12th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2017), TQC 2017, June 14-16, 2017, Paris, France
TQC 2017
June 14-16, 2017
Paris, France
Conference on the Theory of Quantum Computation, Communication and Cryptography
TQC
https://www.tqcconference.org/
https://dblp.org/db/conf/tqc
Leibniz International Proceedings in Informatics
LIPIcs
https://www.dagstuhl.de/dagpub/1868-8969
https://dblp.org/db/series/lipics
1868-8969
Mark M.
Wilde
Mark M. Wilde
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
73
2018
978-3-95977-034-7
https://www.dagstuhl.de/dagpub/978-3-95977-034-7
Front Matter, Table of Contents, Preface, Conference Organization
Front Matter, Table of Contents, Preface, Conference Organization
Front Matter
Table of Contents
Preface
Conference Organization
0:i-0:x
Front Matter
Mark M.
Wilde
Mark M. Wilde
10.4230/LIPIcs.TQC.2017.0
Creative Commons Attribution 3.0 Unported license
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A Single Entangled System Is an Unbounded Source of Nonlocal Correlations and of Certified Random Numbers
The outcomes of local measurements made on entangled systems can be certified to be random provided that the generated statistics violate a Bell inequality. This way of producing randomness relies only on a minimal set of assumptions because it is independent of the internal functioning of the devices generating the random outcomes. In this context it is crucial to understand both qualitatively and quantitatively how the three fundamental quantities – entanglement, non-locality and randomness – relate to each other. To explore these relationships, we consider the case where repeated (non projective) measurements are made on the physical systems, each measurement being made on the post-measurement state of the previous measurement. In this work, we focus on the following questions: Given a single entangled system, how many nonlocal correlations in a sequence can we obtain? And from this single entangled system, how many certified random numbers is it possible to generate? In the standard scenario with a single measurement in the sequence, it is possible to generate non-local correlations between two distant observers only and the amount of random numbers is very limited. Here we show that we can overcome these limitations and obtain any amount of certified random numbers from a single entangled pair of qubit in a pure state by making sequences of measurements on it. Moreover, the state can be arbitrarily weakly entangled. In addition, this certification is achieved by near-maximal violation of a particular Bell inequality for each measurement in the sequence. We also present numerical results giving insight on the resistance to imperfections and on the importance of the strength of the measurements in our scheme.
Randomness certification
Nonlocality
Entanglement
Sequences of measurements
1:1-1:23
Regular Paper
Florian J.
Curchod
Florian J. Curchod
Markus
Johansson
Markus Johansson
Remigiusz
Augusiak
Remigiusz Augusiak
Matty J.
Hoban
Matty J. Hoban
Peter
Wittek
Peter Wittek
Antonio
Acín
Antonio Acín
10.4230/LIPIcs.TQC.2017.1
Antonio Acín, Serge Massar, and Stefano Pironio. Randomness versus nonlocality and entanglement. Phys. Rev. Lett., 108:100402, Mar 2012. URL: http://dx.doi.org/10.1103/PhysRevLett.108.100402.
http://dx.doi.org/10.1103/PhysRevLett.108.100402
Antonio Acín, Stefano Pironio, Tamás Vértesi, and Peter Wittek. Optimal randomness certification from one entangled bit. Phys. Rev. A, 93(4):040102, April 2016. URL: http://dx.doi.org/10.1103/PhysRevA.93.040102.
http://dx.doi.org/10.1103/PhysRevA.93.040102
Jean-Daniel Bancal, Lana Sheridan, and Valerio Scarani. More randomness from the same data. New J. Phys., 16(3):033011, 2014. URL: http://dx.doi.org/10.1088/1367-2630/16/3/033011.
http://dx.doi.org/10.1088/1367-2630/16/3/033011
John S. Bell. On the Einstein Podolsky Rosen paradox. Physics, 1:195, 1964.
Nicolas Brunner, Daniel Cavalcanti, Stefano Pironio, Valerio Scarani, and Stephanie Wehner. Bell nonlocality. Rev. Mod. Phys., 86:419-478, Apr 2014. URL: http://dx.doi.org/10.1103/RevModPhys.86.419.
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Roger Colbeck. Quantum and Relativistic Protocols for Secure Multi-Party Computation. PhD thesis, University of Cambridge, 2006.
Roger Colbeck and Renato Renner. Free randomness can be amplified. Nat. Phys., 8(6):450-454, May 2012. URL: http://dx.doi.org/10.1038/nphys2300.
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Florian J. Curchod, Markus Johansson, Remigiusz Augusiak, Matty J. Hoban, Peter Wittek, and Antonio Acín. Unbounded randomness certification using sequences of measurements. Phys. Rev. A, 95(2), feb 2017. URL: http://dx.doi.org/10.1103/physreva.95.020102.
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Gonzalo de la Torre, Matty J. Hoban, Chirag Dhara, Giuseppe Prettico, and Antonio Acín. Maximally nonlocal theories cannot be maximally random. Phys. Rev. Lett., 114(16):160502, 2015. URL: http://dx.doi.org/10.1103/physrevlett.114.160502.
http://dx.doi.org/10.1103/physrevlett.114.160502
Rodrigo Gallego, Lluis Masanes, Gonzalo De La Torre, Chirag Dhara, Leandro Aolita, and Antonio Acín. Full randomness from arbitrarily deterministic events. Nat. Commun., 4:2654, 2013. URL: http://dx.doi.org/10.1038/ncomms3654.
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Rodrigo Gallego, Lars Erik Würflinger, Rafael Chaves, Antonio Acín, and Miguel Navascués. Nonlocality in sequential correlation scenarios. New J. Phys., 16(3):033037, 2014. URL: http://dx.doi.org/10.1088/1367-2630/16/3/033037.
http://dx.doi.org/10.1088/1367-2630/16/3/033037
Meng-Jun Hu, Zhi-Yuan Zhou, Xiao-Min Hu, Chuan-Feng Li, Guang-Can Guo, and Yong-Sheng Zhang. Experimental sharing of nonlocality among multiple observers with one entangled pair via optimal weak measurements. arXiv:1609.01863, Sep 2016. URL: http://arxiv.org/abs/1609.01863.
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http://dx.doi.org/10.1088/1367-2630/16/1/013035
Stefano Pironio, Antonio Acín, Serge Massar, Antoine Boyer de la Giroday, Dzmitry N. Matsukevich, Peter Maunz, Steven Matthew Olmschenk, David Hayes, Le Luo, T. Andrew Manning, and Christopher R. Monroe. Random numbers certified by bell’s theorem. Nature, 464(7291):1021-1024, 2010. URL: http://dx.doi.org/10.1038/nature09008.
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The Complexity of Simulating Local Measurements on Quantum Systems
An important task in quantum physics is the estimation of local quantities for ground states of local Hamiltonians. Recently, Ambainis defined the complexity class P^QMA[log], and motivated its study by showing that the physical task of estimating the expectation value of a local observable against the ground state of a local Hamiltonian is P^QMA[log]-complete. In this paper, we continue the study of P^QMA[log], obtaining the following results.
The P^QMA[log]-completeness result of Ambainis requires O(log n)-local observ- ables and Hamiltonians. We show that simulating even a single qubit measurement on ground states of 5-local Hamiltonians is P^QMA[log]-complete, resolving an open question of Ambainis. We formalize the complexity theoretic study of estimating two-point correlation functions against ground states, and show that this task is similarly P^QMA[log]-complete.
P^QMA[log] is thought of as "slightly harder" than QMA. We justify this formally by exploiting the hierarchical voting technique of Beigel, Hemachandra, and Wechsung to show P^QMA[log] \subseteq PP. This improves the containment QMA \subseteq PP from Kitaev and Watrous. A central theme of this work is the subtlety involved in the study of oracle classes in which the oracle solves a promise problem. In this vein, we identify a flaw in Ambainis' prior work regarding a P^UQMA[log]-hardness proof for estimating spectral gaps of local Hamiltonians. By introducing a "query validation" technique, we build on his prior work to obtain P^UQMA[log]-hardness for estimating spectral gaps under polynomial-time Turing reductions.
Complexity theory
Quantum Merlin Arthur (QMA)
local Hamiltonian
local measurement
spectral gap
2:1-2:17
Regular Paper
Sevag
Gharibian
Sevag Gharibian
Justin
Yirka
Justin Yirka
10.4230/LIPIcs.TQC.2017.2
D. Aharonov, M. Ben-Or, F. Brandão, and O. Sattath. The pursuit for uniqueness: Extending Valiant-Vazirani theorem to the probabilistic and quantum settings. Available at arXiv.org e-Print quant-ph/0810.4840v1, 2008.
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A. Ambainis. On physical problems that are slightly more difficult than QMA. In Proceedings of 29th IEEE Conference on Computational Complexity (CCC 2014), pages 32-43, 2014.
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Provably Secure Key Establishment Against Quantum Adversaries
At Crypto 2011, some of us had proposed a family of cryptographic protocols for key establishment capable of protecting quantum and classical legitimate parties unconditionally against a quantum eavesdropper in the query complexity model. Unfortunately, our security proofs were unsatisfactory from a cryptographically meaningful perspective because they were sound only in a worst-case scenario. Here, we extend our results and prove that for any \eps > 0, there is a classical protocol that allows the legitimate parties to establish a common key after O(N) expected queries to a random oracle, yet any quantum eavesdropper will have a vanishing probability of learning their key after O(N^(1.5-\eps)) queries to the same oracle. The vanishing probability applies to a typical run of the protocol. If we allow the legitimate parties to use a quantum computer as well, their advantage over the quantum eavesdropper becomes arbitrarily close to the quadratic advantage that classical legitimate parties enjoyed over classical eavesdroppers in the seminal 1974 work of Ralph Merkle. Along the way, we develop new tools to give lower bounds on the number of quantum queries required to distinguish two probability distributions. This method in itself could have multiple applications in cryptography. We use it here to study average-case quantum query complexity, for which we develop a new composition theorem of independent interest.
Merkle puzzles
Key establishment schemes
Quantum cryptography
Adversary method
Average-case analysis
3:1-3:17
Regular Paper
Aleksandrs
Belovs
Aleksandrs Belovs
Gilles
Brassard
Gilles Brassard
Peter
Høyer
Peter Høyer
Marc
Kaplan
Marc Kaplan
Sophie
Laplante
Sophie Laplante
Louis
Salvail
Louis Salvail
10.4230/LIPIcs.TQC.2017.3
Creative Commons Attribution 3.0 Unported license
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Quantum Coin Hedging, and a Counter Measure
A quantum board game is a multi-round protocol between a single quantum player against the quantum board. Molina and Watrous discovered quantum hedging. They gave an example for perfect quantum hedging: a board game with winning probability < 1, such that the player can win with certainty at least 1-out-of-2 quantum board games played in parallel. Here we show that perfect quantum hedging occurs in a cryptographic protocol – quantum coin flipping. For this reason, when cryptographic protocols are composed in parallel, hedging may introduce serious challenges into their analysis.
We also show that hedging cannot occur when playing two-outcome board games in sequence. This is done by showing a formula for the value of sequential two-outcome board games, which depends only on the optimal value of a single board game; this formula applies in a more general setting of possible target functions, in which hedging is only a special case.
quantum coin hedging
quantum board games
4:1-4:15
Regular Paper
Maor
Ganz
Maor Ganz
Or
Sattath
Or Sattath
10.4230/LIPIcs.TQC.2017.4
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Quantum Hedging in Two-Round Prover-Verifier Interactions
We consider the problem of a particular kind of quantum correlation that arises in some two-party games. In these games, one player is presented with a question they must answer, yielding an outcome of either "win" or "lose". Molina and Watrous previously studied such a game that exhibited a perfect form of hedging, where the risk of losing a first game can completely offset the corresponding risk for a second game. This is a non-classical quantum phenomenon, and establishes the impossibility of performing strong error-reduction for quantum interactive proof systems by parallel repetition, unlike for classical interactive proof systems. We take a step in this article towards a better understanding of the hedging phenomenon by giving a complete characterization of when perfect hedging is possible for a natural generalization of the game in the prior work of Molina and Watrous. Exploring in a different direction the subject of quantum hedging, and motivated by implementation concerns regarding loss-tolerance, we also consider a variation of the protocol where the player who receives the question can choose to restart the game rather than return an answer. We show that in this setting there is no possible hedging for any game played with state spaces corresponding to finite-dimensional complex Euclidean spaces.
prover-verifier interactions
parallel repetition
quantum information
5:1-5:30
Regular Paper
Srinivasan
Arunachalam
Srinivasan Arunachalam
Abel
Molina
Abel Molina
Vincent
Russo
Vincent Russo
10.4230/LIPIcs.TQC.2017.5
Scott Aaronson. Quantum computing, postselection, and probabilistic polynomial-time. In Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, volume 461, pages 3473-3482. The Royal Society, 2005.
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Srinivasan Arunachalam, Abel Molina, and Vincent Russo. Software for implementing some of the semidefinite programs in this paper. Available at https://bitbucket.org/vprusso/quantum-hedging, 2013.
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Gus Gutoski. Quantum strategies and local operations. arXiv preprint arXiv:1003.0038, 2010.
Gus Gutoski and John Watrous. Toward a general theory of quantum games. In Proceedings of the thirty-ninth annual ACM symposium on Theory of computing, pages 565-574. ACM, 2007.
Patrick Hayden, Kevin Milner, and Mark Wilde. Two-message quantum interactive proofs and the quantum separability problem. Quantum Information & Computation, 14(5&6):384-416, 2014.
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Rahul Jain, Sarvagya Upadhyay, and John Watrous. Two-message quantum interactive proofs are in PSPACE. In 50th Annual IEEE Symposium on Foundations of Computer Science, pages 534-543. IEEE, 2009.
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Hari Krovi, Saikat Guha, Zachary Dutton, and Marcus P da Silva. Optimal measurements for symmetric quantum states with applications to optical communication. Physical Review A, 92(6):062333, 2015.
Urmila Mahadev and Ronald de Wolf. Rational approximations and quantum algorithms with postselection. Quantum Information &Computation, 15(3&4):295-307, 2015.
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Abel Molina and John Watrous. Hedging bets with correlated quantum strategies. In Proc. R. Soc. A. The Royal Society, 2012.
Fernando Pastawski, Norman Y Yao, Liang Jiang, Mikhail D Lukin, and J Ignacio Cirac. Unforgeable noise-tolerant quantum tokens. Proceedings of the National Academy of Sciences, 109(40):16079-16082, 2012.
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Sheng Zhang and Yuexin Zhang. Quantum coin flipping secure against channel noises. Physical Review A, 92(2):022313, 2015.
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Multiparty Quantum Communication Complexity of Triangle Finding
Triangle finding (deciding if a graph contains a triangle or not) is a central problem in quantum query complexity. The quantum communication complexity of this problem, where the edges of the graph are distributed among the players, was considered recently by Ivanyos et al. in the two- party setting. In this paper we consider its k-party quantum communication complexity with k >= 3. Our main result is a ~O(m^(7/12))-qubit protocol, for any constant number of players k, deciding with high probability if a graph with m edges contains a triangle or not. Our approach makes connections between the multiparty quantum communication complexity of triangle finding and the quantum query complexity of graph collision, a well-studied problem in quantum query complexity.
Quantum communication complexity
triangle finding
graph collision
6:1-6:11
Regular Paper
François
Le Gall
François Le Gall
Shogo
Nakajima
Shogo Nakajima
10.4230/LIPIcs.TQC.2017.6
Scott Aaronson and Andris Ambainis. Quantum search of spatial regions. In Proceedings of the 51st Symposium on Foundations of Computer Science, pages 200-209, 2003.
Andris Ambainis. Quantum walk algorithm for element distinctness. SIAM Journal on Computing, 37(1):210-239, 2007.
Andris Ambainis. Quantum search with variable times. Theory of Computing Systems, 47(3):786-807, 2010.
Aleksandrs Belovs. Span programs for functions with constant-sized 1-certificates. In Proceedings of the 44th Symposium on Theory of Computing, pages 77-84, 2012.
Harry Buhrman, Richard Cleve, and Avi Wigderson. Quantum vs. classical communication and computation. In Proceedings of the 30th Symposium on Theory of Computing, pages 63-68, 1998.
Harry Buhrman, Christoph Dürr, Mark Heiligman, and Peter Høyer. Quantum algorithms for element distinctness. SIAM Journal on Computing, 34(6):1324-1330, 2005.
Titouan Carette, Mathieu Laurière, and Frédéric Magniez. Extended learning graphs for triangle finding. In Proceedings of the 34th International Symposium on Theoretical Aspects of Computer Science, pages 20:1-20:14, 2017.
Andrew M. Childs and Robin Kothari. Quantum query complexity of minor-closed graph properties. SIAM Journal on Computing, 41(6):1426-1450, 2012.
Gábor Ivanyos, Hartmut Klauck, Troy Lee, Miklos Santha, and Ronald de Wolf. New bounds on the classical and quantum communication complexity of some graph properties. In Proceedings of the 32nd International Conference on Foundations of Software Technology and Theoretical Computer Science, pages 148-159, 2012.
Stacey Jeffery, Robin Kothari, and Frédéric Magniez. Nested quantum walks with quantum data structures. In Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1474-1485, 2013.
Bala Kalyanasundaram and Georg Schintger. The probabilistic communication complexity of set intersection. SIAM Journal on Discrete Mathematics, 5(4):545-557, 1992.
François Le Gall. Improved quantum algorithm for triangle finding via combinatorial arguments. In Proceedings of the 28th Symposium on the Theory of Computing, pages 216-225, 2014.
François Le Gall and Shogo Nakajima. Quantum algorithm for triangle finding in sparse graphs. In Proceedings of the 26th International Symposium on Algorithms and Computation, pages 590-600, 2015.
Troy Lee, Frédéric Magniez, and Miklos Santha. Improved quantum query algorithms for triangle finding and associativity testing. In Proceedings of the 24th Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1486-1502, 2013.
Frédéric Magniez, Ashwin Nayak, Jérémie Roland, and Miklos Santha. Search via quantum walk. SIAM Journal on Computing, 40(1):142-164, 2011.
Frédéric Magniez, Miklos Santha, and Mario Szegedy. Quantum algorithms for the triangle problem. SIAM Journal on Computing, 37(2):413-424, 2007.
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Alexander A. Razborov. Quantum communication complexity of symmetric predicates. Izvestiya Mathematics, 67(1):145-159, 2003.
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Virginia Vassilevska Williams and Ryan Williams. Finding, minimizing, and counting weighted subgraphs. SIAM Journal on Computing, 42(3):831-854, 2013.
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Andrew C. Yao. Quantum circuit complexity. In Proceedings of the 34st Symposium on Foundations of Computer Science, pages 352-361, 1993.
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Improved reversible and quantum circuits for Karatsuba-based integer multiplication
Integer arithmetic is the underpinning of many quantum algorithms, with applications ranging from Shor's algorithm over HHL for matrix inversion to Hamiltonian simulation algorithms. A basic objective is to keep the required resources to implement arithmetic as low as possible. This applies in particular to the number of qubits required in the implementation as for the foreseeable future this number is expected to be small. We present a reversible circuit for integer multiplication that is inspired by Karatsuba's recursive method. The main improvement over circuits that have been previously reported in the literature is an asymptotic reduction of the amount of space required from O(n^1.585) to O(n^1.427). This improvement is obtained in exchange for a small constant increase in the number of operations by a factor less than 2 and a small asymptotic increase in depth for the parallel version. The asymptotic improvement are obtained from analyzing pebble games on complete ternary trees.
Quantum algorithms
reversible circuits
quantum circuits
integer multiplication
pebble games
Karatsuba's method
7:1-7:15
Regular Paper
Alex
Parent
Alex Parent
Martin
Roetteler
Martin Roetteler
Michele
Mosca
Michele Mosca
10.4230/LIPIcs.TQC.2017.7
Matthew Amy, Dmitri Maslov, Michele Mosca, and Martin Roetteler. A meet-in-the-middle algorithm for fast synthesis of depth-optimal quantum circuits. IEEE Trans. on CAD of Integrated Circuits and Systems, 32(6):818-830, 2013. URL: http://dx.doi.org/10.1109/TCAD.2013.2244643.
http://dx.doi.org/10.1109/TCAD.2013.2244643
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Dominic W. Berry, Andrew M. Childs, Richard Cleve, Robin Kothari, and Rolando D. Somma. Exponential improvement in precision for simulating sparse Hamiltonians. In Symposium on Theory of Computing, STOC 2014, pages 283-292, 2014.
Dominic W. Berry, Andrew M. Childs, and Robin Kothari. Hamiltonian simulation with nearly optimal dependence on all parameters. In IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015, pages 792-809, 2015.
Jean-François Biasse and Fang Song. Efficient quantum algorithms for computing class groups and solving the principal ideal problem in arbitrary degree number fields. In Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2016, pages 893-902, 2016.
Alex Bocharov, Martin Roetteler, and Krysta M. Svore. Efficient synthesis of probabilistic quantum circuits with fallback. Physical Review A, 91:052317, 2015.
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Vadym Kliuchnikov, Dmitri Maslov, and Michele Mosca. Asymptotically optimal approximation of single qubit unitaries by Clifford and T circuits using a constant number of ancillary qubits. Physical Review Letters, 110:190502, 2013.
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Guang Hao Low and Isaac L. Chuang. Hamiltonian simulation by qubitization, 2016. arXiv:1610.06546.
Michael A. Nielsen and Isaac L. Chuang. Quantum Computation and Quantum Information. Cambridge University Press, 2000.
Neil J. Ross and Peter Selinger. Optimal ancilla-free Clifford+T approximation of z-rotations. Quantum Information & Computation, 16(11&12):901-953, 2016.
Mehdi Saeedi and Igor L. Markov. Constant-optimized quantum circuits for modular multiplication and exponentiation. Quantum Information and Computation, 12(5&6):361-394, 2012.
Mehdi Saeedi and Igor L. Markov. Synthesis and optimization of reversible circuits - a survey. ACM Comput. Surv., 45(2):21, 2013.
Peter Selinger. Quantum circuits of T-depth one. Phys. Rev. A, 87:042302, 2013.
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Peter W. Shor. Algorithms for quantum computation: discrete logarithm and factoring. In Proc. FOCS'94, pages 124-134. IEEE Computer Society Press, 1994.
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Fidelity of Quantum Strategies with Applications to Cryptography
We introduce a definition of the fidelity function for multi-round quantum strategies, which we call the strategy fidelity, that is a generalization of the fidelity function for quantum states. We provide many interesting properties of the strategy fidelity including a Fuchs-van de Graaf relationship with the strategy norm. We illustrate an operational interpretation of the strategy fidelity in the spirit of Uhlmann's Theorem and discuss its application to the security analysis of quantum protocols for interactive cryptographic tasks such as bit-commitment and oblivious string transfer. Our analysis is very general in the sense that the actions of the protocol need not be fully specified, which is in stark contrast to most other security proofs. Lastly, we provide a semidefinite programming formulation of the strategy fidelity.
Quantum strategies
cryptography
fidelity
semidefinite programming
8:1-8:13
Regular Paper
Gus
Gutoski
Gus Gutoski
Ansis
Rosmanis
Ansis Rosmanis
Jamie
Sikora
Jamie Sikora
10.4230/LIPIcs.TQC.2017.8
Andris Ambainis, Harry Buhrman, Yevgeniy Dodis, and Hein Röhrig. Multiparty quantum coin flipping. In Proceedings of the 19th IEEE Annual Conference on Computational Complexity, pages 250-259. IEEE Computer Society, 2004. URL: http://dx.doi.org/10.1109/CCC.2004.19.
http://dx.doi.org/10.1109/CCC.2004.19
Viacheslav P. Belavkin, Giacomo Mauro D'Ariano, and Maxim Raginsky. Operational distance and fidelity for quantum channels. Journal of Mathematical Physics, 46(6):062106, 2005. arXiv:quant-ph/0408159.
Charles Bennett and Gilles Brassard. Quantum cryptography: Public key distribution and coin tossing. In Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing, pages 175-179. IEEE Computer Society, 1984.
André Chailloux, Gus Gutoski, and Jamie Sikora. Optimal bounds for semi-honest quantum oblivious transfer. Chicago Journal of Theoretical Computer Science, 2016.
André Chailloux and Iordanis Kerenidis. Optimal quantum strong coin flipping. In Proceedings of the 50th IEEE Symposium on Foundations of Computer Science, FOCS 2009, pages 527-533, 2009. arXiv:0904.1511 [quant-ph].
André Chailloux and Iordanis Kerenidis. Optimal bounds for quantum bit commitment. In Rafail Ostrovsky, editor, IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011, Palm Springs, CA, USA, October 22-25, 2011, pages 354-362. IEEE Computer Society, 2011. URL: http://dx.doi.org/10.1109/FOCS.2011.42.
http://dx.doi.org/10.1109/FOCS.2011.42
André Chailloux, Iordanis Kerenidis, and Jamie Sikora. Lower bounds for quantum oblivious transfer. Quantum Information and Computation, 13(1&2):158-177, 2013. arXiv:1007.1875 [quant-ph].
André Chailloux, Iordanis Kerenidis, and Jamie Sikora. Strong connections between quantum encodings, nonlocality, and quantum cryptography. Phys. Rev. A, 89:022334, 2014. arXiv:1304.0983 [quant-ph].
Giulio Chiribella, Giacomo Mauro D'Ariano, and Paolo Perinotti. Theoretical framework for quantum networks. Physical Review A, 80(2):022339, 2009. arXiv:0904.4483 [quant-ph].
Giulio Chiribella, Giacomo Mauro D'Ariano, Paolo Perinotti, Dirk Schlingemann, and Reinhard F. Werner. A short impossibility proof of quantum bit commitment. Physics Letters A, 377(15):1076-1087, 2013. arXiv:0905.3801v1 [quant-ph].
Gus Gutoski. Quantum strategies and local operations. PhD thesis, University of Waterloo, 2009. arXiv:1003.0038 [quant-ph].
Gus Gutoski. On a measure of distance for quantum strategies. Journal of Mathematical Physics, 53(3):032202, 2012. arXiv:1008.4636 [quant-ph].
Gus Gutoski and John Watrous. Toward a general theory of quantum games. In Proceedings of the 39th ACM Symposium on Theory of Computing (STOC 2007), pages 565-574, 2007. arXiv:quant-ph/0611234.
Iordanis Kerenidis and Ashwin Nayak. Weak coin flipping with small bias. Information Processing Letters, 89(3):131-135, 2004. arXiv:quant-ph/0206121. URL: http://dx.doi.org/10.1016/j.ipl.2003.07.007.
http://dx.doi.org/10.1016/j.ipl.2003.07.007
Alexei Kitaev. Quantum coin-flipping. Presentation at the 6th Workshop on Quantum Information Processing (QIP 2003), 2002.
Hoi-Kwong Lo and Hoi Fung Chau. Is quantum bit commitment really possible? Physical Review Letters, 78(17):3410-3413, 1997. URL: http://dx.doi.org/10.1103/PhysRevLett.78.3410.
http://dx.doi.org/10.1103/PhysRevLett.78.3410
Hoi-Kwong Lo and Hoi Fung Chau. Why quantum bit commitment and ideal quantum coin tossing are impossible. Physica D: Nonlinear Phenomena, 120(1-2):177-187, 1998. Proceedings of the Fourth Workshop on Physics and Consumption. URL: http://dx.doi.org/10.1016/S0167-2789(98)00053-0.
http://dx.doi.org/10.1016/S0167-2789(98)00053-0
Dominic Mayers. Unconditionally secure quantum bit commitment is impossible. Physical Review Letters, 78(17):3414-3417, 1997. URL: http://dx.doi.org/10.1103/PhysRevLett.78.3414.
http://dx.doi.org/10.1103/PhysRevLett.78.3414
Ashwin Nayak and Peter Shor. Bit-commitment based quantum coin flipping. Physical Review A, 67(1):012304, 2003. arXiv:quant-ph/0206123. URL: http://dx.doi.org/10.1103/PhysRevA.67.012304.
http://dx.doi.org/10.1103/PhysRevA.67.012304
Ashwin Nayak, Jamie Sikora, and Levent Tunçel. Quantum and classical coin-flipping protocols based on bit-commitment and their point games. Available as arXiv.org e-Print quant-ph/1504.04217, 2015.
Ashwin Nayak, Jamie Sikora, and Levent Tunçel. A search for quantum coin-flipping protocols using optimization techniques. Mathematical Programming, 156(1):581-613, 2016.
Jamie Sikora. Simple, near-optimal quantum protocols for die-rolling. In Theory of Quantum Computation, Communication and Cryptography (TQC 2016), pages 1-14, 2016.
Robert W. Spekkens and Terence Rudolph. Degrees of concealment and bindingness in quantum bit commitment protocols. Physical Review A, 65:012310, 2001. URL: http://dx.doi.org/10.1103/PhysRevA.65.012310.
http://dx.doi.org/10.1103/PhysRevA.65.012310
A. Uhlmann. The "transition probability" in the state space of a *-algebra. Reports on Mathematical Physics, 9(2):273-279, 1976.
Salil P. Vadhan. An unconditional study of computational zero knowledge. In 45th Symposium on Foundations of Computer Science (FOCS 2004), 17-19 October 2004, Rome, Italy, Proceedings, pages 176-185. IEEE Computer Society, 2004. URL: http://dx.doi.org/10.1109/FOCS.2004.13.
http://dx.doi.org/10.1109/FOCS.2004.13
John Watrous. Semidefinite programs for completely bounded norms. Theory of Computing, 5:217-238, 2009. arXiv:0901.4709v2 [quant-ph].
John Watrous. Simpler semidefinite programs for completely bounded norms. Chicago Journal of Theoretical Computer Science, 2013.
Stephen Wiesner. Conjugate coding. SIGACT News, 15(1):78-88, 1983. URL: http://dx.doi.org/10.1145/1008908.1008920.
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Minimum Quantum Resources for Strong Non-Locality
We analyse the minimum quantum resources needed to realise strong non-locality, as exemplified e.g. by the classical GHZ construction. It was already known that no two-qubit system, with any finite number of local measurements, can realise strong non-locality. For three-qubit systems, we show that strong non-locality can only be realised in the GHZ SLOCC class, and with equatorial measurements. However, we show that in this class there is an infinite family of states which are pairwise non LU-equivalent that realise strong non-locality with finitely many measurements. These states have decreasing entanglement between one qubit and the other two, necessitating an increasing number of local measurements on the latter.
strong non-locality
maximal non-locality
quantum resources
three-qubit states
9:1-9:20
Regular Paper
Samson
Abramsky
Samson Abramsky
Rui Soares
Barbosa
Rui Soares Barbosa
Giovanni
Carù
Giovanni Carù
Nadish
de Silva
Nadish de Silva
Kohei
Kishida
Kohei Kishida
Shane
Mansfield
Shane Mansfield
10.4230/LIPIcs.TQC.2017.9
Samson Abramsky, Rui Soares Barbosa, Kohei Kishida, Raymond Lal, and Shane Mansfield. Contextuality, cohomology and paradox. In Stephan Kreutzer, editor, 24th EACSL Annual Conference on Computer Science Logic, CSL 2015, September 7-10, 2015, Berlin, Germany, volume 41 of LIPIcs, pages 211-228. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2015. URL: http://dx.doi.org/10.4230/LIPIcs.CSL.2015.211.
http://dx.doi.org/10.4230/LIPIcs.CSL.2015.211
Samson Abramsky, Rui Soares Barbosa, and Shane Mansfield. The contextual fraction as a measure of contextuality. to appear, 2017.
Samson Abramsky and Adam Brandenburger. The sheaf-theoretic structure of non-locality and contextuality. New Journal of Physics, 13(11):113036, 2011. URL: http://dx.doi.org/10.1088/1367-2630/13/11/113036.
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Samson Abramsky, Carmen M. Constantin, and Shenggang Ying. Hardy is (almost) everywhere: nonlocality without inequalities for almost all entangled multipartite states. Information and Computation, 250:3-14, 2016.
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Approximate Reversal of Quantum Gaussian Dynamics
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.
Gaussian dynamics
Petz recovery map
10:1-10:18
Regular Paper
Ludovico
Lami
Ludovico Lami
Siddhartha
Das
Siddhartha Das
Mark M.
Wilde
Mark M. Wilde
10.4230/LIPIcs.TQC.2017.10
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