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Passive decoy-state quantum key distribution with practical light sources

Physical Review A 2010年第2期81卷 022310-022310页

作者： Marcos Curty Xiongfeng Ma Bing Qi Tobias Moroder ETSI Telecomunicación Department of Signal Theory and Communications University of Vigo Campus Universitario E-36310 Vigo (Pontevedra) Spain Institute for Quantum Computing & Department of Physics and Astronomy University of Waterloo N2L 3G1 Waterloo Ontario Canada Center for Quantum Information and Quantum Control Department of Physics and Department of Electrical & Computer Engineering University of Toronto M5S 3G4 Toronto Ontario Canada Quantum Information Theory Group Institute of Theoretical Physics I University of Erlangen-Nürnberg D-91058 Erlangen Germany Max Planck Institute for the Science of Light D-91058 Erlangen Germany

Decoy states have been proven to be a very useful method for significantly enhancing the performance of quantum key distribution systems with practical light sources. Although active modulation of the intensity of the laser pulses is an effective way of preparing decoy states in principle, in practice passive preparation might be desirable in some scenarios. Typical passive schemes involve parametric down-conversion. More recently, it has been shown that phase-randomized weak coherent pulses (WCP) can also be used for the same purpose [M. Curty et al., Opt. Lett. 34, 3238 (2009).] This proposal requires only linear optics together with a simple threshold photon detector, which shows the practical feasibility of the method. Most importantly, the resulting secret key rate is comparable to the one delivered by an active decoy-state setup with an infinite number of decoy settings. In this article we extend these results, now showing specifically the analysis for other practical scenarios with different light sources and photodetectors. In particular, we consider sources emitting thermal states, phase-randomized WCP, and strong coherent light in combination with several types of photodetectors, like, for instance, threshold photon detectors, photon number resolving detectors, and classical photodetectors. Our analysis includes as well the effect that detection inefficiencies and noise in the form of dark counts shown by current threshold detectors might have on the final secret key rate. Moreover, we provide estimations on the effects that statistical fluctuations due to a finite data size can have in practical implementations.

关键词： Photodetectors

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Upper bounds for the secure key rate of the decoy-state quantum key distribution

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Physical Review A 2009年第3期79卷 032335-032335页

作者： Marcos Curty Tobias Moroder Xiongfeng Ma Hoi-Kwong Lo Norbert Lütkenhaus Department of Signal Theory and Communications ETSI Telecomunicación University of Vigo Campus Universitario E-36310 Vigo (Pontevedra) Spain Institute for Quantum Computing University of Waterloo Waterloo Ontario Canada N2L 3G1 Quantum Information Theory Group Institut für Theoretische Physik I and Max-Planck Research Group Institute of Optics Information and Photonics University of Erlangen–Nürnberg 91058 Erlangen Germany Department of Electrical and Computer Engineering and Department of Physics Center for Quantum Information and Quantum Control (CQIQC) University of Toronto Toronto Ontario Canada M5S 3G4

The use of decoy states in quantum key distribution (QKD) has provided a method for substantially increasing the secret key rate and distance that can be covered by QKD protocols with practical signals. The security analysis of these schemes, however, leaves open the possibility that the development of better proof techniques or better classical postprocessing methods might further improve their performance in realistic scenarios. In this paper, we derive upper bounds on the secure key rate for decoy-state QKD. These bounds are based basically only on the classical correlations established by the legitimate users during the quantum communication phase of the protocol. The only assumption about the possible postprocessing methods is that double click events are randomly assigned to single click events. Further, we consider only secure key rates based on the uncalibrated device scenario which assigns imperfections such as detection inefficiency to the eavesdropper. Our analysis relies on two preconditions for secure two-way and one-way QKD. The legitimate users need to prove that there exists no separable state (in the case of two-way QKD) or that there exists no quantum state having a symmetric extension (one-way QKD) that is compatible with the available measurements results. Both criteria have been previously applied to evaluate single-photon implementations of QKD. Here we use them to investigate a realistic source of weak coherent pulses. The resulting upper bounds can be formulated as a convex optimization problem known as a semidefinite program which can be efficiently solved. For the standard four-state QKD protocol, they are quite close to known lower bounds, thus showing that there are clear limits to the further improvement of classical postprocessing techniques in decoy-state QKD.

关键词： quantum cryptography

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Passive sources for the Bennett-Brassard 1984 quantum-key-distribution protocol with practical signals

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Physical Review A 2010年第5期82卷 052325-052325页

作者： Marcos Curty Xiongfeng Ma Hoi-Kwong Lo Norbert Lütkenhaus ETSI Telecomunicación Department of Signal Theory and Communications University of Vigo Campus Universitario E-36310 Vigo Pontevedra Spain Institute for Quantum Computing & Department of Physics and Astronomy University of Waterloo Waterloo Ontario N2L 3G1 Canada Center for Quantum Information and Quantum Control Department of Physics and Department of Electrical & Computer Engineering University of Toronto Toronto Ontario M5S 3G4 Canada

Most experimental realizations of quantum key distribution are based on the Bennett-Brassard 1984 (the so-called BB84) protocol. In a typical optical implementation of this scheme, the sender uses an active source to produce the required BB84 signal states. While active state preparation of BB84 signals is a simple and elegant solution in principle, in practice passive state preparation might be desirable in some scenarios, for instance, in those experimental setups operating at high transmission rates. Passive schemes might also be more robust against side-channel attacks than active sources. Typical passive devices involve parametric down-conversion. In this paper, we show that both coherent light and practical single-photon sources are also suitable for passive generation of BB84 signal states. Our method does not require any externally driven element, but only linear optical components and photodetectors. In the case of coherent light, the resulting key rate is similar to the one delivered by an active source. When the sender uses practical single-photon sources, however, the distance covered by a passive transmitter might be longer than that of an active configuration.

关键词： Side channel attack

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Single-photon quantum key distribution in the presence of loss

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Physical Review A 2007年第5期75卷 052336-052336页

作者： Marcos Curty Tobias Moroder Center for Quantum Information and Quantum Control Department of Physics and Department of Electrical & Computer Engineering University of Toronto Toronto Ontario Canada M5S 3G4 Institute for Quantum Computing University of Waterloo 200 University Avenue West Waterloo Ontario Canada N2L 3G1 Quantum Information Theory Group Institut für Theoretische Physik I and Max-Planck Research Group Institute of Optics Information and Photonics Universität Erlangen-Nürnberg D-91058 Erlangen Germany

We investigate two-way and one-way single-photon quantum key distribution (QKD) protocols in the presence of loss introduced by the quantum channel. Our analysis is based on a simple precondition for secure QKD in each case. In particular, the legitimate users need to prove that there exists no separable state (in the case of two-way QKD), or that there exists no quantum state having a symmetric extension (one-way QKD), that is compatible with the available measurements results. We show that both criteria can be formulated as a convex optimization problem known as a semidefinite program, which can be efficiently solved. Moreover, we prove that the solution to the dual optimization corresponds to the evaluation of an optimal witness operator that belongs to the minimal verification set of them for the given two-way (or one-way) QKD protocol. A positive expectation value of this optimal witness operator states that no secret key can be distilled from the available measurements results. We apply such analysis to several well-known single-photon QKD protocols under losses.

关键词： SEPARABILITY CRITERION NONORTHOGONAL STATES COHERENT STATES CRYPTOGRAPHY PROTOCOL DIFFERENTIATE SECURITY THEOREM PROOF

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Symmetries, graph properties, and quantum speedups

arXiv

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arXiv 2020年

作者： Ben-David, Shalev Childs, Andrew M. Gilyén, András Kretschmer, William Podder, Supartha Wang, Daochen Cheriton School of Computer Science University of Waterloo Canada Department of Computer Science Institute for Advanced Computer Studies University of Maryland United States Joint Center for Quantum Information and Computer Science University of Maryland United States Institute for Quantum Information and Matter California Institute of Technology United States Simons Institute for the Theory of Computing University of California Berkeley United States Department of Computer Science University of Texas Austin United States Department of Mathematics and Statistics University of Ottawa Canada Department of Mathematics University of Maryland United States

Aaronson and Ambainis (2009) and Chailloux (2018) showed that fully symmetric (partial) functions do not admit exponential quantum query speedups. This raises a natural question: how symmetric must a function be before it cannot exhibit a large quantum speedup? In this work, we prove that hypergraph symmetries in the adjacency matrix model allow at most a polynomial separation between randomized and quantum query complexities. We also show that, remarkably, permutation groups constructed out of these symmetries are essentially the only permutation groups that prevent super-polynomial quantum speedups. We prove this by fully characterizing the primitive permutation groups that allow super-polynomial quantum speedups. In contrast, in the adjacency list model for bounded-degree graphs-where graph symmetry is manifested differently-we exhibit a property testing problem that shows an exponential quantum speedup. These results resolve open questions posed by Ambainis, Childs, and Liu (2010) and Montanaro and de Wolf (2013). Copyright © 2020, The Authors. All rights reserved.

关键词： Group theory

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Geometric structure and transversal logic of quantum Reed–Muller codes

arXiv

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arXiv 2024年

作者： Barg, Alexander Coble, Nolan J. Hangleiter, Dominik Kang, Christopher Joint Center for Quantum Information and Computer Science University of Maryland & NIST United States Institute for Systems Research Department of Electrical & Computer Engineering University of Maryland United States Department of Computer Science University of Maryland College Park United States Simons Institute for the Theory of Computing University of California at Berkeley United States Department of Computer Science University of Chicago United States

Designing efficient and noise-tolerant quantum computation protocols generally begins with an understanding of quantum error-correcting codes and their native logical operations. The simplest class of native operations are transversal gates, which are naturally fault-tolerant. In this paper, we aim to characterize the transversal gates of quantum Reed–Muller (RM) codes by exploiting the well-studied properties of their classical counterparts. We start our work by establishing a new geometric characterization of quantum RM codes via the Boolean hypercube and its associated subcube complex. More specifically, a set of stabilizer generators for a quantum RM code can be described via transversal X and Z operators acting on subcubes of particular dimensions. This characterization leads us to define subcube operators composed of single-qubit π/2k Z-rotations that act on subcubes of given dimensions. We first characterize the action of subcube operators on the code space: depending on the dimension of the subcube, these operators either (1) act as a logical identity on the code space, (2) implement non-trivial logic, or (3) rotate a state away from the code space. Second, and more remarkably, we uncover that the logic implemented by these operators corresponds to circuits of multi-controlled-Z gates that have an explicit and simple combinatorial description. Overall, this suite of results yields a comprehensive understanding of a class of natural transversal operators for quantum RM codes. Copyright © 2024, The Authors. All rights reserved.

关键词： quantum computers

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Opacity of Parametric Discrete Event Systems: Models, Decidability, and Algorithms

arXiv

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arXiv 2023年

作者： Deng, Weilin Qiu, Daowen Yang, Jingkai The School of Internet Finance and Information Engineering Guangdong University of Finance Guangzhou510521 China The Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China The School of Mathematics and Statistics Yulin Normal University Yulin537000 China

Finite automata (FAs) model is a popular tool to characterize discrete event systems (DESs) due to its succinctness. However, for some complex systems, it is difficult to describe the necessary details by means of FAs model. In this paper, we consider a kind of extended finite automata (EFAs) in which each transition carries a predicate over state and event parameters. We also consider a type of simplified EFAs, called Event-Parameters EFAs (EP-EFAs), where the state parameters are removed. Based upon these two parametric models, we investigate the problem of opacity analysis for parametric DESs. First of all, it is shown that EFAs model is more expressive than EP-EFAs model. Secondly, it is proved that the opacity properties for EFAs are undecidable in general. Moreover, the decidable opacity properties for EP-EFAs are investigated. We present the verification algorithms for current-state opacity, initial-state opacity and infinite-step opacity, and then discuss the complexity. This paper establishes a preliminary theory for the opacity of parametric DESs, which lays a foundation for the opacity analysis of complex systems. Copyright © 2023, The Authors. All rights reserved.

关键词： Finite automata

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Opacity of Parametric Discrete Event Systems: Models, Decidability, and Algorithms

TechRxiv

引用

TechRxiv 2023年

作者： Deng, Weilin Qiu, Daowen Yang, Jingkai School of Internet Finance and Information Engineering Guangdong University of Finance Guangzhou510521 China Institute of Quantum Computing and Computer Theory School of Computer Science and Engineering Sun Yat-Sen University Guangzhou510006 China School of Mathematics and Statistics Yulin Normal University Yulin537000 China

关键词： Opacity

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quantum Depth in the Random Oracle Model

arXiv

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arXiv 2022年

作者： Arora, Atul Singh Coladangelo, Andrea Coudron, Matthew Gheorghiu, Alexandru Singh, Uttam Waldner, Hendrik Institute for Quantum Information and Matter California Institute of Technology Department of Computing and Mathematical Sciences California Institute of Technology United States University of California Berkeley Simons Institute The Theory of Computing United States Department of Computer Science University of Maryland United States Department of Computer Science and Engineering Chalmers University of Technology Institute for Theoretical Studies ETH Zürich Switzerland Center for Theoretical Physics Polish Academy of Sciences Poland Department of Computer Science University of Maryland Max Planck Institute for Security and Privacy United States

We give a comprehensive characterization of the computational power of shallow quantum circuits combined with classical computation. Specifically, for classes of search problems, we show that the following statements hold, relative to a random oracle: (a) BPPQNCBPP ≠ BQP. This refutes Jozsa's conjecture [Joz05] in the random oracle model. As a result, this gives the first instantiatable separation between the classes by replacing the oracle with a cryptographic hash function, yielding a resolution to one of Aaronson's ten semi-grand challenges in quantum computing [Aar05]. (b) BPPQNC ⊆ QNCBPP and QNCBPP ⊆ BPPQNC. This shows that there is a subtle interplay between classical computation and shallow quantum computation. In fact, for the second separation, we establish that, for some problems, the ability to perform adaptive measurements in a single shallow quantum circuit, is more useful than the ability to perform polynomially many shallow quantum circuits without adaptive measurements. (c) There exists a 2-message proof of quantum depth protocol. Such a protocol allows a classical verifier to efficiently certify that a prover must be performing a computation of some minimum quantum depth. Our proof of quantum depth can be instantiated using the recent proof of quantumness construction by Yamakawa and Zhandry [YZ22]. Copyright © 2022, The Authors. All rights reserved.

关键词： Hash functions

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quantum speedup for twin support vector machine

arXiv

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arXiv 2019年

作者： Ye, Zekun Li, Lvzhou Situ, Haozhen Institute of Computer Science Theory School of Data and Computer Science Sun Yat-sen University Guangzhou510006 China College of Mathematics and Informatics South China Agricultural University Guangzhou510642 China Center for Quantum Computing Pengcheng Laboratory Shenzhen518055 China The Key Laboratory of Machine Intelligence and Advanced Computing Sun Yat-sen University Ministry of Education China

In this work, we investigate how to speed up machine learning tasks based on quantum computation. We show an important classifier in machine learning, the twin support vector machine, can be exponentially speeded up on quantum computers. Specifically, for a training set with m samples which are represented by n-dimensional vectors, the proposed quantum algorithm can learn two non-parallel hyperplanes in O(log mn) time, and then classify a new sample in O(log n) time by comparing the distances from the simple to the two hyperplanes. Note that the classical algorithm requires polynomial time both in the training and classification procedures. Copyright © 2019, The Authors. All rights reserved.

关键词： Classification (of information)

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