ludovico Lami, Siddhartha Das, and Mark M. Wilde

Published in: LIPIcs, Volume 73, 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)

Abstract
Recently, there has been focus on determining the conditions under which the data processing inequality for quantum relative entropy is satisfied with approximate equality. The solution of the exact equality case is due to Petz, who showed that the quantum relative entropy between two quantum states stays the same after the action of a quantum channel if and only if there is a reversal channel that recovers the original states after the channel acts. Furthermore, this reversal channel can be constructed explicitly and is now called the Petz recovery map. Recent developments have shown that a variation of the Petz recovery map works well for recovery in the case of approximate equality of the data processing inequality. Our main contribution here is a proof that bosonic Gaussian states and channels possess a particular closure property, namely, that the Petz recovery map associated to a bosonic Gaussian state \sigma and a bosonic Gaussian channel N is itself a bosonic Gaussian channel. We furthermore give an explicit construction of the Petz recovery map in this case, in terms of the mean vector and covariance matrix of the state \sigma and the Gaussian specification of the channel N.
Cite as

Ludovico Lami, Siddhartha Das, and Mark M. Wilde. Approximate Reversal of Quantum Gaussian Dynamics. In 12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 73, pp. 10:1-10:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{lami_et_al:LIPIcs.TQC.2017.10,
  author =	{Lami, Ludovico and Das, Siddhartha and Wilde, Mark M.},
  title =	{{Approximate Reversal of Quantum Gaussian Dynamics}},
  booktitle =	{12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017)},
  pages =	{10:1--10:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-034-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{73},
  editor =	{Wilde, Mark M.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2017.10},
  URN =		{urn:nbn:de:0030-drops-85751},
  doi =		{10.4230/LIPIcs.TQC.2017.10},
  annote =	{Keywords: Gaussian dynamics, Petz recovery map}
}
Document
DOI: 10.4230/LIPIcs.TQC.2014.52
Strong Converse for the Quantum Capacity of the Erasure Channel for Almost All Codes

Authors: Mark M. Wilde and Andreas Winter

Published in: LIPIcs, Volume 27, 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)

Abstract
A strong converse theorem for channel capacity establishes that the error probability in any communication scheme for a given channel necessarily tends to one if the rate of communication exceeds the channel's capacity. Establishing such a theorem for the quantum capacity of degradable channels has been an elusive task, with the strongest progress so far being a so-called "pretty strong converse." In this work, Morgan and Winter proved that the quantum error of any quantum communication scheme for a given degradable channel converges to a value larger than 1/sqrt(2) in the limit of many channel uses if the quantum rate of communication exceeds the channel's quantum capacity. The present paper establishes a theorem that is a counterpart to this "pretty strong converse." We prove that the large fraction of codes having a rate exceeding the erasure channel's quantum capacity have a quantum error tending to one in the limit of many channel uses. Thus, our work adds to the body of evidence that a fully strong converse theorem should hold for the quantum capacity of the erasure channel. As a side result, we prove that the classical capacity of the quantum erasure channel obeys the strong converse property.
Cite as

Mark M. Wilde and Andreas Winter. Strong Converse for the Quantum Capacity of the Erasure Channel for Almost All Codes. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 52-66, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{wilde_et_al:LIPIcs.TQC.2014.52,
  author =	{Wilde, Mark M. and Winter, Andreas},
  title =	{{Strong Converse for the Quantum Capacity of the Erasure Channel for Almost All Codes}},
  booktitle =	{9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
  pages =	{52--66},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-73-6},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{27},
  editor =	{Flammia, Steven T. and Harrow, Aram W.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.52},
  URN =		{urn:nbn:de:0030-drops-48068},
  doi =		{10.4230/LIPIcs.TQC.2014.52},
  annote =	{Keywords: strong converse, quantum erasure channel, quantum capacity}
}
Document
DOI: 10.4230/LIPIcs.TQC.2013.157
Towards Efficient Decoding of Classical-Quantum Polar Codes

Authors: Mark M. Wilde, Olivier Landon-Cardinal, and Patrick Hayden

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

Abstract
Known strategies for sending bits at the capacity rate over a general channel with classical input and quantum output (a cq channel) require the decoder to implement impractically complicated collective measurements. Here, we show that a fully collective strategy is not necessary in order to recover all of the information bits. In fact, when coding for a large number N uses of a cq channel W, N*I(W_{acc}) of the bits can be recovered by a non-collective strategy which amounts to coherent quantum processing of the results of product measurements, where I(W_{acc}) is the accessible information of the channel W. In order to decode the other N(I(W)-I(W_{acc})) bits, where I(W) is the Holevo rate, our conclusion is that the receiver should employ collective measurements. We also present two other results: 1) collective Fuchs-Caves measurements (quantum likelihood ratio measurements) can be used at the receiver to achieve the Holevo rate and 2) we give an explicit form of the Helstrom measurements used in small-size polar codes. The main approach used to demonstrate these results is a quantum extension of Arikan's polar codes.
Cite as

Mark M. Wilde, Olivier Landon-Cardinal, and Patrick Hayden. Towards Efficient Decoding of Classical-Quantum Polar Codes. In 8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 22, pp. 157-177, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{wilde_et_al:LIPIcs.TQC.2013.157,
  author =	{Wilde, Mark M. and Landon-Cardinal, Olivier and Hayden, Patrick},
  title =	{{Towards Efficient Decoding of Classical-Quantum Polar Codes}},
  booktitle =	{8th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2013)},
  pages =	{157--177},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2013.157},
  URN =		{urn:nbn:de:0030-drops-43141},
  doi =		{10.4230/LIPIcs.TQC.2013.157},
  annote =	{Keywords: classical-quantum channel, classical-quantum polar codes, quantum likelihood ratio, quantum successive cancellation decoder}
}
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