Quantum Information and Computing : Waseda University, Tokyo, Japan 29-31 October 2003, Tokyo University of Science, Tokyo, Japan 1-3 November 2003, International Institute of Advanced Study, Kyoto, Japan 5-7 November 2003, Mei.

By: Accardi, LContributor(s): Ohya, Masanori | Watanabe, NSeries: Qp-Pq: Quantum Probability and White Noise Analysis SerPublisher: Singapore : World Scientific Publishing Co Pte Ltd, 2006Copyright date: ©2006Description: 1 online resource (396 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9789812774491Subject(s): Quantum computers -- Congresses.;Quantum theory -- CongressesGenre/Form: Electronic books. Additional physical formats: Print version:: Quantum Information and Computing : Waseda University, Tokyo, Japan 29-31 October 2003, Tokyo University of Science, Tokyo, Japan 1-3 November 2003, International Institute of Advanced Study, Kyoto, Japan 5-7 November 2003, MeiDDC classification: 004.7 LOC classification: QA76.889.Q8484 2006Online resources: Click to View
Contents:
Intro -- Contents -- Preface -- Coherent Quantum Control of A-Atoms through the Stochastic Limit -- 1 Introduction -- 2 An atom in a laser field -- 3 The stochastic limit -- 4 The quantum master equation -- 5 Stationary states for a two-level atom -- 6 Stationary states for a three-level atom -- 7 Three-level lambda-atom -- 8 Two-level 3-times degenerate atom -- 9 Conclusions -- References -- Recent Advances in Quantum White Noise Calculus -- 1 Emergence of white noise equations from classical quantum mechanics -- 2 Quantum white noise unitary evolutions -- 3 Higher powers of white noise -- 4 Appplications to quantum stochastic control -- References -- Control of Quantum States by Decoherence -- 1 Introduction -- 2 A master equation driving to a pre-assigned state -- 3 A microscopic model -- 4 The Master equation -- 5 Assimilation of the state -- 6 Purification -- 7 Example: Entangled state with Spin-Boson model -- References -- Logical Operations Realized on the Ising Chain of N Qubits -- Joint Extension of States of Fermion Subsystems -- 1 Introduction -- 2 Notation for Fermion Systems -- 3 Product Extension -- 4 A Pair of Pure and General States for Two Subsystems -- 5 Examples -- References -- Quantum Filtering and Optimal Feedback Control of a Gaussian Quantum Free Particle -- 1 Inroduction -- 2 The Model -- 3 Quantum Filtering -- 4 Control -- 5 Discussion -- References -- On Existence of Quantum Zeno Dynamics -- 1 Introduction and the result -- 2 Proof sketch of Theorems 1.1 and 1.2 -- 3 An example -- References -- Invariant Subspaces and Control of Decoherence -- 1 Introduction -- 2 Generalities and notation -- 3 Control procedures -- 4 The Zeno subspaces -- 5 Summary and concluding remarks -- References -- Clauser-Horne Inequality for Electron Counting Statistics in Multiterminal Mesoscopic Conductors -- 1 Introduction.
2 CH inequality for the full counting statistics -- 3 Results -- 4 Conclusions -- References -- Fidelity of Quantum Teleportation Model Using Beam Splittings -- 1 Introduction -- 2 Basic Notions and Notations -- 3 Teleportation scheme with tests 4 -- 4 Teleportation and fidelity -- References -- Quantum Logical Gates Realized by Beam Splittings -- 1 Introduction -- 2 The Boson Fock Space -- 3 A General Beam Splitting Model -- 4 The Splitting Procedures -- 5 Splitting Functions fulfilling the Truth Table -- References -- Information Divergence for Quantum Channels -- 1 Introduction -- 2 Axiomatic Properties of Relative Information -- 3 Examples of Relative Information for States -- 4 Relative Information for Channels -- References -- On the Uniqueness Theorem in Quantum Information Geometry -- 0 Introduction -- 1 Extended Chentsov Theorem for noncommutative (finite-dimensional matrix) manifolds -- 2 Derivation and Frechet differentiation -- 3 Classical and quantum a-divergence -- 4 Proof of the uniqueness for matrix manifolds-Main theorem in the nonparametric version -- 5 Parametrization of the matrix manifold -- 6 A Concluding Remark-on Tsallis statistics -- References -- Noncanonical Representations of a Multi-dimensional Brownian Motion -- 1 Introduction -- 2 d-dimensional Brownian motions -- References -- Some of Future Directions of White Noise Theory -- 1 Introduction -- 2 White noise analysis -- 3 New directions. (Our plans.) -- 4 Innovation -- References -- Information Innovation and Elemental Random Field -- 1 Introduction -- 2 White noise analysis -- 3 Our plans -- 4 Innovation -- 5 Path integrals -- 6 Concluding remark -- References -- Generalized Quantum Turing Machine and Its Application to the SAT Chaos Algorithm -- 1 Introduction -- 2 Generalized Quantum Turing Machine -- 3 SAT Problem -- 4 SAT Algorithm -- 5 SAT algorithm in GQTM.
References -- A Stroboscopic Approach to Quantum Tomography -- 1 Introduction -- 2 Polynomial Representation of Flows -- 3 The Minimal Number of Observables for Qudits Governed by Gaussian Semigroups -- References -- Positive Maps and Separable States in Matrix Algebras -- 1 Introduction -- 2 A Class of Positive Maps in Mn -- References -- Simulating Open Quantum Systems with Trapped Ions -- 1 Introduction -- 2 Quantum Brownian motion: the exact dynamics -- 3 Time evolution of the mean energy: Lindblad-type and non-Lindblad-type dynamics -- 4 Experiment for simulating QBM with trapped ions -- 5 Conclusions -- References -- A Purification Scheme and Entanglement Distillations -- 1 Introduction -- 2 General Framework of Purification Through Repeated Measurements -- 3 Purification of a Qubit -- 4 Entanglement Distillation I -- 5 Entanglement Distillation II -- 6 Summary -- References -- Generalized Sectors and Adjunctions to Control Micro-Macro Transitions -- 1 Unified scheme for micro and macro -- 2 Broken symmetry in micro-macro composite system -- B=order parameter of broken scale inv. -- 3 Summary and outlook: method of "variation of natural constants" -- References -- Saturation of an Entropy Bound and Quantum Markov States -- 1 Introduction -- 2 Strong subadditivity of entropy -- 3 Quantum Markov states -- References -- An Infinite Dimensional Laplacian Acting on Some Class of Levy White Noise Functionals -- 1 Introduction -- 2 Basic Elememts of White Noise Calculus -- 3 The Levy Laplacian Acting on Levy White Noise Functionals -- 4 The Levy Laplacian Acting on WNF-valued Functions -- 5 An Infinite Dimensional Stochastic Process Associated with the Levy Laplacian -- References -- Structure of Linear Processes -- 1 Introduction -- 2 An illustrative example Linear functionals of Poisson noise -- 3 Innovation of a linear process.
4 Determination of kernels -- References -- Group Theory of Dynamical Maps -- On Quantum Analysis Quantum Transfer-Matrix Method and Effective Information Entropy -- 1 Introduction -- 2 Quantum Analysis -- 3 Quantum Transfer-Matrix Method based on Exponential Product Formulas and its Connection with Quantum Information -- 4 Effective Information Entropy -- 5 Summary and Discussion -- References -- Nonequilibrium Steady States for a Harmonic Oscillator Interacting with Two Bose Fields - Stochastic Limit Approach and C* Algebraic Approach -- 1 Introduction -- 2 Model -- 3 Stochastic Limit Approach -- 4 Nonequilibrium Steady States in C*-algebraic Approach -- 5 Weak coupling limits -- 6 Summary and Discussion -- References -- Control of Decoherence with Multipulse Application -- 1 Introduction -- 2 Formulation -- 3 Numerical evaluation -- 4 Discussion and Concluding Remarks -- References -- Quantum Entanglement Purification and Linear-optics Quantum Gates with Photonic Qubits -- 1 Entanglement -- 2 Quantum Key Distribution using Polarization Entangled Photons -- 3 Purification of Entanglement -- References -- On Quantum Mutual Type Measures and Capacity -- 1 Quantum Channels -- 2 Ohya Mutual Entropy -- 3 Comparison of various quantum mutual type entropies -- 4 Quantum Capacity -- References.
Summary: The main purpose of this volume is to emphasize the multidisciplinary aspects of this very active new line of research in which concrete technological and industrial realizations require the combined efforts of experimental and theoretical physicists, mathematicians and engineers. Contents: Coherent Quantum Control of Λ-Atoms through the Stochastic Limit (L Accardi et al.); Recent Advances in Quantum White Noise Calculus (L Accardi & A Boukas); Joint Extension of States of Fermion Subsystems (H Araki); Fidelity of Quantum Teleportation Model Using Beam Splittings (K-H Fichtner et al.); Quantum Logical Gates Realized by Beam Splittings (W Freudenberg et al.); Noncanonical Representations of a Multi-dimensional Brownian Motion (Y Hibino); Information, Innovation and Elemental Random Field (T Hida); Generalized Sectors and Adjunctions to Control Micro-Macro Transitions (I Ojima); Saturation of an Entropy Bound and Quantum Markov States (D Petz); An Infinite Dimensional Laplacian Acting on Some Class of Lévy White Noise Functionals (K Saitô); Structure of Linear Processes (S Si & W W Htay); Group Theory of Dynamical Maps (E C G Sudarshan); Quantum Entanglement, Purification, and Linear-optics Quantum Gates with Photonic Qubits (P Walther & A Zeilinger); On Quantum Mutual Type Measures and Capacity (N Watanabe); and other papers. Readership: Researchers in quantum physics and theoretical physics.
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Intro -- Contents -- Preface -- Coherent Quantum Control of A-Atoms through the Stochastic Limit -- 1 Introduction -- 2 An atom in a laser field -- 3 The stochastic limit -- 4 The quantum master equation -- 5 Stationary states for a two-level atom -- 6 Stationary states for a three-level atom -- 7 Three-level lambda-atom -- 8 Two-level 3-times degenerate atom -- 9 Conclusions -- References -- Recent Advances in Quantum White Noise Calculus -- 1 Emergence of white noise equations from classical quantum mechanics -- 2 Quantum white noise unitary evolutions -- 3 Higher powers of white noise -- 4 Appplications to quantum stochastic control -- References -- Control of Quantum States by Decoherence -- 1 Introduction -- 2 A master equation driving to a pre-assigned state -- 3 A microscopic model -- 4 The Master equation -- 5 Assimilation of the state -- 6 Purification -- 7 Example: Entangled state with Spin-Boson model -- References -- Logical Operations Realized on the Ising Chain of N Qubits -- Joint Extension of States of Fermion Subsystems -- 1 Introduction -- 2 Notation for Fermion Systems -- 3 Product Extension -- 4 A Pair of Pure and General States for Two Subsystems -- 5 Examples -- References -- Quantum Filtering and Optimal Feedback Control of a Gaussian Quantum Free Particle -- 1 Inroduction -- 2 The Model -- 3 Quantum Filtering -- 4 Control -- 5 Discussion -- References -- On Existence of Quantum Zeno Dynamics -- 1 Introduction and the result -- 2 Proof sketch of Theorems 1.1 and 1.2 -- 3 An example -- References -- Invariant Subspaces and Control of Decoherence -- 1 Introduction -- 2 Generalities and notation -- 3 Control procedures -- 4 The Zeno subspaces -- 5 Summary and concluding remarks -- References -- Clauser-Horne Inequality for Electron Counting Statistics in Multiterminal Mesoscopic Conductors -- 1 Introduction.

2 CH inequality for the full counting statistics -- 3 Results -- 4 Conclusions -- References -- Fidelity of Quantum Teleportation Model Using Beam Splittings -- 1 Introduction -- 2 Basic Notions and Notations -- 3 Teleportation scheme with tests 4 -- 4 Teleportation and fidelity -- References -- Quantum Logical Gates Realized by Beam Splittings -- 1 Introduction -- 2 The Boson Fock Space -- 3 A General Beam Splitting Model -- 4 The Splitting Procedures -- 5 Splitting Functions fulfilling the Truth Table -- References -- Information Divergence for Quantum Channels -- 1 Introduction -- 2 Axiomatic Properties of Relative Information -- 3 Examples of Relative Information for States -- 4 Relative Information for Channels -- References -- On the Uniqueness Theorem in Quantum Information Geometry -- 0 Introduction -- 1 Extended Chentsov Theorem for noncommutative (finite-dimensional matrix) manifolds -- 2 Derivation and Frechet differentiation -- 3 Classical and quantum a-divergence -- 4 Proof of the uniqueness for matrix manifolds-Main theorem in the nonparametric version -- 5 Parametrization of the matrix manifold -- 6 A Concluding Remark-on Tsallis statistics -- References -- Noncanonical Representations of a Multi-dimensional Brownian Motion -- 1 Introduction -- 2 d-dimensional Brownian motions -- References -- Some of Future Directions of White Noise Theory -- 1 Introduction -- 2 White noise analysis -- 3 New directions. (Our plans.) -- 4 Innovation -- References -- Information Innovation and Elemental Random Field -- 1 Introduction -- 2 White noise analysis -- 3 Our plans -- 4 Innovation -- 5 Path integrals -- 6 Concluding remark -- References -- Generalized Quantum Turing Machine and Its Application to the SAT Chaos Algorithm -- 1 Introduction -- 2 Generalized Quantum Turing Machine -- 3 SAT Problem -- 4 SAT Algorithm -- 5 SAT algorithm in GQTM.

References -- A Stroboscopic Approach to Quantum Tomography -- 1 Introduction -- 2 Polynomial Representation of Flows -- 3 The Minimal Number of Observables for Qudits Governed by Gaussian Semigroups -- References -- Positive Maps and Separable States in Matrix Algebras -- 1 Introduction -- 2 A Class of Positive Maps in Mn -- References -- Simulating Open Quantum Systems with Trapped Ions -- 1 Introduction -- 2 Quantum Brownian motion: the exact dynamics -- 3 Time evolution of the mean energy: Lindblad-type and non-Lindblad-type dynamics -- 4 Experiment for simulating QBM with trapped ions -- 5 Conclusions -- References -- A Purification Scheme and Entanglement Distillations -- 1 Introduction -- 2 General Framework of Purification Through Repeated Measurements -- 3 Purification of a Qubit -- 4 Entanglement Distillation I -- 5 Entanglement Distillation II -- 6 Summary -- References -- Generalized Sectors and Adjunctions to Control Micro-Macro Transitions -- 1 Unified scheme for micro and macro -- 2 Broken symmetry in micro-macro composite system -- B=order parameter of broken scale inv. -- 3 Summary and outlook: method of "variation of natural constants" -- References -- Saturation of an Entropy Bound and Quantum Markov States -- 1 Introduction -- 2 Strong subadditivity of entropy -- 3 Quantum Markov states -- References -- An Infinite Dimensional Laplacian Acting on Some Class of Levy White Noise Functionals -- 1 Introduction -- 2 Basic Elememts of White Noise Calculus -- 3 The Levy Laplacian Acting on Levy White Noise Functionals -- 4 The Levy Laplacian Acting on WNF-valued Functions -- 5 An Infinite Dimensional Stochastic Process Associated with the Levy Laplacian -- References -- Structure of Linear Processes -- 1 Introduction -- 2 An illustrative example Linear functionals of Poisson noise -- 3 Innovation of a linear process.

4 Determination of kernels -- References -- Group Theory of Dynamical Maps -- On Quantum Analysis Quantum Transfer-Matrix Method and Effective Information Entropy -- 1 Introduction -- 2 Quantum Analysis -- 3 Quantum Transfer-Matrix Method based on Exponential Product Formulas and its Connection with Quantum Information -- 4 Effective Information Entropy -- 5 Summary and Discussion -- References -- Nonequilibrium Steady States for a Harmonic Oscillator Interacting with Two Bose Fields - Stochastic Limit Approach and C* Algebraic Approach -- 1 Introduction -- 2 Model -- 3 Stochastic Limit Approach -- 4 Nonequilibrium Steady States in C*-algebraic Approach -- 5 Weak coupling limits -- 6 Summary and Discussion -- References -- Control of Decoherence with Multipulse Application -- 1 Introduction -- 2 Formulation -- 3 Numerical evaluation -- 4 Discussion and Concluding Remarks -- References -- Quantum Entanglement Purification and Linear-optics Quantum Gates with Photonic Qubits -- 1 Entanglement -- 2 Quantum Key Distribution using Polarization Entangled Photons -- 3 Purification of Entanglement -- References -- On Quantum Mutual Type Measures and Capacity -- 1 Quantum Channels -- 2 Ohya Mutual Entropy -- 3 Comparison of various quantum mutual type entropies -- 4 Quantum Capacity -- References.

The main purpose of this volume is to emphasize the multidisciplinary aspects of this very active new line of research in which concrete technological and industrial realizations require the combined efforts of experimental and theoretical physicists, mathematicians and engineers. Contents: Coherent Quantum Control of Λ-Atoms through the Stochastic Limit (L Accardi et al.); Recent Advances in Quantum White Noise Calculus (L Accardi & A Boukas); Joint Extension of States of Fermion Subsystems (H Araki); Fidelity of Quantum Teleportation Model Using Beam Splittings (K-H Fichtner et al.); Quantum Logical Gates Realized by Beam Splittings (W Freudenberg et al.); Noncanonical Representations of a Multi-dimensional Brownian Motion (Y Hibino); Information, Innovation and Elemental Random Field (T Hida); Generalized Sectors and Adjunctions to Control Micro-Macro Transitions (I Ojima); Saturation of an Entropy Bound and Quantum Markov States (D Petz); An Infinite Dimensional Laplacian Acting on Some Class of Lévy White Noise Functionals (K Saitô); Structure of Linear Processes (S Si & W W Htay); Group Theory of Dynamical Maps (E C G Sudarshan); Quantum Entanglement, Purification, and Linear-optics Quantum Gates with Photonic Qubits (P Walther & A Zeilinger); On Quantum Mutual Type Measures and Capacity (N Watanabe); and other papers. Readership: Researchers in quantum physics and theoretical physics.

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