Zhao, Shuang

English

ARTS repository - University of Groningen

   University of GroningenEvent-based simulation of quantum phenomenaZhao, ShuangIMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite fromit. Please check the document version below.Document VersionPublisher's PDF, also known as Version of recordPublication date:2009Link to publication in University of Groningen/UMCG research databaseCitation for published version (APA):Zhao, S. (2009). Event-based simulation of quantum phenomena: application to quantum interference,Einstein-Podolsky-Rosen experiments, quantum computation and quantum cryptography. s.n.CopyrightOther than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of theauthor(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons).The publication may also be distributed here under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license.More information can be found on the University of Groningen website: https://www.rug.nl/library/open-access/self-archiving-pure/taverne-amendment.Take-down policyIf you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediatelyand investigate your claim.Downloaded from the University of Groningen/UMCG research database (Pure): http://www.rug.nl/research/portal. For technical reasons thenumber of authors shown on this cover page is limited to 10 maximum.Download date: 07-06-2022Event-based Simulation ofQuantum PhenomenaApplication to Quantum Interference, Einstein-Podolsky-Rosen Experiments,Quantum Computation and Quantum CryptographyShuang Zhao2009To my parents and my husbandZernike Institute PhD thesis series 2009-05ISSN 1570-1530The work described in this thesis was performed at the Department of AppliedPhysics of the Rijksuniversiteit Groningen, the Netherlands.ISBN electronic version: 978-90-367-3745-6ISBN printed version: 978-90-367-3746-3Printed by Ipskamp Drukkers, the NetherlandsCopyright c© 2009, S. ZhaoRIJKSUNIVERSITEIT GRONINGENEvent-based Simulation of QuantumPhenomenaApplication to Quantum Interference, Einstein-Podolsky-Rosen Experiments,Quantum Computation and Quantum CryptographyProefschriftter verkrijging van het doctoraat in deWiskunde en Natuurwetenschappenaan de Rijksuniversiteit Groningenop gezag van deRector Magnificus, dr. F. Zwarts,in het openbaar te verdedigen opvrijdag 13 maart 2009om 14:45 uurdoorShuang Zhaogeboren op 21 mei 1979te Harbin ChinaPromotor: Prof.dr. H.A. De RaedtBeoordelingscommissie: Prof.dr. S. MiyashitaProf.dr. J.Th.M. De HossenProf.dr. P. RudolfIContents1 Introduction 12 Simulation Method 72.1 General description of the LM . . . . . . . . . . . . . . . . . . . . . . 72.2 DLM-based processing unit – Learning on a hypersphere . . . . . . . 82.2.1 Description of the processing unit . . . . . . . . . . . . . . . . 82.2.2 Analysis of the dynamic behavior . . . . . . . . . . . . . . . . 122.2.3 Output sequence analysis . . . . . . . . . . . . . . . . . . . . . 142.3 DLM-based processing unit – Learning on a finite interval . . . . . . 152.3.1 Description of the processing unit . . . . . . . . . . . . . . . . 152.3.2 Analysis of the dynamic behavior . . . . . . . . . . . . . . . . 182.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183 Randomness and Quantum Mechanics 213.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.1.1 Random variables and probability distribution . . . . . . . . . 223.1.2 Shannon entropy and Kolmogorov complexity . . . . . . . . . 243.1.3 Randomness in quantum mechanics . . . . . . . . . . . . . . . 273.2 QRNG with single photon beam splitting . . . . . . . . . . . . . . . . 303.2.1 Description of the real QRNG . . . . . . . . . . . . . . . . . . 303.2.2 Theoretical analysis . . . . . . . . . . . . . . . . . . . . . . . . 323.3 Statistical analysis of simulated binary sequences . . . . . . . . . . . 323.3.1 Tests for randomness . . . . . . . . . . . . . . . . . . . . . . . 323.3.2 Statistical test of the simulation samples . . . . . . . . . . . . 333.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36II CONTENTS4 Quantum Interference 394.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 394.2 Simulation of ideal single photon MZI . . . . . . . . . . . . . . . . . . 404.3 Simulation of non-monochromatic single photon MZI . . . . . . . . . 434.4 Simulation of Wheeler’s gedanken experiment . . . . . . . . . . . . . 454.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454.4.2 Simulation model . . . . . . . . . . . . . . . . . . . . . . . . . 474.4.3 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . 514.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535 Einstein-Podolsky-Rosen-Bohm experiments with photons 555.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.2 EPRB experiment with photons . . . . . . . . . . . . . . . . . . . . . 585.3 Quantum Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 615.4 Data analysis of a real EPRB experiment with photons . . . . . . . . 625.5 Simulation model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.5.1 Source and particles . . . . . . . . . . . . . . . . . . . . . . . 665.5.2 Observation stations . . . . . . . . . . . . . . . . . . . . . . . 665.5.3 Polarizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.5.4 Time delay . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.5.5 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.6 Probabilistic treatment . . . . . . . . . . . . . . . . . . . . . . . . . . 685.7 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.8 Comparison with experimental data . . . . . . . . . . . . . . . . . . . 765.9 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 805.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816 Quantum Computation 836.1 Introduction of quantum computation . . . . . . . . . . . . . . . . . . 836.1.1 The concept of qubit and the state of a quantum system . . . 846.1.2 Three stages of quantum computation . . . . . . . . . . . . . 856.2 Quantum gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 866.2.1 Single-qubit operations . . . . . . . . . . . . . . . . . . . . . . 87CONTENTS III6.2.2 Two-qubit operations: CNOT and controlled phase shift . . . 906.2.3 Three-qubit operations: TOFFOLI gate . . . . . . . . . . . . 926.3 Some examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926.3.1 Shor’s algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 926.3.1.1 Algorithm description . . . . . . . . . . . . . . . . . 936.3.1.2 Simulation of Shor’s algorithm . . . . . . . . . . . . 966.3.2 Error correction . . . . . . . . . . . . . . . . . . . . . . . . . . 976.3.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 976.3.2.2 Three-qubit bit flip error correction code . . . . . . . 986.3.2.3 Event-based simulation of the three-qubit bit flip er-ror correction code . . . . . . . . . . . . . . . . . . . 1026.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1037 Quantum Cryptography 1057.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1057.2 BB84 protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1077.3 Ekert’s protocol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1087.4 Event-based simulation of a polarizer . . . . . . . . . . . . . . . . . . 1117.5 Event-based simulation of the BB84 protocol . . . . . . . . . . . . . . 1127.5.1 Simulation of the BB84 protocol in the absence of an eaves-dropper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137.5.2 Simulation of the BB84 protocol in the presence of an eaves-dropper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1147.5.3 Misalignment of the measurement basis . . . . . . . . . . . . . 1147.5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1157.6 Event-based simulation of the Ekert protocol . . . . . . . . . . . . . . 1177.6.1 Simulation of the Ekert protocol in the absence of an eaves-dropper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1177.6.2 Simulation of the Ekert protocol in the presence of an eaves-dropper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1237.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1257.8 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125Reference 129References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129IV CONTENTSSummary 141Samenvatting 143Publications 145Acknowledgments 147

Event-based simulation of quantum phenomena:application to quantum interference, Einstein-Podolsky-Rosen experiments, quantum computation and quantum cryptography

https://pure.rug.nl/ws/files/14669172/00titlecon.pdf

Event-based simulation of quantum phenomena:application to quantum interference, Einstein-Podolsky-Rosen experiments, quantum computation and quantum cryptography

Abstract

Similar works

Full text

Available Versions

ARTS repository - University of Groningen