Introduction to Quantum Key Distribution
|
|
- Adele Lawson
- 5 years ago
- Views:
Transcription
1 Fakultät für Physik Ludwig-Maximilians-Universität München January 2010
2 Overview Introduction Security Proof
3 Introduction What is information? A mathematical concept describing knowledge. Basic unit is the bit 0 / 1. A physical concept 0 ˆ= and 1 ˆ=
4 Introduction What is information? A mathematical concept describing knowledge. Basic unit is the bit 0 / 1. A physical concept 0 ˆ= and 1 ˆ= The world is not made up of light switches, the world is made up of atoms and photons Atoms and photons are described by quantum mechanics The spin of an atom describes the information we have about it
5 Introduction spin- 1 2 system: points on the sphere unit of information is the quantum bit or qubit
6 Introduction spin- 1 2 system: points on the sphere unit of information is the quantum bit or qubit we can manipulate and transmit qubits ion trap optical fibre
7 Introduction Quantum Information Science Quantum Computation Shor s Factoring Algorithm Quantum Information Theory Quantum Communication Entanglement Quantum Cryptography Online Games Foundations of Quantum Mechanics Bell Inequalities
8 Alice und Bob want to communicate in secrecy, but their phone is tapped. Eve Alice phone Bob
9 Alice und Bob want to communicate in secrecy, but their phone is tapped. Eve Alice phone Bob If they share key (string of secret random numbers), Alice Eve Bob message +key cipher cipher - key message cipher is random and message secure (Vernam, 1926)
10 Alice und Bob want to communicate in secrecy, but their phone is tapped. Eve Alice phone Bob If they share key (string of secret random numbers), Alice Eve Bob cipher is random and message secure (Vernam, 1926)
11 key is as long as the message Shannon (1949): this is optimal secret communication ˆ= key distribution
12 key is as long as the message Shannon (1949): this is optimal secret communication ˆ= key distribution possible key distribution schemes:
13 key is as long as the message Shannon (1949): this is optimal secret communication ˆ= key distribution possible key distribution schemes: Alice and Bob meet impractical
14 key is as long as the message Shannon (1949): this is optimal secret communication ˆ= key distribution possible key distribution schemes: Alice and Bob meet impractical Weaker level of security assumptions on speed of Eve s computer (public key cryptography) assumptions on size of Eve s harddrive (bounded storage model)
15 key is as long as the message Shannon (1949): this is optimal secret communication ˆ= key distribution possible key distribution schemes: Alice and Bob meet impractical Weaker level of security assumptions on speed of Eve s computer (public key cryptography) assumptions on size of Eve s harddrive (bounded storage model) Use quantum mechanical effects (Bennett & Brassard 1984, Ekert 1991)
16 prepare & measure (Wiesner 1970 s, Bennett & Brassard 1984) Eve Alice glass fibre phone Bob
17 prepare & measure (Wiesner 1970 s, Bennett & Brassard 1984) Eve Alice glass fibre phone Bob Security guaranteed by uncertainty principle Alice sends eigenstates of σ z or σ x. Bob measures observable σ z or σ x. They tell each other the observable, but not the result. They should obtain the same result when they used the same observable key If Eve measures in the wrong observable, they have an error with probability 1 2, since [σ z, σ x ] 0.
18 entanglement-based (Ekert 1991) Eve Alice glass fibre phone Bob
19 entanglement-based (Ekert 1991) Eve Alice glass fibre phone Bob Security guaranteed by monogamy of entanglement Alice and Bob check (Bell inequality): ψ ABE? = 1 2 ( 0 A 0 B + 1 A 1 B ) φ E. If YES: Eve does not know their measurement results. Results are random key If NO: they abort the protocol.
20 Entangled state of two qubits 1 2 ( 0 A 0 B + 1 A 1 B )
21 Entangled state of two qubits 1 2 ( 0 A 0 B + 1 A 1 B ) New basis + = 1 ( ) = 1 ( 0 1 ) 2 2 easy calculation 1 ( 0 A 0 B + 1 A 1 B ) = 1 ( + A + B + A B ) 2 2
22 Entangled state of two qubits 1 2 ( 0 A 0 B + 1 A 1 B ) New basis + = 1 ( ) = 1 ( 0 1 ) 2 2 easy calculation 1 ( 0 A 0 B + 1 A 1 B ) = 1 ( + A + B + A B ) 2 2 If Alice and Bob measure observable σ z same result If Alice and Bob measure observable σ x same result
23 Entangled state of two qubits 1 2 ( 0 A 0 B + 1 A 1 B ) New basis + = 1 ( ) = 1 ( 0 1 ) 2 2 easy calculation 1 ( 0 A 0 B + 1 A 1 B ) = 1 ( + A + B + A B ) 2 2 If Alice and Bob measure observable σ z same result If Alice and Bob measure observable σ x same result Converse is true, too: same measurement result they have state 1 2 ( 0 A 0 B + 1 A 1 B ) Alice and Bob can test whether or not they have the state 1 2 ( 0 A 0 B + 1 A 1 B )!
24 Assume that Alice and Bob have the state φ AB = 1 2 ( 0 A 0 B + 1 A 1 B ) and measure in the same basis. Can someone else guess the result?
25 Assume that Alice and Bob have the state φ AB = 1 2 ( 0 A 0 B + 1 A 1 B ) and measure in the same basis. Can someone else guess the result? No! The measurement result is secure! Total state of Alice, Bob and Eve ψ ABE = φ AB φ E, because Alice and Bob have a pure state Eve is not at all correlated with Alice and Bob! Monogamy of entanglement Try: ψ ABE = 1 2 ( 0 A 0 B 0 E + 1 A 1 B 1 E ) ρ AB = 1 2 ( 0 A 0 B 0 A 0 B + 1 A 1 B 1 A 1 B ) different from φ φ AB = 1 2 ( 0 A 0 B 0 A 0 B + 1 A 1 B 0 A 0 B + 0 A 0 B 1 A 1 B + 1 A 1 B 1 A 1 B )
26 The Protocol Distribution Eve 1 Alice glass fibre 1 1 Bob
27 The Protocol Distribution Eve Alice 1 2 glass fibre Bob
28 The Protocol Distribution Eve Alice 1 2 n Bob glass fibre 1 2 n 1 2 n
29 The Protocol Distribution Eve Alice 1 2 n Bob glass fibre 1 2 n 1 2 n Measurement with σ x or σ z
30 The Protocol Distribution Eve Alice 1 2 n Bob glass fibre 1 2 n 1 2 n Measurement with σ x or σ z Error-free? φ AB? = 1 2 ( 0 A 0 B + 1 A 1 B ) phone
31 The Protocol Distribution Eve Alice 1 2 n Bob glass fibre 1 2 n 1 2 n Measurement with σ x or σ z Error-free? φ AB? = 1 2 ( 0 A 0 B + 1 A 1 B ) phone If YES: key. If NO: no key
32 entanglement key key perfectly secure communication not possible with classical physics future (quantum) technology!
33 Security Proof The Protocol Distribution Eve Alice 1 2 n Bob glass fibre 1 2 n 1 2 n Measurement with σ x or σ z Error-free? φ AB? = 1 2 ( 0 A 0 B + 1 A 1 B ) phone If YES: key. If NO: no key
34 Security Proof Honest Eve would distribute Ψ n ABC = ψ n ABE bits are independent ψ ABE = φ AB φ E Eve knows nothing φ AB = 1 ( 0 A 0 B + 1 A 1 B ) bits are random 2 Alice and Bob need to test whether Eve is honest or not.
35 Security Proof If Eve sends states of the form Ψ n ABC = ψ n ABE Alice and Bob test (on a subset): Are the pairs are of the form φ AB = 1 2 ( 0 A 0 B + 1 A 1 B ) i.e. is the data error-free? If YES, standard statistical analysis implies (almost) all remaining triples are of the form φ AB φ E resulting bits are (almost) identical and random Eve has (almost) no information about bits Alice and Bob perform error correction Alice and Bob delete a few random bits Eve has no information about remaining bits (privacy amplification) key If NO, abort the protocol
36 Security Proof The Protocol Distribution Ψ n ABC = ψ n ABE Measurement Alice Eve 1 2 n Bob 1 2 n 1 2 n compare subset Error Estimation φ AB? = 1 2 ( 0 A 0 B + 1 A 1 B ) NO: Abort protocol YES: error correction & privacy amplification
37 Security Proof Proof works as long as Ψ n ABC = ψ n ABE. Alice Bob But why should Eve prepare such a state? Why not the following? Alice Bob
38 Security Proof De Finetti Theorem (Diaconis and Freedman, 1980) Drawing balls from an urn with or without replacement results in almost the same probability distribution. If k are drawn out of n, then P k i p i Q k i 1 const k n.
39 Security Proof Quantum generalisations have been obtained by Størmer, Hudson & Moody, and Werner et al.. (n = ) Quantum De Finetti Theorem Ch., König, Mitchison, Renner, Comm. Math. Phys. 273, (2007) Let ρ n be a permutation-invariant state πρπ 1 = ρ, then ρ k i p i σ k i 1 const k n const = 4d 2 d dependence is necessary classically, k 2 /n bound exists
40 Security Proof Proof sketch reduce problem to the Bosonic case πρ = ρ, for all π S n ρ lives on Sym n (C d ) Sym k (C d ) Sym n k (C d ) measurement with SU(d) coherent states φ n = φ k φ n k post-measurement on k particles: ρ k post = µ(φ) φ φ k gentle measurement ρ k ρ k post (error k/n). generalises to arbitrary irreducible representations of SU(d).
41 Security Proof Alice and Bob select a random sample of pairs (after pairs have been distributed!) Alice Bob Alice Quantum de Finetti Bob can use proof from before (tensor product) proof of the security of!
42 Security Proof Closer look: deviation from perfect key (due to quantum de Finetti theorem) ɛ k/n n: number of pairs that Eve distributed k: number of bits of key
43 Security Proof Closer look: deviation from perfect key (due to quantum de Finetti theorem) ɛ k/n n: number of pairs that Eve distributed k: number of bits of key key rate r k/n ɛ 0 not good enough need replacement for de Finetti theorem Renner s exp. de Finetti theorem, involved, non-optimal
44 Security Proof Post-selection Technique Ch., König, Renner, Phys. Rev. Lett. 102, (2009) Idea: Compare actual protocol with an ideal protocol (which produces perfect key) Theorem about permutation-covariant maps, rather than permutation-invariant states.
45 Security Proof Post-selection Technique Ch., König, Renner, Phys. Rev. Lett. 102, (2009) Idea: Compare actual protocol with an ideal protocol (which produces perfect key) Theorem about permutation-covariant maps, rather than permutation-invariant states. In QKD: r k/n 1 δ and ɛ exp( δ 2 n) optimal parameters relevant in current experiments (since n 10 5 ) Eve s best attack Ψ n ABE = ψ ABE n conceptual and technical simplification of security proofs Other applications: Quantum Reverse Shannon Theorem Berta, Ch. and Renner, arxiv:
Quantum Cryptography. Areas for Discussion. Quantum Cryptography. Photons. Photons. Photons. MSc Distributed Systems and Security
Areas for Discussion Joseph Spring Department of Computer Science MSc Distributed Systems and Security Introduction Photons Quantum Key Distribution Protocols BB84 A 4 state QKD Protocol B9 A state QKD
More informationPing Pong Protocol & Auto-compensation
Ping Pong Protocol & Auto-compensation Adam de la Zerda For QIP seminar Spring 2004 02.06.04 Outline Introduction to QKD protocols + motivation Ping-Pong protocol Security Analysis for Ping-Pong Protocol
More informationQuantum key distribution for the lazy and careless
Quantum key distribution for the lazy and careless Noisy preprocessing and twisted states Joseph M. Renes Theoretical Quantum Physics, Institut für Angewandte Physik Technische Universität Darmstadt Center
More information+ = OTP + QKD = QC. ψ = a. OTP One-Time Pad QKD Quantum Key Distribution QC Quantum Cryptography. θ = 135 o state 1
Quantum Cryptography Quantum Cryptography Presented by: Shubhra Mittal Instructor: Dr. Stefan Robila Intranet & Internet Security (CMPT-585-) Fall 28 Montclair State University, New Jersey Introduction
More informationPractical quantum-key. key- distribution post-processing
Practical quantum-key key- distribution post-processing processing Xiongfeng Ma 马雄峰 IQC, University of Waterloo Chi-Hang Fred Fung, Jean-Christian Boileau, Hoi Fung Chau arxiv:0904.1994 Hoi-Kwong Lo, Norbert
More informationQuantum Technologies for Cryptography
University of Sydney 11 July 2018 Quantum Technologies for Cryptography Mario Berta (Department of Computing) marioberta.info Quantum Information Science Understanding quantum systems (e.g., single atoms
More information5th March Unconditional Security of Quantum Key Distribution With Practical Devices. Hermen Jan Hupkes
5th March 2004 Unconditional Security of Quantum Key Distribution With Practical Devices Hermen Jan Hupkes The setting Alice wants to send a message to Bob. Channel is dangerous and vulnerable to attack.
More informationUnconditional Security of the Bennett 1992 quantum key-distribution protocol over a lossy and noisy channel
Unconditional Security of the Bennett 1992 quantum key-distribution protocol over a lossy and noisy channel Kiyoshi Tamaki *Perimeter Institute for Theoretical Physics Collaboration with Masato Koashi
More informationSecrecy and the Quantum
Secrecy and the Quantum Benjamin Schumacher Department of Physics Kenyon College Bright Horizons 35 (July, 2018) Keeping secrets Communication Alice sound waves, photons, electrical signals, paper and
More informationPerfectly secure cipher system.
Perfectly secure cipher system Arindam Mitra Lakurdhi, Tikarhat Road, Burdwan 713102 India Abstract We present a perfectly secure cipher system based on the concept of fake bits which has never been used
More informationQuantum Cryptography
Quantum Cryptography (Notes for Course on Quantum Computation and Information Theory. Sec. 13) Robert B. Griffiths Version of 26 March 2003 References: Gisin = N. Gisin et al., Rev. Mod. Phys. 74, 145
More informationChapter 13: Photons for quantum information. Quantum only tasks. Teleportation. Superdense coding. Quantum key distribution
Chapter 13: Photons for quantum information Quantum only tasks Teleportation Superdense coding Quantum key distribution Quantum teleportation (Theory: Bennett et al. 1993; Experiments: many, by now) Teleportation
More informationCryptography in a quantum world
T School of Informatics, University of Edinburgh 25th October 2016 E H U N I V E R S I T Y O H F R G E D I N B U Outline What is quantum computation Why should we care if quantum computers are constructed?
More informationA probabilistic quantum key transfer protocol
SECURITY AND COMMUNICATION NETWORKS Security Comm. Networks 013; 6:1389 1395 Published online 13 March 013 in Wiley Online Library (wileyonlinelibrary.com)..736 RESEARCH ARTICLE Abhishek Parakh* Nebraska
More informationEntanglement and information
Ph95a lecture notes for 0/29/0 Entanglement and information Lately we ve spent a lot of time examining properties of entangled states such as ab è 2 0 a b è Ý a 0 b è. We have learned that they exhibit
More informationCryptography CS 555. Topic 25: Quantum Crpytography. CS555 Topic 25 1
Cryptography CS 555 Topic 25: Quantum Crpytography CS555 Topic 25 1 Outline and Readings Outline: What is Identity Based Encryption Quantum cryptography Readings: CS555 Topic 25 2 Identity Based Encryption
More informationPhysics is becoming too difficult for physicists. David Hilbert (mathematician)
Physics is becoming too difficult for physicists. David Hilbert (mathematician) Simple Harmonic Oscillator Credit: R. Nave (HyperPhysics) Particle 2 X 2-Particle wave functions 2 Particles, each moving
More informationQuantum Cryptography and Security of Information Systems
Quantum Cryptography and Security of Information Systems Dalibor Hrg University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb dalix@fly.srk.fer.hr Leo Budin University of Zagreb, Faculty
More informationHigh Fidelity to Low Weight. Daniel Gottesman Perimeter Institute
High Fidelity to Low Weight Daniel Gottesman Perimeter Institute A Word From Our Sponsor... Quant-ph/0212066, Security of quantum key distribution with imperfect devices, D.G., H.-K. Lo, N. Lutkenhaus,
More informationarxiv:quant-ph/ v1 6 Dec 2005
Quantum Direct Communication with Authentication Hwayean Lee 1,,4, Jongin Lim 1,, HyungJin Yang,3 arxiv:quant-ph/051051v1 6 Dec 005 Center for Information Security TechnologiesCIST) 1, Graduate School
More informationDevice-Independent Quantum Information Processing (DIQIP)
Device-Independent Quantum Information Processing (DIQIP) Maciej Demianowicz ICFO-Institut de Ciencies Fotoniques, Barcelona (Spain) Coordinator of the project: Antonio Acín (ICFO, ICREA professor) meeting,
More informationC. QUANTUM INFORMATION 111
C. QUANTUM INFORMATION 111 C Quantum information C.1 Qubits C.1.a Single qubits 1. Qubit: Just as the bits 0 and 1 are represented by distinct physical states, so the quantum bits (or qubits) 0i and 1i
More informationSecurity Implications of Quantum Technologies
Security Implications of Quantum Technologies Jim Alves-Foss Center for Secure and Dependable Software Department of Computer Science University of Idaho Moscow, ID 83844-1010 email: jimaf@cs.uidaho.edu
More informationA Genetic Algorithm to Analyze the Security of Quantum Cryptographic Protocols
A Genetic Algorithm to Analyze the Security of Quantum Cryptographic Protocols Walter O. Krawec walter.krawec@gmail.com Iona College Computer Science Department New Rochelle, NY USA IEEE WCCI July, 2016
More informationLECTURE NOTES ON Quantum Cryptography
Department of Software The University of Babylon LECTURE NOTES ON Quantum Cryptography By Dr. Samaher Hussein Ali College of Information Technology, University of Babylon, Iraq Samaher@itnet.uobabylon.edu.iq
More informationQuantum sampling of mixed states
Quantum sampling of mixed states Philippe Lamontagne January 7th Philippe Lamontagne Quantum sampling of mixed states January 7th 1 / 9 The setup Philippe Lamontagne Quantum sampling of mixed states January
More informationTransmitting and Hiding Quantum Information
2018/12/20 @ 4th KIAS WORKSHOP on Quantum Information and Thermodynamics Transmitting and Hiding Quantum Information Seung-Woo Lee Quantum Universe Center Korea Institute for Advanced Study (KIAS) Contents
More informationQuantum Cryptography
Quantum Cryptography Christian Schaffner Research Center for Quantum Software Institute for Logic, Language and Computation (ILLC) University of Amsterdam Centrum Wiskunde & Informatica Winter 17 QuantumDay@Portland
More informationQuantum Information Transfer and Processing Miloslav Dušek
Quantum Information Transfer and Processing Miloslav Dušek Department of Optics, Faculty of Science Palacký University, Olomouc Quantum theory Quantum theory At the beginning of 20 th century about the
More informationChallenges in Quantum Information Science. Umesh V. Vazirani U. C. Berkeley
Challenges in Quantum Information Science Umesh V. Vazirani U. C. Berkeley 1 st quantum revolution - Understanding physical world: periodic table, chemical reactions electronic wavefunctions underlying
More informationQuantum Cryptography
http://tph.tuwien.ac.at/ svozil/publ/2005-qcrypt-pres.pdf Institut für Theoretische Physik, University of Technology Vienna, Wiedner Hauptstraße 8-10/136, A-1040 Vienna, Austria svozil@tuwien.ac.at 16.
More informationPERFECT SECRECY AND ADVERSARIAL INDISTINGUISHABILITY
PERFECT SECRECY AND ADVERSARIAL INDISTINGUISHABILITY BURTON ROSENBERG UNIVERSITY OF MIAMI Contents 1. Perfect Secrecy 1 1.1. A Perfectly Secret Cipher 2 1.2. Odds Ratio and Bias 3 1.3. Conditions for Perfect
More informationUnconditionally secure deviceindependent
Unconditionally secure deviceindependent quantum key distribution with only two devices Roger Colbeck (ETH Zurich) Based on joint work with Jon Barrett and Adrian Kent Physical Review A 86, 062326 (2012)
More informationC. QUANTUM INFORMATION 99
C. QUANTUM INFORMATION 99 C Quantum information C.1 Qubits C.1.a Single qubits Just as the bits 0 and 1 are represented by distinct physical states in a conventional computer, so the quantum bits (or qubits)
More informationQuantum Correlations as Necessary Precondition for Secure Communication
Quantum Correlations as Necessary Precondition for Secure Communication Phys. Rev. Lett. 92, 217903 (2004) quant-ph/0307151 Marcos Curty 1, Maciej Lewenstein 2, Norbert Lütkenhaus 1 1 Institut für Theoretische
More informationSecurity of Quantum Key Distribution with Imperfect Devices
Security of Quantum Key Distribution with Imperfect Devices Hoi-Kwong Lo Dept. of Electrical & Comp. Engineering (ECE); & Dept. of Physics University of Toronto Email:hklo@comm.utoronto.ca URL: http://www.comm.utoronto.ca/~hklo
More information10 - February, 2010 Jordan Myronuk
10 - February, 2010 Jordan Myronuk Classical Cryptography EPR Paradox] The need for QKD Quantum Bits and Entanglement No Cloning Theorem Polarization of Photons BB84 Protocol Probability of Qubit States
More informationQuantum Cryptography. Marshall Roth March 9, 2007
Quantum Cryptography Marshall Roth March 9, 2007 Overview Current Cryptography Methods Quantum Solutions Quantum Cryptography Commercial Implementation Cryptography algorithms: Symmetric encrypting and
More informationEntropy Accumulation in Device-independent Protocols
Entropy Accumulation in Device-independent Protocols QIP17 Seattle January 19, 2017 arxiv: 1607.01796 & 1607.01797 Rotem Arnon-Friedman, Frédéric Dupuis, Omar Fawzi, Renato Renner, & Thomas Vidick Outline
More informationQuantum Dense Coding and Quantum Teleportation
Lecture Note 3 Quantum Dense Coding and Quantum Teleportation Jian-Wei Pan Bell states maximally entangled states: ˆ Φ Ψ Φ x σ Dense Coding Theory: [C.. Bennett & S. J. Wiesner, Phys. Rev. Lett. 69, 88
More informationInformation-theoretic treatment of tripartite systems and quantum channels. Patrick Coles Carnegie Mellon University Pittsburgh, PA USA
Information-theoretic treatment of tripartite systems and quantum channels Patrick Coles Carnegie Mellon University Pittsburgh, PA USA ArXiv: 1006.4859 a c b Co-authors Li Yu Vlad Gheorghiu Robert Griffiths
More informationDetection of Eavesdropping in Quantum Key Distribution using Bell s Theorem and Error Rate Calculations
Detection of Eavesdropping in Quantum Key Distribution using Bell s Theorem and Error Rate Calculations David Gaharia Joel Wibron under the direction of Prof. Mohamed Bourennane Quantum Information & Quantum
More informationTutorial: Device-independent random number generation. Roger Colbeck University of York
Tutorial: Device-independent random number generation Roger Colbeck University of York Outline Brief motivation of random number generation Discuss what we mean by a random number Discuss some ways of
More informationQuantum Error Correcting Codes and Quantum Cryptography. Peter Shor M.I.T. Cambridge, MA 02139
Quantum Error Correcting Codes and Quantum Cryptography Peter Shor M.I.T. Cambridge, MA 02139 1 We start out with two processes which are fundamentally quantum: superdense coding and teleportation. Superdense
More informationResearch, Development and Simulation of Quantum Cryptographic Protocols
http://dx.doi.org/1.5755/j1.eee.19.4.17 Research, Development and Simulation of Quantum Cryptographic Protocols C. Anghel 1 1 University Dunărea de Jos Galati, 2 Științei, 8146 Galati, Romania, phone:
More informationarxiv:quant-ph/ v2 3 Oct 2000
Quantum key distribution without alternative measurements Adán Cabello Departamento de Física Aplicada, Universidad de Sevilla, 0 Sevilla, Spain January, 0 arxiv:quant-ph/990v Oct 000 Entanglement swapping
More informationarxiv:quant-ph/ v2 17 Sep 2002
Proof of security of quantum key distribution with two-way classical communications arxiv:quant-ph/0105121 v2 17 Sep 2002 Daniel Gottesman EECS: Computer Science Division University of California Berkeley,
More information9. Distance measures. 9.1 Classical information measures. Head Tail. How similar/close are two probability distributions? Trace distance.
9. Distance measures 9.1 Classical information measures How similar/close are two probability distributions? Trace distance Fidelity Example: Flipping two coins, one fair one biased Head Tail Trace distance
More informationAn Introduction to Quantum Information. By Aditya Jain. Under the Guidance of Dr. Guruprasad Kar PAMU, ISI Kolkata
An Introduction to Quantum Information By Aditya Jain Under the Guidance of Dr. Guruprasad Kar PAMU, ISI Kolkata 1. Introduction Quantum information is physical information that is held in the state of
More informationQuantum Cryptography
Quantum Cryptography Umesh V. Vazirani CS 161/194-1 November 28, 2005 Why Quantum Cryptography? Unconditional security - Quantum computers can solve certain tasks exponentially faster; including quantum
More informationEntanglement and Quantum Teleportation
Entanglement and Quantum Teleportation Stephen Bartlett Centre for Advanced Computing Algorithms and Cryptography Australian Centre of Excellence in Quantum Computer Technology Macquarie University, Sydney,
More informationAn Introduction to Quantum Information and Applications
An Introduction to Quantum Information and Applications Iordanis Kerenidis CNRS LIAFA-Univ Paris-Diderot Quantum information and computation Quantum information and computation How is information encoded
More informationBit-Commitment and Coin Flipping in a Device-Independent Setting
Bit-Commitment and Coin Flipping in a Device-Independent Setting J. Silman Université Libre de Bruxelles Joint work with: A. Chailloux & I. Kerenidis (LIAFA), N. Aharon (TAU), S. Pironio & S. Massar (ULB).
More informationMassachusetts Institute of Technology Department of Electrical Engineering and Computer Science Quantum Optical Communication
Massachusetts Institute of Technology Department of Electrical Engineering and Computer Science 6.453 Quantum Optical Communication Date: Thursday, November 3, 016 Lecture Number 16 Fall 016 Jeffrey H.
More informationQuantum Cryptographic Network based on Quantum Memories. Abstract
Quantum Cryptographic Network based on Quantum Memories Eli Biham Computer Science Department Technion Haifa 32000, Israel Bruno Huttner Group of Applied Physics University of Geneva CH-2, Geneva 4, Switzerland
More informationarxiv:quant-ph/ v1 13 Jan 2003
Deterministic Secure Direct Communication Using Ping-pong protocol without public channel Qing-yu Cai Laboratory of Magentic Resonance and Atom and Molecular Physics, Wuhan Institute of Mathematics, The
More information1 1D Schrödinger equation: Particle in an infinite box
1 OF 5 1 1D Schrödinger equation: Particle in an infinite box Consider a particle of mass m confined to an infinite one-dimensional well of width L. The potential is given by V (x) = V 0 x L/2, V (x) =
More informationQuantum Key Distribution. The Starting Point
Quantum Key Distribution Norbert Lütkenhaus The Starting Point Quantum Mechanics allows Quantum Key Distribution, which can create an unlimited amount of secret key using -a quantum channel -an authenticated
More informationThe BB84 cryptologic protocol
The cryptologic protocol of quantum key distribution Dimitri Petritis Institut de recherche mathématique de Rennes Université de Rennes 1 et CNRS (UMR 6625) Vernam s ciphering Principles of coding and
More information1 1D Schrödinger equation: Particle in an infinite box
1 OF 5 NOTE: This problem set is to be handed in to my mail slot (SMITH) located in the Clarendon Laboratory by 5:00 PM (noon) Tuesday, 24 May. 1 1D Schrödinger equation: Particle in an infinite box Consider
More informationQUANTUM INFORMATION -THE NO-HIDING THEOREM p.1/36
QUANTUM INFORMATION - THE NO-HIDING THEOREM Arun K Pati akpati@iopb.res.in Instititute of Physics, Bhubaneswar-751005, Orissa, INDIA and Th. P. D, BARC, Mumbai-400085, India QUANTUM INFORMATION -THE NO-HIDING
More informationA Matlab Realization of Shor s Quantum Factoring Algorithm
1 A Matlab Realization of Shor s Quantum Factoring Algorithm S. Jha, P. Chatterjee, A.Falor and M. Chakraborty, Member IEEE Department of Information Technology Institute of Engineering & Management Kolkata,
More informationLecture 2: Perfect Secrecy and its Limitations
CS 4501-6501 Topics in Cryptography 26 Jan 2018 Lecture 2: Perfect Secrecy and its Limitations Lecturer: Mohammad Mahmoody Scribe: Mohammad Mahmoody 1 Introduction Last time, we informally defined encryption
More informationIntroduction to Quantum Information Hermann Kampermann
Introduction to Quantum Information Hermann Kampermann Heinrich-Heine-Universität Düsseldorf Theoretische Physik III Summer school Bleubeuren July 014 Contents 1 Quantum Mechanics...........................
More informationarxiv:quant-ph/ v2 11 Jan 2006
Diss. ETH No. 16242 Security of Quantum Key Distribution arxiv:quant-ph/0512258v2 11 Jan 2006 A dissertation submitted to SWISS FEDERAL INSTITUTE OF TECHNOLOGY ZURICH for the degree of Doctor of Natural
More informationAn Introduction. Dr Nick Papanikolaou. Seminar on The Future of Cryptography The British Computer Society 17 September 2009
An Dr Nick Papanikolaou Research Fellow, e-security Group International Digital Laboratory University of Warwick http://go.warwick.ac.uk/nikos Seminar on The Future of Cryptography The British Computer
More informationKey distillation from quantum channels using two-way communication protocols
Key distillation from quantum channels using two-way communication protocols Joonwoo Bae and Antonio Acín ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona,
More informationEPR paradox, Bell inequality, etc.
EPR paradox, Bell inequality, etc. Compatible and incompatible observables AA, BB = 0, then compatible, can measure simultaneously, can diagonalize in one basis commutator, AA, BB AAAA BBBB If we project
More informationDevice-Independent Quantum Information Processing
Device-Independent Quantum Information Processing Antonio Acín ICREA Professor at ICFO-Institut de Ciencies Fotoniques, Barcelona Chist-Era kick-off seminar, March 2012, Warsaw, Poland Quantum Information
More informationEntanglement. arnoldzwicky.org. Presented by: Joseph Chapman. Created by: Gina Lorenz with adapted PHYS403 content from Paul Kwiat, Brad Christensen
Entanglement arnoldzwicky.org Presented by: Joseph Chapman. Created by: Gina Lorenz with adapted PHYS403 content from Paul Kwiat, Brad Christensen PHYS403, July 26, 2017 Entanglement A quantum object can
More informationarxiv:quant-ph/ v2 2 Jan 2007
Revisiting controlled quantum secure direct communication using a non-symmetric quantum channel with quantum superdense coding arxiv:quant-ph/06106v Jan 007 Jun Liu 1, Yan Xia and Zhan-jun Zhang 1,, 1
More informationQuantum Entanglement, Quantum Cryptography, Beyond Quantum Mechanics, and Why Quantum Mechanics Brad Christensen Advisor: Paul G.
Quantum Entanglement, Quantum Cryptography, Beyond Quantum Mechanics, and Why Quantum Mechanics Brad Christensen Advisor: Paul G. Kwiat Physics 403 talk: December 2, 2014 Entanglement is a feature of compound
More informationProblem Set: TT Quantum Information
Problem Set: TT Quantum Information Basics of Information Theory 1. Alice can send four messages A, B, C, and D over a classical channel. She chooses A with probability 1/, B with probability 1/4 and C
More informationEnigma Marian Rejewski, Jerzy Róz ycki, Henryk Zygalski
1 Enigma Marian Rejewski, Jerzy Róz ycki, Henryk Zygalski What is the problem with classical cryptography? Secret key cryptography Requires secure channel for key distribution In principle every
More informationTeleportation of Quantum States (1993; Bennett, Brassard, Crepeau, Jozsa, Peres, Wootters)
Teleportation of Quantum States (1993; Bennett, Brassard, Crepeau, Jozsa, Peres, Wootters) Rahul Jain U. Waterloo and Institute for Quantum Computing, rjain@cs.uwaterloo.ca entry editor: Andris Ambainis
More informationarxiv: v7 [quant-ph] 20 Mar 2017
Quantum oblivious transfer and bit commitment protocols based on two non-orthogonal states coding arxiv:1306.5863v7 [quant-ph] 0 Mar 017 Li Yang State Key Laboratory of Information Security, Institute
More informationQuantum key distribution with 2-bit quantum codes
Quantum key distribution with -bit quantum codes Xiang-Bin Wang Imai Quantum Computation and Information project, ERATO, Japan Sci. and Tech. Corp. Daini Hongo White Bldg. 0, 5-8-3, Hongo, Bunkyo, Tokyo
More informationquantum distribution of a sudoku key Sian K. Jones University of South Wales
Games and Puzzles quantum distribution of a sudoku key Sian K. Jones University of South Wales sian-kathryn.jones@southwales.ac.uk Abstract: Sudoku grids are often cited as being useful in cryptography
More informationQuantum Information Theory and Cryptography
Quantum Information Theory and Cryptography John Smolin, IBM Research IPAM Information Theory A Mathematical Theory of Communication, C.E. Shannon, 1948 Lies at the intersection of Electrical Engineering,
More informationarxiv:quant-ph/ v2 11 Jan 2006
Quantum Authentication and Quantum Key Distribution Protocol Hwayean Lee 1,,3, Jongin Lim 1,, and HyungJin Yang,4 arxiv:quant-ph/0510144v 11 Jan 006 Center for Information Security Technologies(CIST) 1,
More informationSingle and Entangled photons. Edward Pei
Single and Entangled photons Edward Pei War is most commonly thought of as men fighting with their fist, and power is determined by physical strength. Behind the lines, however, knowledge is power. For
More informationQuantum key distribution
Quantum key distribution Eleni Diamanti eleni.diamanti@telecom-paristech.fr LTCI, CNRS, Télécom ParisTech Paris Centre for Quantum Computing Photonics@be doctoral school May 10, 2016 1 Outline Principles
More informationSeminar Report On QUANTUM CRYPTOGRAPHY. Submitted by SANTHIMOL A. K. In the partial fulfillment of requirements in degree of
Seminar Report On QUANTUM CRYPTOGRAPHY Submitted by SANTHIMOL A. K. In the partial fulfillment of requirements in degree of Master of Technology in Computer and Information Science DEPARTMENT OF COMPUTER
More informationThe Relativistic Quantum World
The Relativistic Quantum World A lecture series on Relativity Theory and Quantum Mechanics Marcel Merk University of Maastricht, Sept 24 Oct 15, 2014 Relativity Quantum Mechanics The Relativistic Quantum
More informationQuantum Information Processing
Quantum Information Processing Jonathan Jones http://nmr.physics.ox.ac.uk/teaching The Information Age Communication Shannon Computation Turing Current approaches are essentially classical which is wrong
More informationMobile Free Space Quantum Key Distribution for short distance secure communication
DEPARTMENT OF PHYSICS LUDWIG-MAXIMILIAN-UNIVERSITY OF MUNICH Master s Thesis Mobile Free Space Quantum Key Distribution for short distance secure communication Tobias Vogl January 21, 216 Supervised by
More informationAsymptotic Analysis of a Three State Quantum Cryptographic Protocol
Asymptotic Analysis of a Three State Quantum Cryptographic Protocol Walter O. Krawec walter.krawec@gmail.com Iona College Computer Science Department New Rochelle, NY USA IEEE ISIT July, 2016 Quantum Key
More informationDeterministic secure communications using two-mode squeezed states
Deterministic secure communications using twomode squeezed states Alberto M. Marino* and C. R. Stroud, Jr. The Institute of Optics, University of Rochester, Rochester, New York 467, USA Received 5 May
More informationAPPLICATIONS. Quantum Communications
SOFT PROCESSING TECHNIQUES FOR QUANTUM KEY DISTRIBUTION APPLICATIONS Marina Mondin January 27, 2012 Quantum Communications In the past decades, the key to improving computer performance has been the reduction
More informationarxiv:quant-ph/ v1 13 Mar 2007
Quantum Key Distribution with Classical Bob Michel Boyer 1, Dan Kenigsberg 2 and Tal Mor 2 1. Département IRO, Université de Montréal Montréal (Québec) H3C 3J7 CANADA 2. Computer Science Department, Technion,
More informationQuantum Teleportation Pt. 3
Quantum Teleportation Pt. 3 PHYS 500 - Southern Illinois University March 7, 2017 PHYS 500 - Southern Illinois University Quantum Teleportation Pt. 3 March 7, 2017 1 / 9 A Bit of History on Teleportation
More informationarxiv: v1 [quant-ph] 28 May 2011
Detection of Multiparticle Entanglement: Quantifying the Search for Symmetric Extensions Fernando G.S.L. Brandão 1 and Matthias Christandl 2 1 Departamento de Física, Universidade Federal de Minas Gerais,
More informationSquashed entanglement
Squashed Entanglement based on Squashed Entanglement - An Additive Entanglement Measure (M. Christandl, A. Winter, quant-ph/0308088), and A paradigm for entanglement theory based on quantum communication
More informationOptical Quantum Communication with Quantitative Advantage. Quantum Communication
Optical Quantum Communication with Quantitative Advantage Juan Miguel Arrazola Benjamin Lovitz Ashutosh Marwah Dave Touchette Norbert Lütkenhaus Institute for Quantum Computing & Department of Physics
More informationRealization of B92 QKD protocol using id3100 Clavis 2 system
Realization of B92 QKD protocol using id3100 Clavis 2 system Makhamisa Senekane 1, Abdul Mirza 1, Mhlambululi Mafu 1 and Francesco Petruccione 1,2 1 Centre for Quantum Technology, School of Chemistry and
More informationHacking Quantum Cryptography. Marina von Steinkirch ~ Yelp Security
Hacking Quantum Cryptography Marina von Steinkirch ~ Yelp Security Agenda 1. Quantum Mechanics in 10 mins 2. Quantum Computing in 11 mins 3. Quantum Key Exchange in 100 mins (or more minutes) Some disclaimers
More informationLecture 1: Perfect Secrecy and Statistical Authentication. 2 Introduction - Historical vs Modern Cryptography
CS 7880 Graduate Cryptography September 10, 2015 Lecture 1: Perfect Secrecy and Statistical Authentication Lecturer: Daniel Wichs Scribe: Matthew Dippel 1 Topic Covered Definition of perfect secrecy One-time
More informationQuantum Cryptography: A Short Historical overview and Recent Developments
Quantum Cryptography: A Short Historical overview and Recent Developments Ioannis P. Antoniades Informatics Department, Aristotle University of Thessaloniki, Thessaloniki 541 24, Greece Vasilios G. Chouvardas
More informationBell inequality for qunits with binary measurements
Bell inequality for qunits with binary measurements arxiv:quant-ph/0204122v1 21 Apr 2002 H. Bechmann-Pasquinucci and N. Gisin Group of Applied Physics, University of Geneva, CH-1211, Geneva 4, Switzerland
More informationIntroduction to Quantum Cryptography
Università degli Studi di Perugia September, 12th, 2011 BunnyTN 2011, Trento, Italy This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License. Quantum Mechanics
More information