The Korepin Festschrift : From Statistical Mechanics to Quantum Information Science.

By: Kwek, Leong-ChuanContributor(s): Severini, Simone | Su, HaibinPublisher: Singapore : World Scientific Publishing Co Pte Ltd, 2013Copyright date: ©2013Description: 1 online resource (238 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9789814460323Subject(s): Korepin, V. E. -- (Vladimir E.);Quantum theoryGenre/Form: Electronic books. Additional physical formats: Print version:: The Korepin Festschrift : From Statistical Mechanics to Quantum Information ScienceDDC classification: 530.12 LOC classification: QA268 .K384 2013Online resources: Click to View
Contents:
Intro -- CONTENTS -- Preface -- Organizing Committee -- List of Speakers -- Photos -- Chapter 1: Cancellation of Ultra-Violet Infinities in One Loop Gravity V. E. Korepin -- 1. Introduction -- 2. Covariant Quantization -- 3. Cancelation of Infinities in one Loop Approximation -- 4. Finite Part of the Generating Functional of the Scattering Matrix -- 5. One Loop Diagram with Two Vertices -- References -- Chapter 2: Quantum Discord in a Spin System with Symmetry Breaking B. Tomasello, D. Rossini, A. Hamma and L. Amico -- 1. Introduction -- 2. Quantum, Classical, and Total Correlations -- 3. The XY Model in Transverse Field -- 3.1. The Phase Diagram -- 4. Classical and Quantum Correlations in the Model -- 5. Analysis of Quantum Discord at T = 0 -- 6. Quantum Discord at Finite Temperature -- 7. Discussions -- Acknowledgments -- References -- Chapter 3: Entanglement from the Dynamics of an Ideal Bose Gas in a Lattice S. Bose -- 1. Introduction -- Acknowledgment -- References -- Chapter 4: Aspects of the Riemannian Geometry of Quantum Computation H. E. Brandt -- 1. Introduction -- 2. Riemannian Geometry of SU(2n) -- 3. Summary -- Acknowledgment -- References -- Chapter 5: Quantum Mechanics and the Role of Time: Are Quantum Systems Markovian? T. Durt -- 1. Introduction -- 2. Do Quantum Dice Remember? - Experimental Tests -- 2.1. Bohm-Bub's model and the Papaliolos experiment -- 2.2. Buonomano's model and the Summhammer experiment -- 2.3. Hidden measurement approach and the Paris-Nord experiment -- 2.3.1. The Poissonian paradigm -- 2.3.2. Departures from the Poissonian paradigm -- 2.3.3. Recent results -- 2.4. Shnoll's hypotheses and the Brussels experiment -- 3. Sheldrake and Smolin's Models, and a Related Experimental Proposal -- 3.1. Sheldrake's model -- 3.2. Smolin's model.
3.3. Unfalsifiability of Sheldrake and Smolin's models - New experimental proposals -- 4. Conclusions -- Acknowledgments -- References -- Chapter 6: Explicit Formula of the Separability Criterion for Continuous Variables Systems K. Fujikawa -- 1. Introduction and Summary -- 2. Details of Analyses -- 2.1. Simon's criterion -- 2.2. Gaussian states and P-representation -- 2.3. Duan-Giedke-Chirac-Zoller criterion -- 2.4. Hierarchy of separability criterions -- 3. Discussion and Related References -- References -- Chapter 7: Yang-Baxter Equations in Quantum Information M.-L. Ge and K. Xue -- 1. Introduction -- 2. Two Types of Braiding Matrices. Yang-Baxter Equation and Temperley-Lieb Algebra -- 3. 2-D Topological Basis of Braiding Matrices -- 4. Unified Form for Both Type-1 and Type-2 BRM's -- 5. Two Types of BRM in Physics and Extremization of l1-Norm -- 5.1. Motivation of l1-norm involution -- 5.2. Extremization of D-function and l1-norm -- 6. Bogoliubov's Hamiltonian Induced from Dirac's Hamiltonian via Braid Matrix -- 7. Optical Simulation of YBE -- 8. Topological Basis for BWA -- 8.1. Matrix form of E12, E23, S12 and S23 for S† = S -- 8.2. Application to the "standard" q-deformed spin-1 model -- 9. Conclusion -- Acknowledgments -- References -- Chapter 8: Nondistillable Entanglement Guarantees Distillable Entanglement L. Chen and M. Hayashi -- 1. Introduction -- 2. Unification of Entanglement Criterion -- 3. Classification with Reduced States -- 4. Generalization to Multipartite System -- 5. Conclusions -- 6. Acknowledgments and Appendices -- Appendix -- References -- Chapter 9: Reduced Density Matrix and Entanglement Entropy of Permutationally Invariant Quantum Many-Body Systems V. Popkov and M. Salerno -- 1. Introduction -- 2. Model Equation and Basic Definitions -- 3. RDM Properties and Block Diagonal Form.
4. Analytical Expression of RDM Elements -- 5. Spectral Properties of RDM and Entanglement Entropy -- 6. Moments of the Reduced Density Matrix and Renyi and Tsallis Entropies -- 7. Conclusions -- Acknowledgments -- Appendix A. RDM Elements for Symmetric States -- Appendix B. RDM Elements in the Thermodynamic Limit -- References -- Chapter 10: Solitons Experience for Black Hole Production in Ultrarelativistic Particle Collisions I. Ya. Aref 'eva -- 1. Introduction -- 2. Transition Amplitudes and Cross Section of the BH/WH Production -- 3. Ultrarelativistic Particles on the Brane -- 3.1. D-dimensional Planckian energy -- 3.2. D-dimensional gravitational model of relativistic particles -- 4. Shock Wave as a Model of Ultra Relativistic Moving Particle -- 5. D-Dimensional Thorne Hoop Conjecture and Geometrical Cross Section -- 6. Looking from the Rest Frame of One of the Incident Particles -- 7. BH Formation and the Eikonal Approximation -- 8. Transition Amplitudes and Cross Section for Higher Dimensional Gravity and Matter Living on the Brane -- Acknowledgments -- Appendix A. BH as an Initial/Final Data -- A.1. (Weakly) asymptotically simple space-time -- A.2. Asymptotically flat space-time -- A.3. Global (partial) Cauchy surface -- A.4. Causal future J+(p) and causal past J-(p) of the point -- A.5. BHs in asymptotically flat space-time -- A.6. Future (strongly) asymptotically predictable space-time -- A.7. BH on a surface -- A.8. Boundary conditions in the path integral representation -- References -- Chapter 11: Sine-Gordon Theory in the Repulsive Regime, Thermodynamic Bethe Ansatz and Minimal Models H. Itoyama -- 1. Introduction -- References -- Chapter 12: On Some Algebraic and Combinatorial Properties of Dunkl Elements A. N. Kirillov -- 1. Introduction -- 2. Dunkl Elements -- 3. Algebra 3HTn.
4. Combinatorics of Associative Quasi-Classical Yang-Baxter Algebras -- 4.1. Combinatorics of Coxeter element -- 4.2. Grothendieck and q-Schroderpolynomials -- 4.2.1. Schroder paths and polynomials -- 4.2.2. Principal specialization of Grothendieck polynomials and q-Schroder polynomials -- 4.3. The "longest element" and Chan-Robbins polytope -- Acknowledgments -- References -- Chapter 13: Finite Projective Spaces, Geometric Spreads of Lines and Multi-Qubits M. Saniga -- Acknowledgments -- References -- Chapter 14: Monogamy of Entanglement, N-Representability Problems and Ground States T.-C. Wei -- 1. Introduction -- 2. Mean-Field Approximation -- 3. N-Representability Problem -- 3.1. 3-representable -- 3.2. n-representable -- 3.3. Ground-state entanglement -- 4. Concluding Remarks -- Acknowledgment -- References -- Scientific Programs -- List of Participants.
Summary: This volume mainly summarizes the invited talks presented at the 5th Asia-Pacific Workshop on Quantum Information Science (APWQIS) in conjunction with a Festschrift in honor of Professor Vladimir Korepin's 60th birthday. In this Festschrift, we have assembled a medley of interesting articles from some of his friends, well-wishers and collaborators. Comprising both reviews of the state-of-the-art and the latest results, this book covers various aspects of quantum information science, including topics like quantum discord, quantum computing, quantum entanglement, etc.
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Intro -- CONTENTS -- Preface -- Organizing Committee -- List of Speakers -- Photos -- Chapter 1: Cancellation of Ultra-Violet Infinities in One Loop Gravity V. E. Korepin -- 1. Introduction -- 2. Covariant Quantization -- 3. Cancelation of Infinities in one Loop Approximation -- 4. Finite Part of the Generating Functional of the Scattering Matrix -- 5. One Loop Diagram with Two Vertices -- References -- Chapter 2: Quantum Discord in a Spin System with Symmetry Breaking B. Tomasello, D. Rossini, A. Hamma and L. Amico -- 1. Introduction -- 2. Quantum, Classical, and Total Correlations -- 3. The XY Model in Transverse Field -- 3.1. The Phase Diagram -- 4. Classical and Quantum Correlations in the Model -- 5. Analysis of Quantum Discord at T = 0 -- 6. Quantum Discord at Finite Temperature -- 7. Discussions -- Acknowledgments -- References -- Chapter 3: Entanglement from the Dynamics of an Ideal Bose Gas in a Lattice S. Bose -- 1. Introduction -- Acknowledgment -- References -- Chapter 4: Aspects of the Riemannian Geometry of Quantum Computation H. E. Brandt -- 1. Introduction -- 2. Riemannian Geometry of SU(2n) -- 3. Summary -- Acknowledgment -- References -- Chapter 5: Quantum Mechanics and the Role of Time: Are Quantum Systems Markovian? T. Durt -- 1. Introduction -- 2. Do Quantum Dice Remember? - Experimental Tests -- 2.1. Bohm-Bub's model and the Papaliolos experiment -- 2.2. Buonomano's model and the Summhammer experiment -- 2.3. Hidden measurement approach and the Paris-Nord experiment -- 2.3.1. The Poissonian paradigm -- 2.3.2. Departures from the Poissonian paradigm -- 2.3.3. Recent results -- 2.4. Shnoll's hypotheses and the Brussels experiment -- 3. Sheldrake and Smolin's Models, and a Related Experimental Proposal -- 3.1. Sheldrake's model -- 3.2. Smolin's model.

3.3. Unfalsifiability of Sheldrake and Smolin's models - New experimental proposals -- 4. Conclusions -- Acknowledgments -- References -- Chapter 6: Explicit Formula of the Separability Criterion for Continuous Variables Systems K. Fujikawa -- 1. Introduction and Summary -- 2. Details of Analyses -- 2.1. Simon's criterion -- 2.2. Gaussian states and P-representation -- 2.3. Duan-Giedke-Chirac-Zoller criterion -- 2.4. Hierarchy of separability criterions -- 3. Discussion and Related References -- References -- Chapter 7: Yang-Baxter Equations in Quantum Information M.-L. Ge and K. Xue -- 1. Introduction -- 2. Two Types of Braiding Matrices. Yang-Baxter Equation and Temperley-Lieb Algebra -- 3. 2-D Topological Basis of Braiding Matrices -- 4. Unified Form for Both Type-1 and Type-2 BRM's -- 5. Two Types of BRM in Physics and Extremization of l1-Norm -- 5.1. Motivation of l1-norm involution -- 5.2. Extremization of D-function and l1-norm -- 6. Bogoliubov's Hamiltonian Induced from Dirac's Hamiltonian via Braid Matrix -- 7. Optical Simulation of YBE -- 8. Topological Basis for BWA -- 8.1. Matrix form of E12, E23, S12 and S23 for S† = S -- 8.2. Application to the "standard" q-deformed spin-1 model -- 9. Conclusion -- Acknowledgments -- References -- Chapter 8: Nondistillable Entanglement Guarantees Distillable Entanglement L. Chen and M. Hayashi -- 1. Introduction -- 2. Unification of Entanglement Criterion -- 3. Classification with Reduced States -- 4. Generalization to Multipartite System -- 5. Conclusions -- 6. Acknowledgments and Appendices -- Appendix -- References -- Chapter 9: Reduced Density Matrix and Entanglement Entropy of Permutationally Invariant Quantum Many-Body Systems V. Popkov and M. Salerno -- 1. Introduction -- 2. Model Equation and Basic Definitions -- 3. RDM Properties and Block Diagonal Form.

4. Analytical Expression of RDM Elements -- 5. Spectral Properties of RDM and Entanglement Entropy -- 6. Moments of the Reduced Density Matrix and Renyi and Tsallis Entropies -- 7. Conclusions -- Acknowledgments -- Appendix A. RDM Elements for Symmetric States -- Appendix B. RDM Elements in the Thermodynamic Limit -- References -- Chapter 10: Solitons Experience for Black Hole Production in Ultrarelativistic Particle Collisions I. Ya. Aref 'eva -- 1. Introduction -- 2. Transition Amplitudes and Cross Section of the BH/WH Production -- 3. Ultrarelativistic Particles on the Brane -- 3.1. D-dimensional Planckian energy -- 3.2. D-dimensional gravitational model of relativistic particles -- 4. Shock Wave as a Model of Ultra Relativistic Moving Particle -- 5. D-Dimensional Thorne Hoop Conjecture and Geometrical Cross Section -- 6. Looking from the Rest Frame of One of the Incident Particles -- 7. BH Formation and the Eikonal Approximation -- 8. Transition Amplitudes and Cross Section for Higher Dimensional Gravity and Matter Living on the Brane -- Acknowledgments -- Appendix A. BH as an Initial/Final Data -- A.1. (Weakly) asymptotically simple space-time -- A.2. Asymptotically flat space-time -- A.3. Global (partial) Cauchy surface -- A.4. Causal future J+(p) and causal past J-(p) of the point -- A.5. BHs in asymptotically flat space-time -- A.6. Future (strongly) asymptotically predictable space-time -- A.7. BH on a surface -- A.8. Boundary conditions in the path integral representation -- References -- Chapter 11: Sine-Gordon Theory in the Repulsive Regime, Thermodynamic Bethe Ansatz and Minimal Models H. Itoyama -- 1. Introduction -- References -- Chapter 12: On Some Algebraic and Combinatorial Properties of Dunkl Elements A. N. Kirillov -- 1. Introduction -- 2. Dunkl Elements -- 3. Algebra 3HTn.

4. Combinatorics of Associative Quasi-Classical Yang-Baxter Algebras -- 4.1. Combinatorics of Coxeter element -- 4.2. Grothendieck and q-Schroderpolynomials -- 4.2.1. Schroder paths and polynomials -- 4.2.2. Principal specialization of Grothendieck polynomials and q-Schroder polynomials -- 4.3. The "longest element" and Chan-Robbins polytope -- Acknowledgments -- References -- Chapter 13: Finite Projective Spaces, Geometric Spreads of Lines and Multi-Qubits M. Saniga -- Acknowledgments -- References -- Chapter 14: Monogamy of Entanglement, N-Representability Problems and Ground States T.-C. Wei -- 1. Introduction -- 2. Mean-Field Approximation -- 3. N-Representability Problem -- 3.1. 3-representable -- 3.2. n-representable -- 3.3. Ground-state entanglement -- 4. Concluding Remarks -- Acknowledgment -- References -- Scientific Programs -- List of Participants.

This volume mainly summarizes the invited talks presented at the 5th Asia-Pacific Workshop on Quantum Information Science (APWQIS) in conjunction with a Festschrift in honor of Professor Vladimir Korepin's 60th birthday. In this Festschrift, we have assembled a medley of interesting articles from some of his friends, well-wishers and collaborators. Comprising both reviews of the state-of-the-art and the latest results, this book covers various aspects of quantum information science, including topics like quantum discord, quantum computing, quantum entanglement, etc.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2019. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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