3 Search Results for "Lütkenhaus, Norbert"

Document
DOI: 10.4230/LIPIcs.STACS.2026.66
Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds

Authors: Yupan Liu

Published in: LIPIcs, Volume 364, 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)

Abstract
We investigate the computational hardness of estimating the quantum α-Rényi entropy S^𝚁_α(ρ) = (ln Tr(ρ^α))/(1-α) and the quantum q-Tsallis entropy S^𝚃_q(ρ) = (1-Tr(ρ^q))/(q-1), both converging to the von Neumann entropy as the order approaches 1. The promise problems Quantum α-Rényi Entropy Approximation (RényiQEA_α) and Quantum q-Tsallis Entropy Approximation (TsallisQEA_q) ask whether S^𝚁_α(ρ) or S^𝚃_q(ρ), respectively, is at least τ_Y or at most τ_N, where τ_Y - τ_N is typically a positive constant. Previous hardness results cover only the von Neumann entropy (order 1) and some cases of the quantum q-Tsallis entropy, while existing approaches do not readily extend to other orders. We establish that for all positive real orders, the rank-2 variants Rank2RényiQEA_α and Rank2TsallisQEA_q are BQP-hard. Combined with prior (rank-dependent) quantum query algorithms in Wang, Guan, Liu, Zhang, and Ying (TIT 2024), Wang, Zhang, and Li (TIT 2024), and Liu and Wang (SODA 2025), our results imply: - For all real order α > 0 and 0 < q ≤ 1, LowRankRényiQEA_α and LowRankTsallisQEA_q are BQP-complete, where both are restricted versions of RényiQEA_α and TsallisQEA_q with ρ of polynomial rank. - For all real order q > 1, TsallisQEA_q is BQP-complete. Our hardness results stem from reductions based on new inequalities relating the α-Rényi or q-Tsallis binary entropies of different orders, where the reductions differ substantially from previous approaches, and the inequalities are also of independent interest.
Cite as

Yupan Liu. Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds. In 43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 364, pp. 66:1-66:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{liu:LIPIcs.STACS.2026.66,
  author =	{Liu, Yupan},
  title =	{{Computational Hardness of Estimating Quantum Entropies via Binary Entropy Bounds}},
  booktitle =	{43rd International Symposium on Theoretical Aspects of Computer Science (STACS 2026)},
  pages =	{66:1--66:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-412-3},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{364},
  editor =	{Mahajan, Meena and Manea, Florin and McIver, Annabelle and Thắng, Nguy\~{ê}n Kim},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2026.66},
  URN =		{urn:nbn:de:0030-drops-255550},
  doi =		{10.4230/LIPIcs.STACS.2026.66},
  annote =	{Keywords: computational hardness, quantum state testing, quantum R\'{e}nyi entropy, quantum Tsallis entropy, von Neumann entropy}
}
Document
DOI: 10.4230/LIPIcs.TQC.2014.36
Quantum Communication Complexity with Coherent States and Linear Optics

Authors: Juan Miguel Arrazola and Norbert Lütkenhaus

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

Abstract
We introduce a general mapping for encoding quantum communication protocols involving pure states of multiple qubits, unitary transformations, and projective measurements into another set of protocols that employ coherent states of light in a superposition of optical modes, linear optics transformations and measurements with single-photon threshold detectors. This provides a general framework for transforming a wide class of protocols in quantum communication into a form in which they can be implemented with current technology. In particular, we apply the mapping to quantum communication complexity, providing general conditions under which quantum protocols can be implemented with coherent states and linear optics while retaining exponential separations in communication complexity compared to the classical case. Finally, we make use of our results to construct a protocol for the Hidden Matching problem that retains the known exponential gap between quantum and classical one-way communication complexity.
Cite as

Juan Miguel Arrazola and Norbert Lütkenhaus. Quantum Communication Complexity with Coherent States and Linear Optics. In 9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 27, pp. 36-47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

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@InProceedings{arrazola_et_al:LIPIcs.TQC.2014.36,
  author =	{Arrazola, Juan Miguel and L\"{u}tkenhaus, Norbert},
  title =	{{Quantum Communication Complexity with Coherent States and Linear Optics}},
  booktitle =	{9th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2014)},
  pages =	{36--47},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2014.36},
  URN =		{urn:nbn:de:0030-drops-48044},
  doi =		{10.4230/LIPIcs.TQC.2014.36},
  annote =	{Keywords: Quantum Communication Complexity, Quantum Optics}
}
Document
DOI: 10.4230/DagSemProc.09311.3
Quantum key distribution and cryptography: a survey

Authors: Romain Alléaume, Norbert Lütkenhaus, Renato Renner, Philippe Grangier, Thierry Debuisschert, Gregoire Ribordy, Nicolas Gisin, Philippe Painchault, Thomas Pornin, Louis Slavail, Michel Riguidel, Andrew Shilds, Thomas Länger, Momtchil Peev, Mehrdad Dianati, Anthony Leverrier, Andreas Poppe, Jan Bouda, Cyril Branciard, Mark Godfrey, John Rarity, Harald Weinfurter, Anton Zeilinger, and Christian Monyk

Published in: Dagstuhl Seminar Proceedings, Volume 9311, Classical and Quantum Information Assurance Foundations and Practice (2010)

Abstract
I will try to partially answer, based on a review on recent work, the following question: Can QKD and more generally quantum information be useful to cover some practical security requirements in current (and future) IT infrastructures ? I will in particular cover the following topics - practical performances of QKD - QKD network deployment - SECOQC project - Capabilities of QKD as a cryptographic primitive - comparative advantage with other solution, in order to cover practical security requirements - Quantum information and Side-channels - QKD security assurance - Thoughts about "real" Post-Quantum Cryptography
Cite as

Romain Alléaume, Norbert Lütkenhaus, Renato Renner, Philippe Grangier, Thierry Debuisschert, Gregoire Ribordy, Nicolas Gisin, Philippe Painchault, Thomas Pornin, Louis Slavail, Michel Riguidel, Andrew Shilds, Thomas Länger, Momtchil Peev, Mehrdad Dianati, Anthony Leverrier, Andreas Poppe, Jan Bouda, Cyril Branciard, Mark Godfrey, John Rarity, Harald Weinfurter, Anton Zeilinger, and Christian Monyk. Quantum key distribution and cryptography: a survey. In Classical and Quantum Information Assurance Foundations and Practice. Dagstuhl Seminar Proceedings, Volume 9311, pp. 1-29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{alleaume_et_al:DagSemProc.09311.3,
  author =	{All\'{e}aume, Romain and L\"{u}tkenhaus, Norbert and Renner, Renato and Grangier, Philippe and Debuisschert, Thierry and Ribordy, Gregoire and Gisin, Nicolas and Painchault, Philippe and Pornin, Thomas and Slavail, Louis and Riguidel, Michel and Shilds, Andrew and L\"{a}nger, Thomas and Peev, Momtchil and Dianati, Mehrdad and Leverrier, Anthony and Poppe, Andreas and Bouda, Jan and Branciard, Cyril and Godfrey, Mark and Rarity, John and Weinfurter, Harald and Zeilinger, Anton and Monyk, Christian},
  title =	{{Quantum key distribution and cryptography: a survey}},
  booktitle =	{Classical and Quantum Information Assurance Foundations and Practice},
  pages =	{1--29},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9311},
  editor =	{Samual L. Braunstein and Hoi-Kwong Lo and Kenny Paterson and Peter Ryan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09311.3},
  URN =		{urn:nbn:de:0030-drops-23618},
  doi =		{10.4230/DagSemProc.09311.3},
  annote =	{Keywords: QKD, QKD networks, Security assurance, Post-Quantum Cryptography}
}
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