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Theoretical Foundations of Quantum Cryptography

Titel Englisch Theoretical Foundations of Quantum Cryptography
Gesuchsteller/in Christandl Matthias
Nummer 128455
Förderungsinstrument SNF-Förderungsprofessuren
Forschungseinrichtung
Hochschule ETH Zürich - ETHZ
Hauptdisziplin Theoretische Physik
Beginn/Ende 01.06.2010 - 31.05.2014
Bewilligter Betrag 1'501'702.00
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Alle Disziplinen (3)

Disziplin
Theoretische Physik
Informatik
Mathematik

Keywords (10)

quantum mechanics; quantum information theory; quantum cryptography; quantum key distribution; quantum repeater; quantum marginal problem; entropy inequality; foundations of physics; entropic uncertainty relation; composability in cryptography

Lay Summary (Englisch)

Lead
Lay summary
Quantum cryptography is a novel technology that uses quantum mechanical effects - such as the uncertainty principle - in order to enable secure communication. The aim of this is project to solidify the theoretical foundations of quantum cryptography by studying the underlying quantum mechanical effects themselves and by developing new tools needed for large-scale applications of the technology.Cryptography means "secret writing" and is traditionally considered the art of encrypting a message so that an unwanted listener cannot obtain its meaning. Nowadays, cryptography is a well-established research field within computer science that studies communication and computation among people who do not trust each other. Cryptography impacts our society by providing secure communication over the internet, for instance in the form of online-banking, electronic commerce and, in the future, also electronic voting.In the 1980s and 90s it was proposed to utilise quantum mechanical effects such as Heisenberg's uncertainty principle and strong correlations known as "entanglement" in order to design novel cryptographic protocols. Protocols that guarantee a level of security unattainable by traditional methods. Seminal experiments have been carried out to demonstrate the technological viability of the proposals. These developments have led to the establishment of the young and active research field Quantum Cryptography, which is situated at the intersection of physics and computer science.The proposed research will contribute to the Theoretical Foundations of Quantum Cryptography by providing, on the one hand, a better understanding of the concept of security in quantum physics and, on the other hand, by building up theoretical tools for the study of larger cryptographic systems in realistic environments. In this way, it will aid the development of quantum cryptography as a viable future technology.
Direktlink auf Lay Summary Letzte Aktualisierung: 21.02.2013

Verantw. Gesuchsteller/in und weitere Gesuchstellende

Mitarbeitende

Publikationen

Publikation
A decoupling approach to classical data transmission over quantum channels
Dupuis Frederik, Szehr Oleg, Tomamichel Marco (2014), A decoupling approach to classical data transmission over quantum channels, in IEEE Trans. on Inf. Theory, 60, 1562.
Quantum to Classical Randomness Extractors
Berta M, Fawzi O., Wehner S. (2014), Quantum to Classical Randomness Extractors, in IEEE Trans. Info. Theo., 60, 1168.
The Decoupling Theorem
Dupuis F., Berta M., Wullschleger J., Renner R. (2014), The Decoupling Theorem, in Commun. Math. Phys, 328, 251.
A hierarchy of topological tensor network states
Buerschaper Oliver, Martin Mombelli Juan, Christandl Matthias, Aguado Miguel (2013), A hierarchy of topological tensor network states, in JOURNAL OF MATHEMATICAL PHYSICS, 54(1), 012201.
Chain Rules for Smooth Min- and Max-Entropies
Vitanov Alexander, Dupuis Frederic, Tomamichel Marco, Renner Renato (2013), Chain Rules for Smooth Min- and Max-Entropies, in IEEE TRANSACTIONS ON INFORMATION THEORY, 59(5), 2603-2612.
Decoupling with unitary almost two designs
Szehr O., Dupuis F., Tomamichel M., Renner R. (2013), Decoupling with unitary almost two designs, in New Journal of Physics, 15, 053022.
Electric-magnetic Duality and Topological Order on the Lattice
Buerschaper O., Christandl M., Kong L., Aguado M. (2013), Electric-magnetic Duality and Topological Order on the Lattice, in J. Math. Phys., 54, 012201.
Entanglement Cost of Quantum Channels
Berta M., Brandao F.G.S.L., Christandl M., Wehner S. (2013), Entanglement Cost of Quantum Channels, in IEEE Trans. Information Th., 59, 6779.
Entanglement Polytopes
Walter M., Doran B., Gross D., Christandl M. (2013), Entanglement Polytopes, in Science, 340, 1205.
Memory Attacks on Device-Independent Quantum Cryptography
Barrett Jonathan, Colbeck Roger, Kent Adrian (2013), Memory Attacks on Device-Independent Quantum Cryptography, in PHYSICAL REVIEW LETTERS, 110(1), 010503.
Pinning of Fermionic Occupation Numbers
Schilling Christian, Gross David, Christandl Matthias (2013), Pinning of Fermionic Occupation Numbers, in PHYSICAL REVIEW LETTERS, 110(4), 040404.
Stabilizer information inequalities from phase space distributions
Gross D., Walter M. (2013), Stabilizer information inequalities from phase space distributions, in J. Math. Phys., 54, 082201.
Typical Local Measurements in Generalized Probabilistic Theories: Emergence of Quantum Bipartite Correlations
Kleinmann Matthias, Osborne Tobias J., Scholz Volkher B., Werner Albert H. (2013), Typical Local Measurements in Generalized Probabilistic Theories: Emergence of Quantum Bipartite Correlations, in PHYSICAL REVIEW LETTERS, 110(4), 040403.
When is a pure state of three qubits determined by its single-particle reduced density matrices?
Sawicki A., Walter M., Kus M. (2013), When is a pure state of three qubits determined by its single-particle reduced density matrices?, in JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 46(5), 055304.
Achieving the Capacity of any DMC using only Polar Codes
Sutter David, Renes Joseph M., Dupuis Frederic, Renner Renato (2012), Achieving the Capacity of any DMC using only Polar Codes, in 2012 IEEE INFORMATION THEORY WORKSHOP (ITW), 114-118.
Actively secure two-party evaluation of any quantum operation
Dupuis F, Nielsen JB, Salvail L (2012), Actively secure two-party evaluation of any quantum operation, in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and , 7417 LNCS, 794-811.
Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations
Ahlbrecht Andre, Cedzich Christopher, Matjeschk Robert, Scholz Volkher B., Werner Albert H., Werner Reinhard F. (2012), Asymptotic behavior of quantum walks with spatio-temporal coin fluctuations, in QUANTUM INFORMATION PROCESSING, 11(5), 1219-1249.
Complete insecurity of quantum protocols for classical two-party computation.
Buhrman Harry, Christandl Matthias, Schaffner Christian (2012), Complete insecurity of quantum protocols for classical two-party computation., in Physical review letters, 109(16), 160501-160501.
Computing Multiplicities of Lie Group Representations
Christandl Matthias, Doran Brent, Walter Michael (2012), Computing Multiplicities of Lie Group Representations, in 2012 IEEE 53RD ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS), 639-648.
Detection of multiparticle entanglement: quantifying the search for symmetric extensions.
Brandão Fernando G S L, Christandl Matthias (2012), Detection of multiparticle entanglement: quantifying the search for symmetric extensions., in Physical review letters, 109(16), 160502-160502.
Efficient Polar Coding of Quantum Information
Renes Joseph M., Dupuis Frederic, Renner Renato (2012), Efficient Polar Coding of Quantum Information, in PHYSICAL REVIEW LETTERS, 109(5), 050504.
Entanglement Cost of Quantum Channels
Berta Mario, Christandl Matthias, Brandao Fernando G. S. L., Wehner Stephanie (2012), Entanglement Cost of Quantum Channels, in 2012 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY PROCEEDINGS (ISIT), 900-904.
Entanglement of the Antisymmetric State
Christandl Matthias, Schuch Norbert, Winter Andreas (2012), Entanglement of the Antisymmetric State, in Communications in Mathematical Physics, 397-422.
Experimental bound on the maximum predictive power of physical theories.
Stuart Terence E, Slater Joshua A, Colbeck Roger, Renner Renato, Tittel Wolfgang (2012), Experimental bound on the maximum predictive power of physical theories., in Physical review letters, 109(2), 020402-020402.
Free randomness can be amplified
Colbeck Roger, Renner Renato (2012), Free randomness can be amplified, in Nature Physics, 450-453.
Hypercontractivity, Sum-of-Squares Proofs, and their Applications
Barak Boaz, Brandao Fernando, Harrow Aram W., Kelner Jonathan, Steurer David, Zhou Yuan (2012), Hypercontractivity, Sum-of-Squares Proofs, and their Applications, in STOC 2012, 307-326.
Index Theory of One Dimensional QuantumWalks and Cellular Automata
Gross D., Nesme V., Vogts H., Werner R.F. (2012), Index Theory of One Dimensional QuantumWalks and Cellular Automata, in Communications in Mathematical Physics, 419-454.
Is a System's Wave Function in One-to-One Correspondence with Its Elements of Reality?
Colbeck Roger, Renner Renato (2012), Is a System's Wave Function in One-to-One Correspondence with Its Elements of Reality?, in PHYSICAL REVIEW LETTERS, 108(15), 150402.
Min-entropy uncertainty relation for finite-size cryptography
Ng Nelly Huei Ying, Berta Mario, Wehner Stephanie (2012), Min-entropy uncertainty relation for finite-size cryptography, in PHYSICAL REVIEW A, 86(4), 042315.
Molecular binding in interacting quantum walks
Ahlbrecht Andre, Alberti Andrea, Meschede Dieter, Scholz Volkher B., Werner Albert H., Werner Reinhard F. (2012), Molecular binding in interacting quantum walks, in NEW JOURNAL OF PHYSICS, 14, 073050.
Quantum to classical randomness extractors
Berta M, Fawzi O, Wehner S (2012), Quantum to classical randomness extractors, in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and , 7417 LNCS, 776-793.
Reliable Quantum State Tomography
Christandl Matthias, Renner Renato (2012), Reliable Quantum State Tomography, in PHYSICAL REVIEW LETTERS, 109(12), 120403.
THE MONOMIAL REPRESENTATIONS OF THE CLIFFORD GROUP
Appleby D.M., Bengtsson Ingemar, Brierley Stephen, Grassl Markus, Gross David, Larsson Jan-Ake (2012), THE MONOMIAL REPRESENTATIONS OF THE CLIFFORD GROUP, in Quantum Information and Computation,, 0404-0431.
Uncertainty Relations from Simple Entropic Properties
Coles Patrick J., Colbeck Roger, Yu Li, Zwolak Michael (2012), Uncertainty Relations from Simple Entropic Properties, in PHYSICAL REVIEW LETTERS, 108(21), 210405.
Unconditionally secure device-independent quantum key distribution with only two devices
Barrett Jonathan, Colbeck Roger, Kent Adrian (2012), Unconditionally secure device-independent quantum key distribution with only two devices, in PHYSICAL REVIEW A, 86(6), 062326.
A Conceptually Simple Proof of the Quantum Reverse Shannon Theorem
Berta Mario, Christandl Matthias, Renner Renato (2011), A Conceptually Simple Proof of the Quantum Reverse Shannon Theorem, in THEORY OF QUANTUM COMPUTATION, COMMUNICATION, AND CRYPTOGRAPHY, 6519, 131-140.
A Quasipolynomial-Time Algorithm for the Quantum Separability Problem
Brandao Fernando G. S. L., Christandl Matthias, Yard Jon (2011), A Quasipolynomial-Time Algorithm for the Quantum Separability Problem, in STOC 11: PROCEEDINGS OF THE 43RD ACM SYMPOSIUM ON THEORY OF COMPUTING, 343-351.
Concentration of Measure for Quantum States with a Fixed Expectation Value
Mueller Markus P., Gross David, Eisert Jens (2011), Concentration of Measure for Quantum States with a Fixed Expectation Value, in COMMUNICATIONS IN MATHEMATICAL PHYSICS, 303(3), 785-824.
Even partitions in plethysms
Buergisser Peter, Christandl Matthias, Ikenmeyer Christian (2011), Even partitions in plethysms, in JOURNAL OF ALGEBRA, 328(1), 322-329.
Faithful Squashed Entanglement Fernando
Brandao Fernando, Christandl Matthias, Yard Jon (2011), Faithful Squashed Entanglement Fernando, in Communications in Mathematical Physics, 805-830.
Nonvanishing of Kronecker coefficients for rectangular shapes
Buergisser Peter, Christandl Matthias, Ikenmeyer Christian (2011), Nonvanishing of Kronecker coefficients for rectangular shapes, in ADVANCES IN MATHEMATICS, 227(5), 2082-2091.
Recovering Low-Rank Matrices From Few Coefficients in Any Basis
Gross David (2011), Recovering Low-Rank Matrices From Few Coefficients in Any Basis, in IEEE TRANSACTIONS ON INFORMATION THEORY, 57(3), 1548-1566.
The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory
Berta Mario, Christandl Matthias, Renner Renato (2011), The Quantum Reverse Shannon Theorem Based on One-Shot Information Theory, in Communications in Mathematical Physics, 579-615.
Efficient quantum state tomography
Cramer M, Plenio MB, Flammia ST, Somma R, Gross D, Bartlett SD, Landon-Cardinal O, Poulin D, Liu Y-K (2010), Efficient quantum state tomography, in Nature Communications, 1(9), 1:149.
Highly Entangled States with Almost No Secrecy
Christandl Matthias, Schuch Norbert, Winter Andreas (2010), Highly Entangled States with Almost No Secrecy, in PHYSICAL REVIEW LETTERS, 104(24), 240405.
Permutationally invariant quantum tomography.
Tóth G, Wieczorek W, Gross D, Krischek R, Schwemmer C, Weinfurter H (2010), Permutationally invariant quantum tomography., in Physical review letters, 105(25), 250403-250403.
Probing the negative Wigner function of a pulsed single photon point by point.
Laiho Kaisa, Cassemiro Katiúscia N, Gross David, Silberhorn Christine (2010), Probing the negative Wigner function of a pulsed single photon point by point., in Physical review letters, 105(25), 253603-253603.
The uncertainty principle in the presence of quantum memory
Berta Mario, Christandl Matthias, Colbeck Roger, Renes Joseph M., Renner Renato (2010), The uncertainty principle in the presence of quantum memory, in NATURE PHYSICS, 6(9), 659-662.

Zusammenarbeit

Gruppe / Person Land
Formen der Zusammenarbeit
Prof. Winter Spanien (Europa)
- vertiefter/weiterführender Austausch von Ansätzen, Methoden oder Resultaten
- Publikation
- Austausch von Mitarbeitern
Prof. Doran, ETH Zurich Schweiz (Europa)
- vertiefter/weiterführender Austausch von Ansätzen, Methoden oder Resultaten
- Publikation
Prof. Renner, ETH Zurich Schweiz (Europa)
- vertiefter/weiterführender Austausch von Ansätzen, Methoden oder Resultaten
- Publikation
- Austausch von Mitarbeitern

Veranstaltungen zum Wissenstransfer

Aktiver Beitrag

Titel Art des Beitrags Titel des Artikels oder Beitrages Datum Ort Beteiligte Personen
Vortrag Kantonsschule im Lee Winterthur Vortrag 29.01.2013 Winterthur, Schweiz
Matheolympiade Schweiz Vortrag 03.04.2011 Aarau, Schweiz


Kommunikation mit der Öffentlichkeit

Kommunikation Titel Medien Ort Jahr
Medienarbeit: Radio, Fernsehen Einstein SRF Deutschschweiz 2011

Auszeichnungen

Titel Jahr
ERC Starting Grant "QMULT" 2013

Verbundene Projekte

Nummer Titel Start Förderungsinstrument
150734 Theoretical Foundations of Quantum Cryptography II 01.09.2014 SNF-Förderungsprofessuren
138799 CQC - Composing Quantum Channels 01.07.2012 CHIST-ERA

Abstract

The proposed research contributes to the field of quantum cryptography. Quantum cryptography is part of quantum information science, a research area which is formed in the intersection between computer science and quantum physics. Built on the paradigm that information is stored and processed in physical devices, which are made out of atoms and photons and described by quantum physics, the aim of quantum information science is twofold: on the one hand, it aims to understand the fundamental principles behind information processing in quantum physics and, on the other hand, to take these new possibilities for information processing and develop them into novel information technologies. Cryptography aims at realising secure communication along insecure communication channels and among parties that do not trust each other. Quantum cryptography has been shown to offer levels of security unattainably by classical means and is regarded as the most promising field of research from which quantum technologies will emerge in the near future. In recent years, progress has been made in understanding the concept of security in quantum physics, but a firm theoretical base for quantum cryptography as a future technology is still missing. It is the aim of the proposed project to narrow this gap and to contribute to the Theoretical Foundations of Quantum Cryptography. This will be done on two levels of investigation moving from more fundamental questions in Subproject A to more applied research in Subproject B. In Subproject A, we propose to investigate the structure of quantum states that are divided between different parties. This research is motivated by security requirements which are expressed as conditions on the structure of such states. The proposed research will focus in particular on the quantum marginal problem, which directly concerns structural requirements, on entropy inequalities and their use in quantum communication theory, and on entropic uncertainty relations and their role in proofs of security. The research will contribute to the understanding of the concept of security in quantum physics. In Subproject B, we set out to tackle two important open problems in quantum cryptography. The first problem deals with the issue of composability of quantum protocols. That is, the question of how secure cryptographic components can be assembled into a larger cryptographic system and how it is possible to argue that the security of the larger system is implied by the security of its components. We propose to develop a comprehensive and at the same time practical framework of composability and to apply this framework in order to prove the composable security of existing protocols. The second problem deals with a specific task, namely that of long-distance quantum key distribution. We will develop a theory of the quantum repeater, an amplifier for quantum correlations, that allows to extend quantum key distribution to arbitrary distances. It is our goal to understand the limits and possibilities of this device. In particular, we will aim for the design of quantum repeaters that can work in more noisy and thus more realistic environments, thereby aiding the development of quantum cryptography as a viable future technology.The proposed research will contribute to the Theoretical Foundations of Quantum Cryptography by providing, on the one hand, a better understanding of the concept of security in quantum physics and by providing, on the other hand, the theoretical tools for the study of larger cryptographic systems in realistic environments. On a more general level, we expect the tools developed in this research project to have application in the wider areas of quantum information science and quantum physics.
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