Simulation of BB84 Quantum Key Distribution in Depolarizing Channel
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Security of Quantum Key Distribution with Entangled Qutrits
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by CERN Document Server Security of Quantum Key Distribution with Entangled Qutrits. Thomas Durt,1 Nicolas J. Cerf,2 Nicolas Gisin,3 and Marek Zukowski˙ 4 1 Toegepaste Natuurkunde en Fotonica, Theoeretische Natuurkunde, Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium 2 Ecole Polytechnique, CP 165, Universit´e Libre de Bruxelles, 1050 Brussels, Belgium 3 Group of Applied Physics - Optique, Universit´e de Gen`eve, 20 rue de l’Ecole de M´edecine, Gen`eve 4, Switzerland, 4Instytut Fizyki Teoretycznej i Astrofizyki Uniwersytet, Gda´nski, PL-80-952 Gda´nsk, Poland July 2002 Abstract The study of quantum cryptography and quantum non-locality have traditionnally been based on two-level quantum systems (qubits). In this paper we consider a general- isation of Ekert's cryptographic protocol[20] where qubits are replaced by qutrits. The security of this protocol is related to non-locality, in analogy with Ekert's protocol. In order to study its robustness against the optimal individual attacks, we derive the infor- mation gained by a potential eavesdropper applying a cloning-based attack. Introduction Quantum cryptography aims at transmitting a random key in such a way that the presence of an eavesdropper that monitors the communication is revealed by disturbances in the transmission of the key (for a review, see e.g. [21]). Practically, it is enough in order to realize a crypto- graphic protocol that the key signal is encoded into quantum states that belong to incompatible bases, as in the original protocol of Bennett and Brassard[4]. -
Pilot Quantum Error Correction for Global
Pilot Quantum Error Correction for Global- Scale Quantum Communications Laszlo Gyongyosi*1,2, Member, IEEE, Sandor Imre1, Member, IEEE 1Quantum Technologies Laboratory, Department of Telecommunications Budapest University of Technology and Economics 2 Magyar tudosok krt, H-1111, Budapest, Hungary 2Information Systems Research Group, Mathematics and Natural Sciences Hungarian Academy of Sciences H-1518, Budapest, Hungary *[email protected] Real global-scale quantum communications and quantum key distribution systems cannot be implemented by the current fiber and free-space links. These links have high attenuation, low polarization-preserving capability or extreme sensitivity to the environment. A potential solution to the problem is the space-earth quantum channels. These channels have no absorption since the signal states are propagated in empty space, however a small fraction of these channels is in the atmosphere, which causes slight depolarizing effect. Furthermore, the relative motion of the ground station and the satellite causes a rotation in the polarization of the quantum states. In the current approaches to compensate for these types of polarization errors, high computational costs and extra physical apparatuses are required. Here we introduce a novel approach which breaks with the traditional views of currently developed quantum-error correction schemes. The proposed solution can be applied to fix the polarization errors which are critical in space-earth quantum communication systems. The channel coding scheme provides capacity-achieving communication over slightly depolarizing space-earth channels. I. Introduction Quantum error-correction schemes use different techniques to correct the various possible errors which occur in a quantum channel. In the first decade of the 21st century, many revolutionary properties of quantum channels were discovered [12-16], [19-22] however the efficient error- correction in quantum systems is still a challenge. -
Analysis of Quantum Error-Correcting Codes: Symplectic Lattice Codes and Toric Codes
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Caltech Theses and Dissertations Analysis of quantum error-correcting codes: symplectic lattice codes and toric codes Thesis by James William Harrington Advisor John Preskill In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy California Institute of Technology Pasadena, California 2004 (Defended May 17, 2004) ii c 2004 James William Harrington All rights Reserved iii Acknowledgements I can do all things through Christ, who strengthens me. Phillipians 4:13 (NKJV) I wish to acknowledge first of all my parents, brothers, and grandmother for all of their love, prayers, and support. Thanks to my advisor, John Preskill, for his generous support of my graduate studies, for introducing me to the studies of quantum error correction, and for encouraging me to pursue challenging questions in this fascinating field. Over the years I have benefited greatly from stimulating discussions on the subject of quantum information with Anura Abeyesinge, Charlene Ahn, Dave Ba- con, Dave Beckman, Charlie Bennett, Sergey Bravyi, Carl Caves, Isaac Chenchiah, Keng-Hwee Chiam, Richard Cleve, John Cortese, Sumit Daftuar, Ivan Deutsch, Andrew Doherty, Jon Dowling, Bryan Eastin, Steven van Enk, Chris Fuchs, Sho- hini Ghose, Daniel Gottesman, Ted Harder, Patrick Hayden, Richard Hughes, Deborah Jackson, Alexei Kitaev, Greg Kuperberg, Andrew Landahl, Chris Lee, Debbie Leung, Carlos Mochon, Michael Nielsen, Smith Nielsen, Harold Ollivier, Tobias Osborne, Michael Postol, Philippe Pouliot, Marco Pravia, John Preskill, Eric Rains, Robert Raussendorf, Joe Renes, Deborah Santamore, Yaoyun Shi, Pe- ter Shor, Marcus Silva, Graeme Smith, Jennifer Sokol, Federico Spedalieri, Rene Stock, Francis Su, Jacob Taylor, Ben Toner, Guifre Vidal, and Mas Yamada. -
Progress in Satellite Quantum Key Distribution
www.nature.com/npjqi REVIEW ARTICLE OPEN Progress in satellite quantum key distribution Robert Bedington 1, Juan Miguel Arrazola1 and Alexander Ling1,2 Quantum key distribution (QKD) is a family of protocols for growing a private encryption key between two parties. Despite much progress, all ground-based QKD approaches have a distance limit due to atmospheric losses or in-fibre attenuation. These limitations make purely ground-based systems impractical for a global distribution network. However, the range of communication may be extended by employing satellites equipped with high-quality optical links. This manuscript summarizes research and development which is beginning to enable QKD with satellites. It includes a discussion of protocols, infrastructure, and the technical challenges involved with implementing such systems, as well as a top level summary of on-going satellite QKD initiatives around the world. npj Quantum Information (2017) 3:30 ; doi:10.1038/s41534-017-0031-5 INTRODUCTION losses that increase exponentially with distance, greatly limiting Quantum key distribution (QKD) is a relatively new cryptographic the secure key rates that can be achieved over long ranges. primitive for establishing a private encryption key between two For any pure-loss channel with transmittance η, it has been parties. The concept has rapidly matured into a commercial shown that the secure key rate per mode of any QKD protocol 5, 6, 7 technology since the first proposal emerged in 1984,1 largely scales linearly with η for small η. This places a fundamental because of a very attractive proposition: the security of QKD is not limit to the maximum distance attainable by QKD protocols based on the computational hardness of solving mathematical relying on direct transmission. -
Practical Quantum Key Distribution Based on the BB84 Protocol
Practical Quantum Key Distribution based on the BB84 protocol A. Ruiz-Alba, D. Calvo, V. Garcia-Muñoz, A. Martinez, W. Amaya, J.G. Rozo, J. Mora, J. Capmany Instituto de Telecomunicaciones y Aplicaciones Multimedia, Universitat Politècnica de València, 8G Building-access D-Camino de Vera s/n-46022 Valencia (Spain) Corresponding author: [email protected] Abstract relies on photon sources and the so-called pho- ton guns are far from ready. An alternative and This paper provides a review of the most impor- also a complementary approach to increase the tant and widely used Quantum Key Distribution bit rate is to make QKD systems work in paral- systems and then describes our recently pro- lel. This simple engineering approach becomes a posed scheme based on Subcarrier Multiplexing challenge when working with quantum systems: that opens the possibility of parallel Quantum The system should work in parallel but still rely Key Distribution. We report the first-ever ex- on just one source and its security should still be perimental implementation of parallel quantum guaranteed by the principles of quantum me- key distribution using this technique showing a chanics both when Alice prepares the photons maximum multiplexing gain. and when Bob “measures” the incoming states. At the same time the multiplexing technique Keywords: Optical fiber communications, quan- should be safe to Eve gaining any information. tum information, quantum key distribution, sub- carrier multiplexing. In this context, recent progress in the literature [4] remarks that photonics is a key enabling technology for implementing commercial QKD 1. Introduction systems to become a competitive technology in Information Security. -
Quantum Key Distribution Protocols and Applications
Quantum Key Distribution Protocols and Applications Sheila Cobourne Technical Report RHUL{MA{2011{05 8th March 2011 Department of Mathematics Royal Holloway, University of London Egham, Surrey TW20 0EX, England http://www.rhul.ac.uk/mathematics/techreports Title: Quantum Key Distribution – Protocols and Applications Name: Sheila Cobourne Student Number: 100627811 Supervisor: Carlos Cid Submitted as part of the requirements for the award of the MSc in Information Security at Royal Holloway, University of London. I declare that this assignment is all my own work and that I have acknowledged all quotations from the published or unpublished works of other people. I declare that I have also read the statements on plagiarism in Section 1 of the Regulations Governing Examination and Assessment Offences and in accordance with it I submit this project report as my own work. Signature: Date: Acknowledgements I would like to thank Carlos Cid for his helpful suggestions and guidance during this project. Also, I would like to express my appreciation to the lecturers at Royal Holloway who have increased my understanding of Information Security immensely over the course of the MSc, without which this project would not have been possible. Contents Table of Figures ................................................................................................... 6 Executive Summary ............................................................................................. 7 Chapter 1 Introduction ................................................................................... -
QIP 2010 Tutorial and Scientific Programmes
QIP 2010 15th – 22nd January, Zürich, Switzerland Tutorial and Scientific Programmes asymptotically large number of channel uses. Such “regularized” formulas tell us Friday, 15th January very little. The purpose of this talk is to give an overview of what we know about 10:00 – 17:10 Jiannis Pachos (Univ. Leeds) this need for regularization, when and why it happens, and what it means. I will Why should anyone care about computing with anyons? focus on the quantum capacity of a quantum channel, which is the case we understand best. This is a short course in topological quantum computation. The topics to be covered include: 1. Introduction to anyons and topological models. 15:00 – 16:55 Daniel Nagaj (Slovak Academy of Sciences) 2. Quantum Double Models. These are stabilizer codes, that can be described Local Hamiltonians in quantum computation very much like quantum error correcting codes. They include the toric code This talk is about two Hamiltonian Complexity questions. First, how hard is it to and various extensions. compute the ground state properties of quantum systems with local Hamiltonians? 3. The Jones polynomials, their relation to anyons and their approximation by Second, which spin systems with time-independent (and perhaps, translationally- quantum algorithms. invariant) local interactions could be used for universal computation? 4. Overview of current state of topological quantum computation and open Aiming at a participant without previous understanding of complexity theory, we will discuss two locally-constrained quantum problems: k-local Hamiltonian and questions. quantum k-SAT. Learning the techniques of Kitaev and others along the way, our first goal is the understanding of QMA-completeness of these problems. -
Reliably Distinguishing States in Qutrit Channels Using One-Way LOCC
Reliably distinguishing states in qutrit channels using one-way LOCC Christopher King Department of Mathematics, Northeastern University, Boston MA 02115 Daniel Matysiak College of Computer and Information Science, Northeastern University, Boston MA 02115 July 15, 2018 Abstract We present numerical evidence showing that any three-dimensional subspace of C3 ⊗ Cn has an orthonormal basis which can be reliably dis- tinguished using one-way LOCC, where a measurement is made first on the 3-dimensional part and the result used to select an optimal measure- ment on the n-dimensional part. This conjecture has implications for the LOCC-assisted capacity of certain quantum channels, where coordinated measurements are made on the system and environment. By measuring first in the environment, the conjecture would imply that the environment- arXiv:quant-ph/0510004v1 1 Oct 2005 assisted classical capacity of any rank three channel is at least log 3. Sim- ilarly by measuring first on the system side, the conjecture would imply that the environment-assisting classical capacity of any qutrit channel is log 3. We also show that one-way LOCC is not symmetric, by providing an example of a qutrit channel whose environment-assisted classical capacity is less than log 3. 1 1 Introduction and statement of results The noise in a quantum channel arises from its interaction with the environment. This viewpoint is expressed concisely in the Lindblad-Stinespring representation [6, 8]: Φ(|ψihψ|)= Tr U(|ψihψ|⊗|ǫihǫ|)U ∗ (1) E Here E is the state space of the environment, which is assumed to be initially prepared in a pure state |ǫi. -
Lecture 12: Quantum Key Distribution. Secret Key. BB84, E91 and B92 Protocols. Continuous-Variable Protocols. 1. Secret Key. A
Lecture 12: Quantum key distribution. Secret key. BB84, E91 and B92 protocols. Continuous-variable protocols. 1. Secret key. According to the Vernam theorem, any message (for instance, consisting of binary symbols, 01010101010101), can be encoded in an absolutely secret way if the one uses a secret key of the same length. A key is also a sequence, for instance, 01110001010001. The encoding is done by adding the message and the key modulo 2: 00100100000100. The one who knows the key can decode the encoded message by adding the key to the message modulo 2. The important thing is that the key should be used only once. It is exactly this way that classical cryptography works. Therefore the only task of quantum cryptography is to distribute the secret key between just two users (conventionally called Alice and Bob). This is Quantum Key Distribution (QKD). 2. BB84 protocol, proposed in 1984 by Bennett and Brassard – that’s where the name comes from. The idea is to encode every bit of the secret key into the polarization state of a single photon. Because the polarization state of a single photon cannot be measured without destroying this photon, this information will be ‘fragile’ and not available to the eavesdropper. Any eavesdropper (called Eve) will have to detect the photon, and then she will either reveal herself or will have to re-send this photon. But then she will inevitably send a photon with a wrong polarization state. This will lead to errors, and again the eavesdropper will reveal herself. The protocol then runs as follows. -
Potential Capacities of Quantum Channels 2
WINTER AND YANG: POTENTIAL CAPACITIES OF QUANTUM CHANNELS 1 Potential Capacities of Quantum Channels Andreas Winter and Dong Yang Abstract—We introduce potential capacities of quantum chan- Entangled inputs between different quantum channels open the nels in an operational way and provide upper bounds for these door to all kinds of effects that are impossible in classical quantities, which quantify the ultimate limit of usefulness of a information theory. An extreme phenomenon is superactivation channel for a given task in the best possible context. Unfortunately, except for a few isolated cases, potential capac- [13]; there exist two quantum channels that cannot transmit ities seem to be as hard to compute as their “plain” analogues. quantum information when they are used individually, but can We thus study upper bounds on some potential capacities: For transmit at positive rate when they are used together. the classical capacity, we give an upper bound in terms of the The phenomenon of superactivation, and more broadly of entanglement of formation. To establish a bound for the quantum super-additivity, implies that the capacity of a quantum channel and private capacity, we first “lift” the channel to a Hadamard channel and then prove that the quantum and private capacity does not adequately characterize the channel, since the utility of a Hadamard channel is strongly additive, implying that for of the channel depends on what other contextual channels are these channels, potential and plain capacity are equal. Employing available. So it is natural to ask the following question: What these upper bounds we show that if a channel is noisy, however is the maximum possible capability of a channel to transmit close it is to the noiseless channel, then it cannot be activated information when it is used in combination with any other into the noiseless channel by any other contextual channel; this conclusion holds for all the three capacities. -
Quantum Cryptography: from Theory to Practice
Quantum cryptography: from theory to practice Eleni Diamanti Laboratoire Traitement et Communication de l’Information CNRS – Télécom ParisTech 1 with Anna Pappa, André Chailloux, Iordanis Kerenidis Two-party secure communications: QKD Alice and Bob trust each other but not the channel Primitive for message exchange: key distribution BB84 QKD protocol: possibly the precursor of the entire field 2 Jouguet, Kunz-Jacques, Leverrier, Grangier, D, Nature Photon. 2013 3 Scarani et al, Rev. Mod. Phys. 2009 Two-party secure communications: QKD Information-theoretic security is possible and feasible! Theory adapted to experimental imperfections 2000: Using laser sources opens a disastrous security loophole in BB84 photon number splitting attacks Brassard, Lütkenhaus, Mor, Sanders, Phys. Rev. Lett. 2000 Solution: Decoy state BB84 protocol, and other Lo, Ma, Chen, Phys. Rev. Lett. 2004 2010: Quantum hacking: setup vulnerabilities not taken into account in security proofs Lydersen et al, Nature Photon. 2010 Solution: Exhaustive search for side channels and updated security proofs? Device independence? Measurement device independence? 4 Two-party secure communications: beyond QKD Alice and Bob do not trust each other Primitives for joint operations: bit commitment, coin flipping, oblivious transfer Until recently relatively ignored by physicists perfect unconditionally secure protocols are impossible, but imperfect protocols with information-theoretic security exist ideal framework to demonstrate quantum advantage protocols require inaccessible -
Gr Qkd 003 V2.1.1 (2018-03)
ETSI GR QKD 003 V2.1.1 (2018-03) GROUP REPORT Quantum Key Distribution (QKD); Components and Internal Interfaces Disclaimer The present document has been produced and approved by the Group Quantum Key Distribution (QKD) ETSI Industry Specification Group (ISG) and represents the views of those members who participated in this ISG. It does not necessarily represent the views of the entire ETSI membership. 2 ETSI GR QKD 003 V2.1.1 (2018-03) Reference RGR/QKD-003ed2 Keywords interface, quantum key distribution ETSI 650 Route des Lucioles F-06921 Sophia Antipolis Cedex - FRANCE Tel.: +33 4 92 94 42 00 Fax: +33 4 93 65 47 16 Siret N° 348 623 562 00017 - NAF 742 C Association à but non lucratif enregistrée à la Sous-Préfecture de Grasse (06) N° 7803/88 Important notice The present document can be downloaded from: http://www.etsi.org/standards-search The present document may be made available in electronic versions and/or in print. The content of any electronic and/or print versions of the present document shall not be modified without the prior written authorization of ETSI. In case of any existing or perceived difference in contents between such versions and/or in print, the only prevailing document is the print of the Portable Document Format (PDF) version kept on a specific network drive within ETSI Secretariat. Users of the present document should be aware that the document may be subject to revision or change of status. Information on the current status of this and other ETSI documents is available at https://portal.etsi.org/TB/ETSIDeliverableStatus.aspx If you find errors in the present document, please send your comment to one of the following services: https://portal.etsi.org/People/CommiteeSupportStaff.aspx Copyright Notification No part may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm except as authorized by written permission of ETSI.