DOCSLIB.ORG

Entanglement Quantification and Quantum Benchmarking of Optical

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Entanglement Quantification and Quantum Benchmarking of Optical Entanglement quantification and quantum benchmarking of optical communication devices by Nathan Killoran A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Doctor of Philosophy in Physics Waterloo, Ontario, Canada, 2012 c Nathan Killoran 2012 I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. ii Abstract In this thesis, we develop a number of operational tests and tools for benchmarking the quantum nature of optical quantum communication devices. Using the laws of quantum physics, ideal quantum devices can fundamentally outperform their classical counterparts, or even achieve objectives which are classically impossible. Actual devices will not be ideal, but they may still be capable of facilitating quantum communication. Benchmark- ing tests, based on the presence of entanglement, can be used to verify whether or not imperfect quantum devices offer any advantage over their classical analogs. The general goal in this thesis is to provide strong benchmarking tools which simultaneously require minimal experimental resources but also offer a wide range of applicability. Another major component is the extension of existing qualitative benchmarks (`Is it quantum or classi- cal?') to more quantitative forms (`How quantum is it?'). This thesis is structured as follows. Chapters 1 and 2 provide an introduction and background material on quantum theory and quantum optics. Specifically, we outline the basic notions of quantum mechanics from a quantum information perspective, define some theoretical concepts which are important throughout the thesis, and detail two different methods for encoding quantum information in states of light, namely single-photon and continuous-variable encodings. In Chapter 3, we develop our first benchmarking results, for remote state preparation (RSP) protocols. To do this, we first distinguish quantum RSP protocols from classical RSP protocols by allowing the use of a pre-shared entangled state in the quantum case. Using the average fidelity between the desired target states and the actual remotely-prepared states to measure performance, we show how to calculate the best value achievable by a classical protocol. We apply these results to a number of different ensembles of target states, including pure states, mixed states, discrete ensembles, and continuous ensembles. From this, we propose a number of simple benchmarks based on Platonic solids. Finally, the proposed benchmarks are used to certify a quantum RSP experiment. In Chapters 4-6, we deal with the problem of extending existing continuous-variable (CV) quantum benchmarks to provide useful quantitative information. In Chapter 4, af- ter reviewing the known CV benchmarking results, in particular the entanglement-based approach, we outline a quantification scheme based on entanglement measures and pro- jections of infinite-dimensional optical systems to more managable finite subspaces. From this, two complementary paths are taken for the choice of projection. In Chapter 5, we pur- sue a two-qubit projection, which gives good quantitative results when the tested devices are near their ideal operating point. On the other hand, Chapter 6 follows the approach of iii projecting onto low-energy Fock states. This provides a better capacity to certify devices with larger degrees of imperfection. Finally, in Chapter 7, we show how to perform quantum benchmarking using arbitrary test states. Since many existing benchmarks are still limited to special cases, this provides a much-needed way to certify devices under more realistic testing conditions. We also study how to strengthen such benchmarks, leading to the best chance of certifying quantum devices. We use this approach, along with the quantitative tools developed in Chapters 4 and 6, to certify a real CV quantum memory. Together, the results contained in this thesis comprise a comprehensive suite of tools which can be used to perform efficient benchmarking tests on quantum devices using realistic experimental resources. iv Acknowledgements First of all, I would like to thank my supervisor Norbert L¨utkenhaus for his support and advice over the past four years. He was always willing to discuss my research with me, yet he also gave me space to work independently. As well, I appreciate the numerous opportunities he provided to attend international conferences and visit overseas research institutes. My thanks go as well to the members of my advisory and defense committees, Andrew Childs, Joseph Emerson, David Kribs, Kevin Resch, and to Alex Lvovsky for agreeing to serve as my external examiner. The Institute for Quantum Computing provided a fantastic environment for my grad- uate studies. In particular, I would like to thank the numerous members of the OQCT group who have come and gone during my tenure: Razieh Annabestani, Juan Miguel Ar- razola, Normand Beaudry, Agnes Ferenczi, Oleg Gittsovich, Hauke H¨aseler,Mattias Heid, Xiongfeng Ma, Will Matthews, Sergei Mikheev, Tobias Moroder, Geir-Ove Myhr, Varun Narasimhachar, Marco Piani, Dave Pitkanen, and Mohsen Razavi. As well, I would like to thank my many friends and colleagues in the ever-growing IQC community, in particular the diehards who showed up every week for ball hockey. I would also like to thank the folks at the Max Planck Institute for the Science of Light in Erlangen for providing a welcoming and congenial environment throughout my semester there. During my graduate studies, I lived in three places - the school, the grocery store and the skating rink. I thank my teammates on Smooth Liquid Thunder and Maxwell's Demons for many memorable seasons. I also want to thank Guelph Ultimate and the Waterloo Organization of Disc Sports for facilitating my activities on many summer and fall evenings. Finally, I'd like to thank all the other people who had an impact on me during my graduate studies. Thanks to my erstwhile roommates Devon, Chris, Mike, Osama (and Gina) for many memorable nights. Thanks to my parents for their continuing support and for always welcoming me for visits home. Most importantly, my gratitude to Emma for keeping me well during the thesis-writing process and for her enduring companionship throughout my studies. v Dedication To my fellow scientists. vi Table of Contents List of Figures x List of Tables xii 1 Introduction 1 2 Background 5 2.1 Preparation . 6 2.2 Evolution . 8 2.3 Measurement . 9 2.4 Quantum information theory . 11 2.5 Quantum optical implementations . 14 2.5.1 Single-photon encoding . 15 2.5.2 Continuous-variable encoding . 18 3 Remote state preparation benchmarks 23 3.1 Benchmarking framework . 25 3.1.1 Quantum RSP . 26 3.1.2 Classical RSP . 28 3.2 Threshold calculations . 31 3.2.1 Finite ensembles . 31 vii 3.2.2 Continuous ensemble . 35 3.2.3 Mixed states . 36 3.3 Experimental test . 38 4 Benchmarking continuous variable quantum communication devices 42 4.1 Quantum benchmarking framework . 44 4.1.1 Fidelity-based benchmarking . 45 4.1.2 Entanglement-based benchmarking . 47 4.2 Quantitative benchmarking . 56 4.2.1 Benchmarking with entanglement measures . 56 5 Quantitative benchmarking I: two-qubit projection 61 5.1 Quantification procedure . 62 5.1.1 Choosing the projection . 63 5.1.2 Estimating the constraints . 64 5.1.3 Minimizing the entanglement . 68 5.2 Results . 71 6 Quantitative benchmarking II: Fock-state projection 77 6.1 Quantification procedure . 78 6.1.1 Choosing the projection . 78 6.1.2 Estimating the constraints . 79 6.1.3 Minimizing the entanglement . 84 6.2 Results . 86 7 Benchmarking with realistic states 93 7.1 Benchmarking framework for arbitrary states . 95 7.1.1 Entanglement-based benchmarking with arbitrary states . 95 7.1.2 Optimizing the purifications . 97 viii 7.1.3 Fidelity-based benchmarking with arbitrary states . 102 7.1.4 Benchmarking with phase-symmetric ensembles . 107 7.2 Certifying a quantum memory . 110 7.2.1 Finding the Gram matrix . 111 7.2.2 Computing the entanglement . 113 8 Final remarks 119 APPENDICES 123 A Supplement for remote state preparation benchmarks 124 A.1 Proof of bound for continuous case . 124 A.2 Proof of optimal average fidelity for mixed states . 126 B Supplement for two-qubit projection scheme 128 B.1 Derivation of overlap bounds . 128 B.2 Derivation of supplementary diagonal bounds . 130 B.3 Derivation of off-diagonal bounds . 131 B.4 Constraints for two-qubit optimization . 132 C Supplement for Fock-state projection scheme 133 C.1 Derivation of first order constraint . 133 C.2 Derivation of second order constraint . 134 D Supplement for benchmarking with arbitrary states 136 D.1 Convexity proofs . 136 D.2 Proof of standard form . 137 D.3 Proof of trace norm in standard form . 138 References 141 ix List of Figures 2.1 Representation of a single-qubit state as a vector in the Bloch sphere . 17 2.2 Schematic of balanced homodyne measurement . 21 3.1 Remote state preparation schematic . 26 3.2 Example partitioning in a remote state preparation strategy . 30 3.3 Optimal classical fidelity thresholds for Platonic solid ensembles . 34 3.4 Comparison of experimentally-achieved mean fidelities with benchmark val- ues for pure states . 40 3.5 Comparison of experimentally-achieved mean fidelities with benchmark val- ues for mixed states . 41 4.1 Schematic of a measure and prepare strategy/Example CV test states . 46 4.2 Illustrations of entanglement-based benchmarking and effective entangle- ment concepts . 48 4.3 Quantum domain for test ensemble containing two coherent states |±αi . 53 4.4 Quantum domain for test ensemble containing M = 3; 4; 5; 6 symmetrically k distributed coherent states α!M ....................... 54 4.5 Quantum domain for a squeezed/antisqueezed pair |±ri .
Load more

Recommended publications
  • Arxiv:1707.06910V2 [Physics.Hist-Ph] 22 Feb 2018 Xlntoscnenn H Eei Ftebte-Nw Pa Better-Known the of Genesis D the Park’S Concerning Analyze Explanations I States
    Twelve years before the quantum no-cloning theorem Juan Ortigoso∗ Instituto de Estructura de la Materia, CSIC, Serrano 121, 28006 Madrid, Spain (Dated: January 22, 2018) Abstract The celebrated quantum no-cloning theorem establishes the impossibility of making a perfect copy of an unknown quantum state. The discovery of this important theorem for the field of quantum information is currently dated 1982. I show here that an article published in 1970 [J. L. Park, Foundations of Physics, 1, 23-33 (1970)] contained an explicit mathematical proof of the impossibility of cloning quantum states. I analyze Park’s demonstration in the light of published explanations concerning the genesis of the better-known papers on no-cloning. arXiv:1707.06910v2 [physics.hist-ph] 22 Feb 2018 1 I. INTRODUCTION The no-cloning theorem of quantum mechanics establishes that an arbitrary unknown quantum state cannot be copied.1 A modern proof,2 based on the linearity of quantum mechanics, takes two lines. Suppose that a device can implement a transformation T for copying two orthogonal states ψ and φ of a qubit: T ψ 0 = ψ ψ and T φ 0 = φ φ , | i | i | i| i | i| i | i| i | i| i where 0 is the ready state of the target system. It follows, from linearity, that | i T (a ψ + b φ ) 0 = aT ψ 0 + bT φ 0 = a ψ ψ + b φ φ . (1) | i | i | i | i| i | i| i | i| i | i| i But if the transformation T can clone arbitrary states, it should give, for any a, b values T (a ψ +b φ ) 0 =(a ψ +b φ )(a ψ +b φ )= a2 ψ ψ +b2 φ φ +ab ψ φ +ab φ ψ , (2) | i | i | i | i | i | i | i | i| i | i| i | i| i | i| i which is different from Eq.
    [Show full text]
  • Photonic Quantum Simulator for Unbiased Phase Covariant Cloning
    Applied Physics B manuscript No. (will be inserted by the editor) Photonic quantum simulator for unbiased phase covariant cloning Laura T. Knoll12, Ignacio H. L´opez Grande12, Miguel A. Larotonda123 1 DEILAP, CITEDEF-CONICET, J.B. de La Salle 4397, 1603 Villa Martelli, Buenos Aires, Argentina 2 Departamento de F´ısica, FCEyN, UBA. Ciudad Universitaria, 1428 Buenos Aires, Argentina 3 CONICET, Argentina e-mail: [email protected] The date of receipt and acceptance will be inserted by the editor Abstract We present the results of a linear optics pho- applying a trace-preserving, completely-positive map to tonic implementation of a quantum circuit that simu- the composite system [6,7,8,9,10]. lates a phase covariant cloner, by using two different de- Among the family of Quantum Cloning Machines grees of freedom of a single photon. We experimentally (QCM), one can make a distinction between universal simulate the action of two mirrored 1 ! 2 cloners, each cloning machines (UQCM), which copy all the states of them biasing the cloned states into opposite regions with the same fidelity F , regardless of the state j i of the Bloch sphere. We show that by applying a ran- to be cloned, and state-dependent QCM. For qubits, dom sequence of these two cloners, an eavesdropper can the optimum UQCM can achieve a cloning fidelity F of mitigate the amount of noise added to the original in- 5=6 = 0:833 [6,7,8,11]. UQCMs have been experimen- put state and therefore prepare clones with no bias but tally realized in photon stimulated emission setups [12, with the same individual fidelity, masking its presence in 13,14], linear optics [15] and NMR systems [16].
    [Show full text]
  • Multi-Level Control in Large-Anharmonicity High-Coherence Capacitively Shunted Flux Quantum Circuits
    Multi-level Control in Large-anharmonicity High-coherence Capacitively Shunted Flux Quantum Circuits by Muhammet Ali Yurtalan A thesis presented to the University of Waterloo in fulfillment of the thesis requirements for the degree of Doctor of Philosophy in Electrical and Computer Engineering (Quantum Information) Waterloo, Ontario, Canada, 2019 c Muhammet Ali Yurtalan 2019 Examining Committee Membership The following served on the Examining Committee for this thesis. The decision of the Examining Committee is by majority vote. External Examiner Max Hofheinz Associate Professor Supervisor Adrian Lupascu Associate Professor Supervisor Zbigniew Wasilewski Professor Internal Member Bo Cui Associate Professor Internal Member Guoxing Miao Associate Professor Internal-External Member Jonathan Baugh Associate Professor ii This thesis consists of material all of which I authored or co-authored: see Statement of Contributions included in the thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. iii Statement of Contributions Most of the material in Chapter 5 consists of co-authored content. Muhammet Ali Yur- talan and Adrian Lupascu worked on the design and modeling of the device. Muhammet Ali Yurtalan conducted the experiments and performed device simulations. Muhammet Ali Yurtalan and Jiahao Shi fabricated the sample and performed data analysis. Muhammet Ali Yurtalan and Graydon Flatt performed numerical simulations of randomized bench- marking protocol. Adrian Lupascu supervised the experimental work. Most of the material in Chapter 6 consists of co-authored content. Muhammet Ali Yurtalan conducted the experiments and performed numerical simulations.
    [Show full text]
  • Quantum Cloning and Deletion in Quantum Information Theory
    Quantum Cloning and Deletion in Quantum Information Theory THESIS SUBMITTED FOR THE DEGREE OF DOCTOR OF PHILOSOPHY (SCIENCE) OF BENGAL ENGINEERING AND SCIENCE UNIVERSITY BY SATYABRATA ADHIKARI arXiv:0902.1622v1 [quant-ph] 10 Feb 2009 DEPARTMENT OF MATHEMATICS BENGAL ENGINEERING AND SCIENCE UNIVERSITY UNIVERSITY HOWRAH- 711103, West Bengal INDIA 2006 i DECLARATION I declare that the thesis entitled “Quantum Cloning and Deletion in Quantum Information Theory” is composed by me and that no part of this thesis has formed the basis for the award of any Degree, Diploma, Associateship, Fellowship or any other similar title to me. (Satyabrata Adhikari) Date: Department of Mathematics, Bengal Engineering and Science University, Shibpur Howrah- 711103, West Bengal India ii CERTIFICATE This is to certify that the thesis entitled “Quantum Cloning and Deletion in Quantum Information Theory” submitted by Satyabrata Adhikari who got his name registered on 21.12.2002 for the award of Ph.D.(Science) degree of Bengal Engi- neering and Science University, is absolutely based upon his own work under my super- vision in the Department of Mathematics, Bengal Engineering and Science University, Shibpur, Howrah-711103, and that neither this thesis nor any part of it has been sub- mitted for any degree / diploma or any other academic award anywhere before. (Binayak Samaddar Choudhury) Date: Professor Department of Mathematics, Bengal Engineering and Science University, Shibpur Howrah- 711103, West Bengal India iii Acknowledgements A journey is easier when you travel together. Interdependence is certainly more valuable than independence. This thesis is the result of five years of work whereby I have been accompanied and supported by many people.
    [Show full text]
  • Experimental Investigation of High-Dimensional Quantum Key Distribution Protocols with Twisted Photons
    Experimental investigation of high-dimensional quantum key distribution protocols with twisted photons Frédéric Bouchard1, Khabat Heshami2, Duncan England2, Robert Fickler1, Robert W. Boyd1 3 4, Berthold-Georg Englert5 6 7, Luis L. Sánchez-Soto3 8, and Ebrahim Karimi1 3 9 1Department of physics, University of Ottawa, Advanced Research Complex, 25 Templeton, Ottawa ON Canada, K1N 6N5 2National Research Council of Canada, 100 Sussex Drive, Ottawa ON Canada, K1A 0R6 3Max-Planck-Institut für die Physik des Lichts, Staudtstraße 2, 91058 Erlangen, Germany 4Institute of Optics, University of Rochester, Rochester, NY 14627, USA 5Centre for Quantum Technologies, National University of Singapore, 3 Science Drive 2, Singapore 117543, Singapore 6Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore. 7MajuLab, CNRS-UNS-NUS-NTU International Joint Unit, UMI 3654, Singapore. 8Departamento de Óptica, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain 9Department of Physics, Institute for Advanced Studies in Basic Sciences, 45137-66731 Zanjan, Iran. November 30, 2018 Quantum key distribution is on the verge 1 Introduction of real world applications, where perfectly secure information can be distributed Quantum cryptography allows for the broadcast- among multiple parties. Several quantum ing of information between multiple parties in cryptographic protocols have been theo- a perfectly secure manner under the sole as- retically proposed and independently real- sumption that the laws of quantum physics are ized in different experimental conditions. valid [1]. Quantum Key Distribution (QKD) [2, Here, we develop an experimental plat- 3] is arguably the most well-known and studied form based on high-dimensional orbital an- quantum cryptographic protocol to date.
    [Show full text]
  • Quantum Key Distribution Without the Wavefunction
    Quantum key distribution without the wavefunction Gerd Niestegge Zillertalstrasse 39, 81373 M¨unchen, Germany [email protected] Abstract A well-known feature of quantum mechanics is the secure exchange of secret bit strings which can then be used as keys to encrypt messages transmitted over any classical communication channel. It is demonstrated that this quantum key distribution allows a much more general and ab- stract access than commonly thought. The results include some gener- alizations for the Hilbert space version of quantum key distribution, but base upon a general non-classical extension of conditional probability. A special state-independent conditional probability is identified as origin of the superior security of quantum key distribution and may have more profound implications for the foundations and interpretation of quantum mechanics, quantum information theory, and the philosophical question what actually constitutes physical reality. Key Words: Quantum key distribution, No-cloning theorem, Founda- tions of quantum theory, Quantum logic PACS: 03.67.Dd, 03.65.Ta 1. Introduction In the past thirty years, quantum cryptography has been a large field of exten- sive theoretical and experimental research. Several quantum key distribution protocols have been elaborated, their technical feasibility has been discussed, experimental set-ups and some practical implementations have been realized. Quantum key distribution may be the first commercial application of quantum information theory. A vast amount of papers on these topics are available by now (Each of the two pioneering works [7] and [18] has more than ten thousand and almost eight thousand quotations, respectively; for a review, see [20] or [37]). The present paper, however, focuses on the theoretical foundations and concentrates on the two best-known quantum key distribution protocols.
    [Show full text]
  • Quantum Communication Jubilee of Teleportation
    Quantum Communication Quantum • Rotem Liss and Tal Mor Liss • Rotem and Tal Quantum Communication Celebrating the Silver Jubilee of Teleportation Edited by Rotem Liss and Tal Mor Printed Edition of the Special Issue Published in Entropy www.mdpi.com/journal/entropy Quantum Communication—Celebrating the Silver Jubilee of Teleportation Quantum Communication—Celebrating the Silver Jubilee of Teleportation Editors Rotem Liss Tal Mor MDPI • Basel • Beijing • Wuhan • Barcelona • Belgrade • Manchester • Tokyo • Cluj • Tianjin Editors Rotem Liss Tal Mor Technion–Israel Institute of Technology Technion–Israel Institute of Technology Israel Israel Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Entropy (ISSN 1099-4300) (available at: https://www.mdpi.com/journal/entropy/special issues/Quantum Communication). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: LastName, A.A.; LastName, B.B.; LastName, C.C. Article Title. Journal Name Year, Article Number, Page Range. ISBN 978-3-03943-026-0 (Hbk) ISBN 978-3-03943-027-7 (PDF) c 2020 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license, which allows users to download, copy and build upon published articles, as long as the author and publisher are properly credited, which ensures maximum dissemination and a wider impact of our publications. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons license CC BY-NC-ND. Contents About the Editors .............................................
    [Show full text]
  • Quantum Cryptography with Several Cloning Attacks
    Journal of Computer Science 6 (7): 682-686, 2010 ISSN 1549-3636 © 2010 Science Publications Quantum Cryptography with Several Cloning Attacks Mustapha Dehmani, Hamid Ez-Zahraouy and Abdelilah Benyoussef Laboratory of Magnetism and High Energy Physics, Faculty of Science, University Mohammed V-Agdal, Rabat, Morocco Abstract: Problem statement: In a previous research, we investigated the quantum key distribution of the well known BB84 protocol with several intercept and resend attacks. In the present research, we studied the effect of many eavesdroppers cloning attacks of the Bennett-Brassard cryptographic protocol on the quantum error and mutual information between honest parties and information with sender for each eavesdropper. Approach: The quantum error and the mutual information were calculated analytically and computed for arbitrary number of cloning attacks. Our objective in this study was to know if the number of the eavesdroppers and their angle of cloning act on the safety of information. Results: It was found that the quantum error and the secured/no secured transition depend strongly on the number of eavesdropper and their angle of attacks. The particular cases where all eavesdroppers collaborate were also investigated. Conclusion: Furthermore, the cloning attack’s quantum error is lower than the intercept and resends attacks one, which means that the cloning attacks is the optimal one for arbitrary number of eavesdropper. Key words: Quantum, cryptography, cloning, eavesdroppers INTRODUCTION bases of measurement. In impossibility of doing it, the eavesdropper can decide to copy the qubits in an The quantum mechanics is used by Wiesner (1983) optimal approximate way. It is thus essential for the to serve safety of information and he introduces the transmitter and the receiver to know what eavesdropper concept of quantum conjugate coding.
    [Show full text]
  • Quantum Teleportation Nicolas Gisin H
    Quantum teleportation Nicolas Gisin H. Deriedmatten, I. Marcikic, R. Thew, W. Tittel, H. Zbinden Groupe de Physique Appliquée-unité d’Optique Université de Genène • The science and the science-fiction of quantum teleportation • Intuitive and mathematical introduction • What is teleported ? • Q fax? The no-cloning theorem • The “teleportation channel”: Entanglement • The Geneva experiment Geneva University • Telecom wavelengths • Time-bin qubits • partial Bell measurement and tests of Bell inequality • Applications: Quantum Key Distribution GAP Optique • Simplifications, limitations • Q relays and Q repeaters 1 The Geneva Teleportation experiment over 3x2 km Photon = particle (atom) of light Polarized photon Unpolarized photon ≈ ( structured photon) (≈ unstructured ≈ dust) Geneva University GAP Optique 2 55 metres 2 km of 2 km of optical fibre optical fibre Geneva University Two entangled photons GAP Optique 3 55 metres 2 km of Geneva University optical fibre GAP Optique 4 55 metres Bell measurement (partial) the 2 photons Geneva University interact 4 possible results: 0, 90, 180, 270 degrees GAP Optique 5 55 metres Bell measurement (partial) the 2 photons ion Geneva University at interact rel Cor ect erf 4 possible results: P The correlation is independent of the quantum 0, 90, 180, 270 degrees GAP Optique state which may be unknown or even entangled with a fourth photon 6 Quantum teleportation ψ 2 bits U Bell ψ ⊗ EPR = + ⊗ + (c 0 0 c1 1 ) ( 0,0 1,1 ) / 2 11 = ((00,0,0 ++ 11,1,1 )) ⊗ ( c 0 + c 1 ) 2 0 1 Ψ 2 2 123 1 Geneva University + ((00,0,0 −− 11,1,1 )) ⊗ ( c 0 − c 1 ) 2 0 1 σ Ψ 2 2 123 z 1 + ((00,1,1 ++ 11,0,0 )) ⊗ ( c 0 + c 1 ) 2 22 1 0 σ Ψ x GAP Optique 123 1 + ((00,1,1 −− 11,0,0 )) ⊗ ( c 0 − c 1 ) 2 22 1 0 σ Ψ 123 y 7 What is teleported ? According to Aristotle, objects are constituted by matter and form, ie by elementary particles and quantum states.
    [Show full text]
  • Fundamentals of Quantum Information Theory Michael Keyl
    Physics Reports 369 (2002) 431–548 www.elsevier.com/locate/physrep Fundamentals of quantum information theory Michael Keyl TU-Braunschweig, Institute of Mathematical Physics, Mendelssohnstrae 3, D-38106 Braunschweig, Germany Received 3 June 2002 editor: J. Eichler Abstract In this paper we give a self-contained introduction to the conceptional and mathematical foundations of quantum information theory. In the ÿrst part we introduce the basic notions like entanglement, channels, teleportation, etc. and their mathematical description. The second part is focused on a presentation of the quantitative aspects of the theory. Topics discussed in this context include: entanglement measures, chan- nel capacities, relations between both, additivity and continuity properties and asymptotic rates of quantum operations. Finally, we give an overview on some recent developments and open questions. c 2002 Elsevier Science B.V. All rights reserved. PACS: 03.67.−a; 03.65.−w Contents 1. Introduction ........................................................................................ 433 1.1. What is quantum information? ................................................................... 434 1.2. Tasks of quantum information .................................................................... 436 1.3. Experimental realizations ........................................................................ 438 2. Basic concepts ...................................................................................... 439 2.1. Systems, states and e=ects ......................................................................
    [Show full text]
  • Twenty Years of Quantum State Teleportation at the Sapienza University in Rome
    entropy Review Twenty Years of Quantum State Teleportation at the Sapienza University in Rome Francesco De Martini and Fabio Sciarrino * Dipartimento di Fisica—Sapienza Università di Roma, P.le Aldo Moro 5, I-00185 Roma, Italy * Correspondence: [email protected] Received: 31 July 2018; Accepted: 14 July 2019; Published: 6 August 2019 Abstract: Quantum teleportation is one of the most striking consequence of quantum mechanics and is defined as the transmission and reconstruction of an unknown quantum state over arbitrary distances. This concept was introduced for the first time in 1993 by Charles Bennett and coworkers, it has then been experimentally demonstrated by several groups under different conditions of distance, amount of particles and even with feed forward. After 20 years from its first realization, this contribution reviews the experimental implementations realized at the Quantum Optics Group of the University of Rome La Sapienza. Keywords: quantum teleportation; entanglement; photonics; quantum information 1. Introduction Entanglement is today the core of many key discoveries ranging from quantum teleportation [1], to quantum dense coding [2], quantum computation [3–5] and quantum cryptography [6,7]. Quantum communication protocols such as device-independent quantum key distribution [8] are heavily based on entanglement to reach nonlocality-based communication security [9]. The prototype for quantum information transfer using entanglement as a communication channel is the quantum state teleportation (QST) protocol, introduced for the first time in 1993 by Charles Bennett et al. [1], where a sender and a receiver share a maximally entangled state which they can use to perfectly transfer an unknown quantum state. Undoubtedly, quantum teleportation is one of the most counterintituitive consequences of quantum mechanics and it is defined as the transmission and reconstruction over arbitrary distances of an unknown quantum state.
    [Show full text]
  • Entanglement and Quantum Cryptography
    Entanglement and Quantum Cryptography Joonwoo Bae Barcelona, January, 2007 Universitat de Barcelona Departament d’Estructura i Constituents de la Mat`eria Tesis presentada para optar al grado de doctor, January 2007. Programa de doctorado: F´ısicaAvanzada. Bienio: 2003-2005. Thesis advisor: Dr. Antonio Ac´ınDal Maschio( Assistant Professor in ICFO and ICREA Junior) Dear friend, I pray that you may enjoy good health And that all may go well with you, Even as your soul is getting along well. Acknowledgement I am grateful to all the people who helped me throughout my education. My advisor, Antonio Ac´ın,has patiently guided me with his creative insights. In particular, many thanks for his kind care and ceaseless encouragement. He allowed me to have the journey in quantum information when I was just a beginner, and I am grateful for his clear, ideaful, and well-motivated expla- nations. I thank Ignacio Cirac who allowed me to join Barcelona quantum information. Also, thanks for the opportunity to visit MPQ. I thank Jos´e Ignacio Latorre for his kind support as my university tutor. I would also like to thank collaborators, Maciej Lewenstein, Anna San- pera, Emili Bagan, Ramon Mu˜noz-Tapia, Maria Baig, Lluis Masanes, Ujjwal Sen, Aditi Sen De, and Sofyan Iblisdir. I have enjoyed attending discussions; these helped me improve immensely. Many thanks go to Nicolas Gisin, So- fyan Iblisdir, Renato Renner, Andreas Buchleitner, Anna Sanpera, Maciej Lewenstein, and Ramon Mu˜noz-Tapia, for being on the thesis committee. I am very grateful for the people who assisted me while I was traveling as well.
    [Show full text]