Quantum Key Distribution Networks: Challenges and Future Research Issues in Security

Total Page:16

File Type:pdf, Size:1020Kb

Quantum Key Distribution Networks: Challenges and Future Research Issues in Security applied sciences Article Quantum Key Distribution Networks: Challenges and Future Research Issues in Security Chia-Wei Tsai 1 , Chun-Wei Yang 2 , Jason Lin 3 , Yao-Chung Chang 1,* and Ruay-Shiung Chang 4 1 Department of Computer Science and Information Engineering, National Taitung University, No. 369, University Rd., Taitung 95092, Taiwan; [email protected] 2 Master Program for Digital Health Innovation, College of Humanities and Sciences, China Medical University, No. 100, Sec. 1, Jingmao Rd., Beitun Dist., Taichung 406040, Taiwan; [email protected] 3 Department of Computer Science and Engineering, National Chung Hsing University, No. 145, Xingda Rd., South District, Taichung 40227, Taiwan; [email protected] 4 Department of Institute of Information and Decision Sciences, National Taipei University of Business, No.321, Sec. 1, Jinan Rd., Jhongjheng Dist., Taipei City 100025, Taiwan; [email protected] * Correspondence: [email protected] Abstract: A quantum key distribution (QKD) network is proposed to allow QKD protocols to be the infrastructure of the Internet for distributing unconditional security keys instead of existing public-key cryptography based on computationally complex mathematical problems. Numerous countries and research institutes have invested enormous resources to execute correlation studies on QKD networks. Thus, in this study, we surveyed existing QKD network studies and practical field experiments to summarize the research results (e.g., type and architecture of QKD networks, key generating rate, maximum communication distance, and routing protocol). Furthermore, we highlight the three challenges and future research issues in the security of QKD networks and then provide some feasible resolution strategies for these challenges. Citation: Tsai, C.-W.; Yang, C.-W.; Lin, J.; Chang, Y.-C.; Chang, R.-S. Keywords: quantum key distribution; quantum key distribution network; unconditional security Quantum Key Distribution Networks: Challenges and Future Research Issues in Security. Appl. Sci. 2021, 11, 3767. https://doi.org/10.3390/ 1. Introduction app11093767 In response to the rapid development of the Internet and Internet of Things (IoT) Academic Editor: Davide Bacco technologies, digital applications/services have become mainstream in today’s world. This trend allows more information and data to be transmitted over the Internet. Therefore, the Received: 30 March 2021 provision of complete cryptography mechanisms for protecting the confidentiality and Accepted: 19 April 2021 integrity of data and ensuring authentication between the sender and the receiver are some Published: 22 April 2021 of the important issues in the digital age, among which establishing secure cryptography keys through untrusted networks is a fundamental cryptography task. Although existing Publisher’s Note: MDPI stays neutral public-key cryptography based on computationally complex mathematical problems (e.g., with regard to jurisdictional claims in RSA or Diffie Hellman key exchange protocol) can provide the session key distribution published maps and institutional affil- for end users/applications, the session keys distributed by these algorithms belong to iations. theoretical computational security. That is, the computational security keys can be broken using quantum computation. To overcome this issue, some feasible solutions have been proposed, including quantum cryptography, which uses quantum mechanics to design secure communication protocols, and post-quantum cryptography, which shows that Copyright: © 2021 by the authors. complex computational problems are secure against attacks by quantum computers to Licensee MDPI, Basel, Switzerland. design cryptographic algorithms. This article is an open access article In quantum cryptography, Bennet and Brassard [1] used the properties of quan- distributed under the terms and tum mechanics to propose the first quantum key distribution (QKD) protocol—the BB84 conditions of the Creative Commons protocol—which allows two end users/applications to distribute the session keys between Attribution (CC BY) license (https:// each other. Furthermore, some studies [2–4] have proved that the BB84 protocol is an uncon- creativecommons.org/licenses/by/ ditional security protocol; that is, the session key distributed by the BB84 protocol belongs 4.0/). Appl. Sci. 2021, 11, 3767. https://doi.org/10.3390/app11093767 https://www.mdpi.com/journal/applsci Appl. Sci. 2021, 11, 3767 2 of 15 to unconditional security keys. In classical cryptography, only a one-time pad (OTP) can conform to unconditional security ciphers. Following the BB84 protocol, various QKD pro- tocols [5–14] have been proposed. To enhance the practicality of QKD protocols under the existing quantum technologies, the semi-quantum key distribution key protocols [15–17] and measurement device independent (MDI) QKD key protocols [13,18,19] have also been proposed. In addition, various types of quantum communication protocol have been proposed for different applications, including quantum secure direct communication, quantum secret sharing (QSS), quantum private comparison, and quantum information splitting. However, QKD protocols cannot provide the service of key distribution as the fundamental infrastructure instead of existing public-key cryptography in the existing network environment immediately because of limitations of quantum technology (e.g., the reachable distance of qubit transmission and the accuracy of the qubit detector). Moreover, QKD protocols cannot be integrated with existing network protocols immediately because of the specificity of quantum links and network organization. To address the aforementioned problem, the concept and framework of QKD net- works have been proposed [20–48] to enable QKD protocols to assist the remote end users/applications in distributing security keys under the existing network environment. Previous studies [20–35] indicate the architectures, quantum technologies, and experimen- tal results in the field experiments of QKD networks. Improvement methods of the routing algorithms have also been proposed [36–41] along with evaluation metrics of quantum links, in which notably the first quality of service (QoS) mechanism for QKD networks was designed in [39]. Another study [41] proposed a routing algorithm for hybrid QKD networks. A method that uses a QKD network to protect the security of power microgrids was proposed in [42,43]. In addition, for the security issue of QKD networks, [44,45] proposed feasible resolutions for avoiding the assumption that the quantum nodes must be trusted and [46] discussed how classical end users/applications can access session keys securely from QKD networks. In addition, [47] proposed an architecture of a QKD network, a quantum access network, which allows many end users/applications (up to 64 users/applications) to simultaneously distribute the security keys with a central quan- tum node using fiber channels. Then, [48] extended the quantum access network to the n:n framework, that is, n users could distribute security keys with n central quantum nodes simultaneously. Although these studies discussed above obtained remarkable results within the key generating rate, communication distance, architecture of the QKD network, and routing algorithm, there are still some challenges that need to be overcome in the field of security. Therefore, this study aims to summarize the developmental trends and results of the QKD network first. Then, we highlight the challenges that need to be studied further to perfect QKD networks. For the proposed challenges, we have also provided some feasible solutions and strategies to allow researchers to devise complete solutions. The rest of this paper is organized as follows: Section2 reviews the background of the QKD network, and Section3 summarizes the key results in existing QKD networks. For security issues in QKD networks, we highlight the three challenges and future research issues and provide some feasible resolution strategies in Section4. Finally, a brief conclusion is provided. 2. Background to Quantum Key Distribution (QKD) Networks The QKD network is used to extend the range of the QKD protocol, and it consists of several static quantum nodes that have complete quantum capabilities (e.g., generating a single photon/entanglement state, storing qubits, and performing the quantum unitary operation). The quantum nodes execute the QKD protocol (e.g., the BB84 protocol) to distribute secure keys (also called local keys) between the neighboring nodes, and then, the hop-by-hop manner is adopted to assist the remote end users/applications to distribute unconditional security session keys. The QKD network comprises quantum nodes and quantum links, and the framework of the QKD network can be divided into three layers: a communication layer, a key Appl. Sci. 2021, 11, x FOR PEER REVIEW 3 of 15 Appl. Sci. 2021, 11, 3767 3 of 15 The QKD network comprises quantum nodes and quantum links, and the framework of the QKD network can be divided into three layers: a communication layer, a key man- agement layer, and a quantum layer (shown in Figure 1). The communication layer (the management layer, and a quantum layer (shown in Figure1). The communication layer top layer) manages the routing tasks and provides the application interface (API) to allow (the top layer) manages the routing tasks and provides the application interface (API) to the end users/applications to access the secure session keys generated by QKD protocols. allow the end users/applications
Recommended publications
  • 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].
    [Show full text]
  • Large Scale Quantum Key Distribution: Challenges and Solutions
    Large scale quantum key distribution: challenges and solutions QIANG ZHANG,1,2 FEIHU XU,1,2 YU-AO CHEN,1,2 CHENG-ZHI PENG1,2 AND JIAN-WEI PAN1,2,* 1Shanghai Branch, Hefei National Laboratory for Physical Sciences at Microscale and Department of Modern Physics, University of Science and Technology of China, Shanghai, 201315, China 2CAS Center for Excellence and Synergetic Innovation Center in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, P. R. China *[email protected], [email protected] Abstract: Quantum key distribution (QKD) together with one time pad encoding can provide information-theoretical security for communication. Currently, though QKD has been widely deployed in many metropolitan fiber networks, its implementation in a large scale remains experimentally challenging. This letter provides a brief review on the experimental efforts towards the goal of global QKD, including the security of practical QKD with imperfect devices, QKD metropolitan and backbone networks over optical fiber and satellite-based QKD over free space. 1. Introduction Quantum key distribution (QKD) [1,2], together with one time pad (OTP) [3] method, provides a secure means of communication with information-theoretical security based on the basic principle of quantum mechanics. Light is a natural and optimal candidate for the realization of QKD due to its flying nature and its compatibility with today’s fiber-based telecom network. The ultimate goal of the field is to realize a global QKD network for worldwide applications. Tremendous efforts have been put towards this goal [4–6]. Despite significant progresses over the past decades, there are still two major challenges for large-scale QKD network.
    [Show full text]
  • 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.
    [Show full text]
  • Quantum Computation and Complexity Theory
    Quantum computation and complexity theory Course given at the Institut fÈurInformationssysteme, Abteilung fÈurDatenbanken und Expertensysteme, University of Technology Vienna, Wintersemester 1994/95 K. Svozil Institut fÈur Theoretische Physik University of Technology Vienna Wiedner Hauptstraûe 8-10/136 A-1040 Vienna, Austria e-mail: [email protected] December 5, 1994 qct.tex Abstract The Hilbert space formalism of quantum mechanics is reviewed with emphasis on applicationsto quantum computing. Standardinterferomeric techniques are used to construct a physical device capable of universal quantum computation. Some consequences for recursion theory and complexity theory are discussed. hep-th/9412047 06 Dec 94 1 Contents 1 The Quantum of action 3 2 Quantum mechanics for the computer scientist 7 2.1 Hilbert space quantum mechanics ..................... 7 2.2 From single to multiple quanta Ð ªsecondº ®eld quantization ...... 15 2.3 Quantum interference ............................ 17 2.4 Hilbert lattices and quantum logic ..................... 22 2.5 Partial algebras ............................... 24 3 Quantum information theory 25 3.1 Information is physical ........................... 25 3.2 Copying and cloning of qbits ........................ 25 3.3 Context dependence of qbits ........................ 26 3.4 Classical versus quantum tautologies .................... 27 4 Elements of quantum computatability and complexity theory 28 4.1 Universal quantum computers ....................... 30 4.2 Universal quantum networks ........................ 31 4.3 Quantum recursion theory ......................... 35 4.4 Factoring .................................. 36 4.5 Travelling salesman ............................. 36 4.6 Will the strong Church-Turing thesis survive? ............... 37 Appendix 39 A Hilbert space 39 B Fundamental constants of physics and their relations 42 B.1 Fundamental constants of physics ..................... 42 B.2 Conversion tables .............................. 43 B.3 Electromagnetic radiation and other wave phenomena .........
    [Show full text]
  • 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.
    [Show full text]
  • Analysis of Nonlinear Dynamics in a Classical Transmon Circuit
    Analysis of Nonlinear Dynamics in a Classical Transmon Circuit Sasu Tuohino B. Sc. Thesis Department of Physical Sciences Theoretical Physics University of Oulu 2017 Contents 1 Introduction2 2 Classical network theory4 2.1 From electromagnetic fields to circuit elements.........4 2.2 Generalized flux and charge....................6 2.3 Node variables as degrees of freedom...............7 3 Hamiltonians for electric circuits8 3.1 LC Circuit and DC voltage source................8 3.2 Cooper-Pair Box.......................... 10 3.2.1 Josephson junction.................... 10 3.2.2 Dynamics of the Cooper-pair box............. 11 3.3 Transmon qubit.......................... 12 3.3.1 Cavity resonator...................... 12 3.3.2 Shunt capacitance CB .................. 12 3.3.3 Transmon Lagrangian................... 13 3.3.4 Matrix notation in the Legendre transformation..... 14 3.3.5 Hamiltonian of transmon................. 15 4 Classical dynamics of transmon qubit 16 4.1 Equations of motion for transmon................ 16 4.1.1 Relations with voltages.................. 17 4.1.2 Shunt resistances..................... 17 4.1.3 Linearized Josephson inductance............. 18 4.1.4 Relation with currents................... 18 4.2 Control and read-out signals................... 18 4.2.1 Transmission line model.................. 18 4.2.2 Equations of motion for coupled transmission line.... 20 4.3 Quantum notation......................... 22 5 Numerical solutions for equations of motion 23 5.1 Design parameters of the transmon................ 23 5.2 Resonance shift at nonlinear regime............... 24 6 Conclusions 27 1 Abstract The focus of this thesis is on classical dynamics of a transmon qubit. First we introduce the basic concepts of the classical circuit analysis and use this knowledge to derive the Lagrangians and Hamiltonians of an LC circuit, a Cooper-pair box, and ultimately we derive Hamiltonian for a transmon qubit.
    [Show full text]
  • 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 ...................................................................................
    [Show full text]
  • Machine Learning Aided Carrier Recovery in Continuous-Variable Quantum Key Distribution
    Machine Learning Aided Carrier Recovery in Continuous-Variable Quantum Key Distribution T Gehring1, H-M Chin1,2, N Jain1, D Zibar2, and U L Andersen1 1Department of Physics, Technical University of Denmark, Lyngby, Denmark 2Department of Photonics, Technical University of Denmark, Lyngby, Denmark Contact Email: [email protected] Continuous-variable quantum key distribution (CV-QKD) makes use of in-phase and quadrature mod- ulation and coherent detection to distribute secret keys between two parties for data encryption with future proof security. The secret key rate of such CV-QKD systems is limited by excess noise, which is attributed to an eavesdropper. A key issue typical to all modern CV-QKD systems implemented with a reference or pilot signal and an independent local oscillator is controlling the excess noise generated from the fre- quency and phase noise accrued by the transmitter and receiver. Therefore accurate phase estimation and compensation, so-called carrier recovery, is a critical subsystem of CV-QKD. Here, we present the implementation of a machine learning framework based on Bayesian inference, namely an unscented Kalman filter (UKF), for estimation of phase noise and compare it to a standard reference method. Experimental results obtained over a 20 km fiber-optic link indicate that the UKF can ensure very low excess noise even at low pilot powers. The measurements exhibited low variance and high stability in excess noise over a wide range of pilot signal to noise ratios. The machine learning framework may enable CV-QKD systems with low implementation complexity, which can seamlessly work on diverse transmission lines, and it may have applications in the implemen- tation of other cryptographic protocols, cloud-based photonic quantum computing, as well as in quantum sensing..
    [Show full text]
  • Al Transmon Qubits on Silicon-On-Insulator for Quantum Device Integration Andrew J
    Al transmon qubits on silicon-on-insulator for quantum device integration Andrew J. Keller, Paul B. Dieterle, Michael Fang, Brett Berger, Johannes M. Fink, and Oskar Painter Citation: Appl. Phys. Lett. 111, 042603 (2017); doi: 10.1063/1.4994661 View online: http://dx.doi.org/10.1063/1.4994661 View Table of Contents: http://aip.scitation.org/toc/apl/111/4 Published by the American Institute of Physics Articles you may be interested in Superconducting noise bolometer with microwave bias and readout for array applications Applied Physics Letters 111, 042601 (2017); 10.1063/1.4995981 A silicon nanowire heater and thermometer Applied Physics Letters 111, 043504 (2017); 10.1063/1.4985632 Graphitization of self-assembled monolayers using patterned nickel-copper layers Applied Physics Letters 111, 043102 (2017); 10.1063/1.4995412 Perfectly aligned shallow ensemble nitrogen-vacancy centers in (111) diamond Applied Physics Letters 111, 043103 (2017); 10.1063/1.4993160 Broadband conversion of microwaves into propagating spin waves in patterned magnetic structures Applied Physics Letters 111, 042404 (2017); 10.1063/1.4995991 Ferromagnetism in graphene due to charge transfer from atomic Co to graphene Applied Physics Letters 111, 042402 (2017); 10.1063/1.4994814 APPLIED PHYSICS LETTERS 111, 042603 (2017) Al transmon qubits on silicon-on-insulator for quantum device integration Andrew J. Keller,1,2 Paul B. Dieterle,1,2 Michael Fang,1,2 Brett Berger,1,2 Johannes M. Fink,1,2,3 and Oskar Painter1,2,a) 1Kavli Nanoscience Institute and Thomas J. Watson Laboratory of Applied Physics, California Institute of Technology, Pasadena, California 91125, USA 2Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA 3Institute for Science and Technology Austria, 3400 Klosterneuburg, Austria (Received 3 April 2017; accepted 5 July 2017; published online 25 July 2017) We present the fabrication and characterization of an aluminum transmon qubit on a silicon-on-insulator substrate.
    [Show full text]
  • SECURING CLOUDS – the QUANTUM WAY 1 Introduction
    SECURING CLOUDS – THE QUANTUM WAY Marmik Pandya Department of Information Assurance Northeastern University Boston, USA 1 Introduction Quantum mechanics is the study of the small particles that make up the universe – for instance, atoms et al. At such a microscopic level, the laws of classical mechanics fail to explain most of the observed phenomenon. At such a state quantum properties exhibited by particles is quite noticeable. Before we move forward a basic question arises that, what are quantum properties? To answer this question, we'll look at the basis of quantum mechanics – The Heisenberg's Uncertainty Principle. The uncertainty principle states that the more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa. For instance, if you measure the position of an electron revolving around the nucleus an atom, you cannot accurately measure its velocity. If you measure the electron's velocity, you cannot accurately determine its position. Equation for Heisenberg's uncertainty principle: Where σx standard deviation of position, σx the standard deviation of momentum and ħ is the reduced Planck constant, h / 2π. In a practical scenario, this principle is applied to photons. Photons – the smallest measure of light, can exist in all of their possible states at once and also they don’t have any mass. This means that whatever direction a photon can spin in -- say, diagonally, vertically and horizontally -- it does all at once. This is exactly the same as if you constantly moved east, west, north, south, and up-and-down at the same time.
    [Show full text]
  • The Quantum Bases for Human Expertise, Knowledge, and Problem-Solving (Extended Version with Applications)
    A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Bickley, Steve J.; Chan, Ho Fai; Schmidt, Sascha Leonard; Torgler, Benno Working Paper Quantum-sapiens: The quantum bases for human expertise, knowledge, and problem-solving (Extended version with applications) CREMA Working Paper, No. 2021-14 Provided in Cooperation with: CREMA - Center for Research in Economics, Management and the Arts, Zürich Suggested Citation: Bickley, Steve J.; Chan, Ho Fai; Schmidt, Sascha Leonard; Torgler, Benno (2021) : Quantum-sapiens: The quantum bases for human expertise, knowledge, and problem- solving (Extended version with applications), CREMA Working Paper, No. 2021-14, Center for Research in Economics, Management and the Arts (CREMA), Zürich This Version is available at: http://hdl.handle.net/10419/234629 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten Nutzungsrechte.
    [Show full text]
  • 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.
    [Show full text]