Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's ...
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In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound, and Caratheodory's treatment of the second law of thermodynamics. All mathematical derivations are based on clear physical pictures which make even the most involved results — such as the Holevo bound — look comprehensible and transparent. Quantum information is a fascinating topic precisely because it shows that the laws of information processing are actually dependent on the laws of physics. However, it is also very interesting to see that information theory has something to teach us about physics. Both of these directions are discussed throughout the book. Other topics covered in the book are quantum mechanics, measures of quantum entanglement, general conditions of quantum error correction, pure state entanglement and Pauli matrices, pure states and Bell's inequalities, and computational complexity of quantum algorithms.Less
In addition to treating quantum communication, entanglement, error correction, and algorithms in great depth, this book also addresses a number of interesting miscellaneous topics, such as Maxwell's demon, Landauer's erasure, the Bekenstein bound, and Caratheodory's treatment of the second law of thermodynamics. All mathematical derivations are based on clear physical pictures which make even the most involved results — such as the Holevo bound — look comprehensible and transparent. Quantum information is a fascinating topic precisely because it shows that the laws of information processing are actually dependent on the laws of physics. However, it is also very interesting to see that information theory has something to teach us about physics. Both of these directions are discussed throughout the book. Other topics covered in the book are quantum mechanics, measures of quantum entanglement, general conditions of quantum error correction, pure state entanglement and Pauli matrices, pure states and Bell's inequalities, and computational complexity of quantum algorithms.
Jeffrey Bub and Itamar Pitowsky
- Published in print:
- 2010
- Published Online:
- September 2010
- ISBN:
- 9780199560561
- eISBN:
- 9780191721380
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199560561.003.0016
- Subject:
- Philosophy, Metaphysics/Epistemology, Philosophy of Science
This chapter argues that the intractable part of the measurement problem — the ‘big’ measurement problem — is a pseudo-problem that depends for its legitimacy on the acceptance of two dogmas. The ...
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This chapter argues that the intractable part of the measurement problem — the ‘big’ measurement problem — is a pseudo-problem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell's assertion that measurement should never be introduced as a primitive process in a fundamental mechanical theory like classical or quantum mechanics, but should always be open to a complete analysis, in principle, of how the individual outcomes come about dynamically. The second dogma is the view that the quantum state has an ontological significance analogous to the significance of the classical state as the ‘truthmaker’ for propositions about the occurrence and non-occurrence of events, i.e., that the quantum state is a representation of physical reality. The chapter shows how both dogmas can be rejected in a realist information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. The Everettian, too, regards the ‘big’ measurement problem as a pseudo-problem, because the Everettian rejects the assumption that measurements have definite outcomes, in the sense that one particular outcome, as opposed to other possible outcomes, actually occurs in a quantum measurement process. By contrast with the Everettians, the chapter accepts that measurements have definite outcomes. By contrast with the Bohmians and the GRW ‘collapse’ theorists who add structure to the theory and propose dynamical solutions to the ‘big’ measurement problem, we take the problem to arise from the failure to see the significance of Hilbert space as a new kinematic framework for the physics of an indeterministic universe, in the sense that Hilbert space imposes kinematic (i.e., pre-dynamic) objective probabilistic constraints on correlations between events.Less
This chapter argues that the intractable part of the measurement problem — the ‘big’ measurement problem — is a pseudo-problem that depends for its legitimacy on the acceptance of two dogmas. The first dogma is John Bell's assertion that measurement should never be introduced as a primitive process in a fundamental mechanical theory like classical or quantum mechanics, but should always be open to a complete analysis, in principle, of how the individual outcomes come about dynamically. The second dogma is the view that the quantum state has an ontological significance analogous to the significance of the classical state as the ‘truthmaker’ for propositions about the occurrence and non-occurrence of events, i.e., that the quantum state is a representation of physical reality. The chapter shows how both dogmas can be rejected in a realist information-theoretic interpretation of quantum mechanics as an alternative to the Everett interpretation. The Everettian, too, regards the ‘big’ measurement problem as a pseudo-problem, because the Everettian rejects the assumption that measurements have definite outcomes, in the sense that one particular outcome, as opposed to other possible outcomes, actually occurs in a quantum measurement process. By contrast with the Everettians, the chapter accepts that measurements have definite outcomes. By contrast with the Bohmians and the GRW ‘collapse’ theorists who add structure to the theory and propose dynamical solutions to the ‘big’ measurement problem, we take the problem to arise from the failure to see the significance of Hilbert space as a new kinematic framework for the physics of an indeterministic universe, in the sense that Hilbert space imposes kinematic (i.e., pre-dynamic) objective probabilistic constraints on correlations between events.
Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0014
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the ...
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This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the Shannon coding and channel capacity theorems. The von Neumann entropy plays a role analogous to the Shannon entropy, and the Holevo bound is the analogue of Shannon's mutual information used to quantify the capacity of a classical channel. Quantum systems can process information more efficiently than classical systems in a number of different ways. Quantum teleportation and quantum dense coding can be performed using quantum entanglement. Entanglement is an excess of correlations that can exist in quantum physics and is impossible to reproduce classically (with what is termed “separable” states). The book has also demonstrated how to discriminate entangled from separable states using entanglement witnesses, as well as how to quantify entanglement, and looked at quantum computation and quantum algorithms.Less
This book has discussed the foundations of quantum information science as well as the relationship between physics and information theory in general. It has considered the quantum equivalents of the Shannon coding and channel capacity theorems. The von Neumann entropy plays a role analogous to the Shannon entropy, and the Holevo bound is the analogue of Shannon's mutual information used to quantify the capacity of a classical channel. Quantum systems can process information more efficiently than classical systems in a number of different ways. Quantum teleportation and quantum dense coding can be performed using quantum entanglement. Entanglement is an excess of correlations that can exist in quantum physics and is impossible to reproduce classically (with what is termed “separable” states). The book has also demonstrated how to discriminate entangled from separable states using entanglement witnesses, as well as how to quantify entanglement, and looked at quantum computation and quantum algorithms.
Heinz-Peter Breuer and Francesco Petruccione
- Published in print:
- 2007
- Published Online:
- January 2010
- ISBN:
- 9780199213900
- eISBN:
- 9780191706349
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199213900.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation, the text begins with a ...
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This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation, the text begins with a survey of classical probability theory and with an introduction to the foundations of quantum mechanics, with particular emphasis on its statistical interpretation and on the formulation of generalized measurement theory through quantum operations and effects. The fundamentals of density matrix theory, quantum Markov processes, and completely positive dynamical semigroups are developed. The most important master equations used in quantum optics and condensed matter theory are derived and applied to the study of many examples. Special attention is paid to the Markovian and non-Markovian theory of environment induced decoherence, its role in the dynamical description of the measurement process, and to the experimental observation of decohering electromagnetic field states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics. The fundamentals of the treatment of non-Markovian quantum processes in open systems are developed on the basis of various mathematical techniques, such as projection superoperator methods and influence functional techniques. In addition, the book expounds the relativistic theory of quantum measurements and the density matrix theory of relativistic quantum electrodynamics.Less
This book treats the central physical concepts and mathematical techniques used to investigate the dynamics of open quantum systems. To provide a self-contained presentation, the text begins with a survey of classical probability theory and with an introduction to the foundations of quantum mechanics, with particular emphasis on its statistical interpretation and on the formulation of generalized measurement theory through quantum operations and effects. The fundamentals of density matrix theory, quantum Markov processes, and completely positive dynamical semigroups are developed. The most important master equations used in quantum optics and condensed matter theory are derived and applied to the study of many examples. Special attention is paid to the Markovian and non-Markovian theory of environment induced decoherence, its role in the dynamical description of the measurement process, and to the experimental observation of decohering electromagnetic field states. The book includes the modern formulation of open quantum systems in terms of stochastic processes in Hilbert space. Stochastic wave function methods and Monte Carlo algorithms are designed and applied to important examples from quantum optics and atomic physics. The fundamentals of the treatment of non-Markovian quantum processes in open systems are developed on the basis of various mathematical techniques, such as projection superoperator methods and influence functional techniques. In addition, the book expounds the relativistic theory of quantum measurements and the density matrix theory of relativistic quantum electrodynamics.
Christian Miniatura, Leong-Chuan Kwek, Martial Ducloy, Benoît Grémaud, Berthold-Georg Englert, Leticia Cugliandolo, Artur Ekert, and Kok Khoo Phua (eds)
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199603657
- eISBN:
- 9780191729515
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199603657.001.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
In recent years, there has been much synergy between the exciting areas of quantum information science and ultracold atoms. This volume, as part of the proceedings for the XCI session of Les Houches ...
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In recent years, there has been much synergy between the exciting areas of quantum information science and ultracold atoms. This volume, as part of the proceedings for the XCI session of Les Houches School of Physics (held for the first time outside Europe in Singapore) brings together experts in both fields. The theme of the school focused on two principal topics: quantum information science and ultracold atomic physics. The topics ranged from Bose-Einstein condensates to degenerate Fermi gases to fundamental concepts in quantum information sciences, including some special topics on quantum Hall effects, quantum phase transition, interactions in quantum fluids, disorder and interference phenomenoma, trapped ions and atoms, and quantum optical devices.Less
In recent years, there has been much synergy between the exciting areas of quantum information science and ultracold atoms. This volume, as part of the proceedings for the XCI session of Les Houches School of Physics (held for the first time outside Europe in Singapore) brings together experts in both fields. The theme of the school focused on two principal topics: quantum information science and ultracold atomic physics. The topics ranged from Bose-Einstein condensates to degenerate Fermi gases to fundamental concepts in quantum information sciences, including some special topics on quantum Hall effects, quantum phase transition, interactions in quantum fluids, disorder and interference phenomenoma, trapped ions and atoms, and quantum optical devices.
Christopher G. Timpson
- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199296460
- eISBN:
- 9780191741791
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296460.003.0003
- Subject:
- Philosophy, Philosophy of Science
The approach to thinking about information developed in the previous chapter is turned towards the quantum theory. First, some of the characteristic ideas and applications of quantum information ...
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The approach to thinking about information developed in the previous chapter is turned towards the quantum theory. First, some of the characteristic ideas and applications of quantum information theory are presented, then the nature of quantum information itself is discussed. With the correct conception of Shannon information to hand, the dimension of generalisation which the quantum concept occupies is made clear. Quantum information is simply what is produced by a quantum information source. As in the classical case, a piece of information will be an abstract type (a sequence of quantum states), rather than a concrete thing or physical substance. This conception is defended from a number of potential objections which might be raised. With a clear grasp obtained of the relation between quantum information and the world, it proves short work to dissect the slogan `Information is Physical’ and dispatch the prospect of informational immaterialism.Less
The approach to thinking about information developed in the previous chapter is turned towards the quantum theory. First, some of the characteristic ideas and applications of quantum information theory are presented, then the nature of quantum information itself is discussed. With the correct conception of Shannon information to hand, the dimension of generalisation which the quantum concept occupies is made clear. Quantum information is simply what is produced by a quantum information source. As in the classical case, a piece of information will be an abstract type (a sequence of quantum states), rather than a concrete thing or physical substance. This conception is defended from a number of potential objections which might be raised. With a clear grasp obtained of the relation between quantum information and the world, it proves short work to dissect the slogan `Information is Physical’ and dispatch the prospect of informational immaterialism.
F. Rohde and J. Eschner
- Published in print:
- 2011
- Published Online:
- September 2011
- ISBN:
- 9780199603657
- eISBN:
- 9780191729515
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199603657.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter reviews the basic experimental techniques which enable quantum information processing (QIP) with trapped ions and, more briefly, with trapped atoms. In particular, it is explained how ...
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This chapter reviews the basic experimental techniques which enable quantum information processing (QIP) with trapped ions and, more briefly, with trapped atoms. In particular, it is explained how the fundamental concepts of quantum computing, such as quantum bits (qubits), qubit rotations, and quantum gates, translate into experimental procedures in a quantum optics laboratory. Furthermore, the recent progress of quantum computing with ions and atoms is summarised, and new approaches to meet the future challenges of scaling up QIP and of atom-photon qubit interfacing are discussed. The chapter is intended to provide an intuitive understanding of the subject and enable the non-specialist student to appreciate the paradigmatic role and the potential of trapped single ions and atoms in the field of quantum computation or, more generally, of quantum optical information technology.Less
This chapter reviews the basic experimental techniques which enable quantum information processing (QIP) with trapped ions and, more briefly, with trapped atoms. In particular, it is explained how the fundamental concepts of quantum computing, such as quantum bits (qubits), qubit rotations, and quantum gates, translate into experimental procedures in a quantum optics laboratory. Furthermore, the recent progress of quantum computing with ions and atoms is summarised, and new approaches to meet the future challenges of scaling up QIP and of atom-photon qubit interfacing are discussed. The chapter is intended to provide an intuitive understanding of the subject and enable the non-specialist student to appreciate the paradigmatic role and the potential of trapped single ions and atoms in the field of quantum computation or, more generally, of quantum optical information technology.
Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Quantum mechanics is a more accurate description of the microscopic world than classical mechanics, and quantum information, which is governed by the laws of quantum mechanics, is a more accurate ...
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Quantum mechanics is a more accurate description of the microscopic world than classical mechanics, and quantum information, which is governed by the laws of quantum mechanics, is a more accurate description of information theory. The quantum laws of physics are fundamentally different from the classical laws and so, therefore, is the resulting information processing. In one limit, quantum information reduces to classical information; otherwise, quantum information is a much more general concept that allows information-processing protocols that have no classical analogue whatsoever. This chapter discusses the basics of quantum information, some differences between bits and qubits, quantum cryptography, trace and partial-trace operations, extension of Hilbert spaces, Schmidt decomposition, generalised measurements, CP-maps and positive operator-valued measurements, and the postulates of quantum mechanics.Less
Quantum mechanics is a more accurate description of the microscopic world than classical mechanics, and quantum information, which is governed by the laws of quantum mechanics, is a more accurate description of information theory. The quantum laws of physics are fundamentally different from the classical laws and so, therefore, is the resulting information processing. In one limit, quantum information reduces to classical information; otherwise, quantum information is a much more general concept that allows information-processing protocols that have no classical analogue whatsoever. This chapter discusses the basics of quantum information, some differences between bits and qubits, quantum cryptography, trace and partial-trace operations, extension of Hilbert spaces, Schmidt decomposition, generalised measurements, CP-maps and positive operator-valued measurements, and the postulates of quantum mechanics.
Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0005
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
Information is often considered classical in a definite state rather than in a superposition of states. It seems rather strange to consider information in superpositions. Some people would, on the ...
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Information is often considered classical in a definite state rather than in a superposition of states. It seems rather strange to consider information in superpositions. Some people would, on the basis of this argument, conclude that quantum information can never exist and we can only have access to classical information. It turns out, however, that quantum information can be quantified in the same way as classical information using Shannon's prescription. There is a unique measure (up to a constant additive or multiplicative term) of quantum information such that S (the von Neumann entropy) is purely a function of the probabilities of outcomes of measurements made on a quantum system (that is, a function of a density operator); S is a continuous function of probability; S is additive. This chapter discusses the fidelity of pure quantum states, Helstrom's discrimination, quantum data compression, entropy of observation, conditional entropy and mutual information, relative entropy, and statistical interpretation of relative entropy.Less
Information is often considered classical in a definite state rather than in a superposition of states. It seems rather strange to consider information in superpositions. Some people would, on the basis of this argument, conclude that quantum information can never exist and we can only have access to classical information. It turns out, however, that quantum information can be quantified in the same way as classical information using Shannon's prescription. There is a unique measure (up to a constant additive or multiplicative term) of quantum information such that S (the von Neumann entropy) is purely a function of the probabilities of outcomes of measurements made on a quantum system (that is, a function of a density operator); S is a continuous function of probability; S is additive. This chapter discusses the fidelity of pure quantum states, Helstrom's discrimination, quantum data compression, entropy of observation, conditional entropy and mutual information, relative entropy, and statistical interpretation of relative entropy.
Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This book deals with the basic concept of information, its importance, and the similarities and differences between classical and quantum information. First, classical information theory and its ...
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This book deals with the basic concept of information, its importance, and the similarities and differences between classical and quantum information. First, classical information theory and its application to communication are discussed. Quantum mechanics and communication based on the laws of quantum mechanics are then considered. Quantum entanglement, a key resource in quantum communication, is analysed both from the fundamental perspective and from the perspective of its information-processing capability. This book also introduces quantum computation (in the context of the search and factorisation algorithms) and the basics of quantum error correction. Throughout this book, the connections between information theory, thermodynamics, and (quantum) physics are emphasised and discussed. Other topics covered in the book are data compression, related measures of information such as relative entropy, joint entropy, conditional entropy, and mutual information, along with the capacity of a noisy channel.Less
This book deals with the basic concept of information, its importance, and the similarities and differences between classical and quantum information. First, classical information theory and its application to communication are discussed. Quantum mechanics and communication based on the laws of quantum mechanics are then considered. Quantum entanglement, a key resource in quantum communication, is analysed both from the fundamental perspective and from the perspective of its information-processing capability. This book also introduces quantum computation (in the context of the search and factorisation algorithms) and the basics of quantum error correction. Throughout this book, the connections between information theory, thermodynamics, and (quantum) physics are emphasised and discussed. Other topics covered in the book are data compression, related measures of information such as relative entropy, joint entropy, conditional entropy, and mutual information, along with the capacity of a noisy channel.
Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0006
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter discusses the principles of quantum information. The quantum mechanical equivalent of the Shannon noisy-channel communication theorem is obtained, along with some profound statements ...
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This chapter discusses the principles of quantum information. The quantum mechanical equivalent of the Shannon noisy-channel communication theorem is obtained, along with some profound statements about the behavior of quantum information during generalised quantum measurements. The latter are very important in studies of quantum entanglement, but also in exploring the connections between thermodynamics, information theory, and quantum physics. This chapter also discusses equalities and inequalities related to entropy, the Holevo bound, capacity of a bosonic channel, information gained through measurements, relative entropy and thermodynamics, entropy increase due to erasure, and Landauer's erasure and data compression.Less
This chapter discusses the principles of quantum information. The quantum mechanical equivalent of the Shannon noisy-channel communication theorem is obtained, along with some profound statements about the behavior of quantum information during generalised quantum measurements. The latter are very important in studies of quantum entanglement, but also in exploring the connections between thermodynamics, information theory, and quantum physics. This chapter also discusses equalities and inequalities related to entropy, the Holevo bound, capacity of a bosonic channel, information gained through measurements, relative entropy and thermodynamics, entropy increase due to erasure, and Landauer's erasure and data compression.
S. M. Girvin
- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780199681181
- eISBN:
- 9780191761454
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199681181.003.0003
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter introduces the basic concepts of quantum information processing with superconducting quantum circuits. It starts with a demonstration of how,in these electrodynamic systems, both the ...
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This chapter introduces the basic concepts of quantum information processing with superconducting quantum circuits. It starts with a demonstration of how,in these electrodynamic systems, both the superconducting gap and the long-range Coulomb interactions contribute to the existence of collective modesthat have extremely low dissipationand that can be quantized. The chapter also gives in-depth coverage of quantum harmonic oscillators in all their glory from various perspectives. Superconducting qubits are then introduced, starting with the fundamental theory of the Josephson effect and moving on to a presentation of the variety of existing superconducting qubits. Particular attention is given to the dispersive readout of qubits through their interaction with a cavity into which flying modes can be scattered. Finally, the opportunities offered for quantum information processing by employing the cavity as a quantum bus are presented.Less
This chapter introduces the basic concepts of quantum information processing with superconducting quantum circuits. It starts with a demonstration of how,in these electrodynamic systems, both the superconducting gap and the long-range Coulomb interactions contribute to the existence of collective modesthat have extremely low dissipationand that can be quantized. The chapter also gives in-depth coverage of quantum harmonic oscillators in all their glory from various perspectives. Superconducting qubits are then introduced, starting with the fundamental theory of the Josephson effect and moving on to a presentation of the variety of existing superconducting qubits. Particular attention is given to the dispersive readout of qubits through their interaction with a cavity into which flying modes can be scattered. Finally, the opportunities offered for quantum information processing by employing the cavity as a quantum bus are presented.
Maciej Lewenstein, Anna Sanpera, and Verònica Ahufinger
- Published in print:
- 2012
- Published Online:
- December 2013
- ISBN:
- 9780199573127
- eISBN:
- 9780191775048
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199573127.003.0012
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter deals with the novel characterisation of many-body physics using tools from quantum information theory. The first part focuses on the theory of entanglement, where the basic notions as ...
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This chapter deals with the novel characterisation of many-body physics using tools from quantum information theory. The first part focuses on the theory of entanglement, where the basic notions as bipartite versus multipartite entanglement, measures of entanglement, and the link between entangled states completely positive maps are discussed. The second part deals with the concept of area law, relating the von Neumann measure of the entropy of a subsystem with the size of the system for gapped, critical, and topological systems. The entanglement content in critical quantum systems is studied in reference to quantum phase transitions. Finally, the round states of many-body systems with a tensor network representation are described.Less
This chapter deals with the novel characterisation of many-body physics using tools from quantum information theory. The first part focuses on the theory of entanglement, where the basic notions as bipartite versus multipartite entanglement, measures of entanglement, and the link between entangled states completely positive maps are discussed. The second part deals with the concept of area law, relating the von Neumann measure of the entropy of a subsystem with the size of the system for gapped, critical, and topological systems. The entanglement content in critical quantum systems is studied in reference to quantum phase transitions. Finally, the round states of many-body systems with a tensor network representation are described.
Stephen J. Blundell and Katherine M. Blundell
- Published in print:
- 2009
- Published Online:
- February 2010
- ISBN:
- 9780199562091
- eISBN:
- 9780191718236
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199562091.003.0015
- Subject:
- Physics, Particle Physics / Astrophysics / Cosmology
This chapter examines the concept of information and relates it to thermodynamic entropy. It illustrates the deep connection between these two concepts. It begins by formulating one definition of ...
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This chapter examines the concept of information and relates it to thermodynamic entropy. It illustrates the deep connection between these two concepts. It begins by formulating one definition of information.Less
This chapter examines the concept of information and relates it to thermodynamic entropy. It illustrates the deep connection between these two concepts. It begins by formulating one definition of information.
Christopher G. Timpson
- Published in print:
- 2013
- Published Online:
- September 2013
- ISBN:
- 9780199296460
- eISBN:
- 9780191741791
- Item type:
- book
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199296460.001.0001
- Subject:
- Philosophy, Philosophy of Science
This book is a conceptual analysis of quantum information theory and the questions it raises for our understanding of the quantum world. Beginning from a detailed analysis of the concepts of ...
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This book is a conceptual analysis of quantum information theory and the questions it raises for our understanding of the quantum world. Beginning from a detailed analysis of the concepts of information in the everyday and classical (Shannon) information-theory settings, an ontologically deflationary account of the nature of quantum information is developed. The account provided sheds light on the nature of nonlocality and information flow in the presence of entanglement and, in particular, dissolves puzzles surrounding the process of quantum teleportation. In addition, it permits a clear view of what the ontological and methodological lessons provided by quantum information theory are; lessons which bear on the gripping question of what role a concept like information has to play in fundamental physics. With a clear grasp of the concept of information in hand, attention turns to the pressing question whether advances in quantum information theory pave the way for the resolution of the traditional conceptual problems of quantum mechanics: the deep problems which loom over measurement, nonlocality and the general nature of quantum ontology. A number of common pitfalls are marked-out to be avoided before some concrete proposals are analysed in detail, including the radical quantum Bayesian programme of Caves, Fuchs and Schack. One central moral which is drawn is that, for all the interest that the quantum information-inspired approaches hold, no cheap resolutions to the traditional problems of quantum mechanics are to be had.Less
This book is a conceptual analysis of quantum information theory and the questions it raises for our understanding of the quantum world. Beginning from a detailed analysis of the concepts of information in the everyday and classical (Shannon) information-theory settings, an ontologically deflationary account of the nature of quantum information is developed. The account provided sheds light on the nature of nonlocality and information flow in the presence of entanglement and, in particular, dissolves puzzles surrounding the process of quantum teleportation. In addition, it permits a clear view of what the ontological and methodological lessons provided by quantum information theory are; lessons which bear on the gripping question of what role a concept like information has to play in fundamental physics. With a clear grasp of the concept of information in hand, attention turns to the pressing question whether advances in quantum information theory pave the way for the resolution of the traditional conceptual problems of quantum mechanics: the deep problems which loom over measurement, nonlocality and the general nature of quantum ontology. A number of common pitfalls are marked-out to be avoided before some concrete proposals are analysed in detail, including the radical quantum Bayesian programme of Caves, Fuchs and Schack. One central moral which is drawn is that, for all the interest that the quantum information-inspired approaches hold, no cheap resolutions to the traditional problems of quantum mechanics are to be had.
Stephen M. Barnett
- Published in print:
- 2017
- Published Online:
- August 2017
- ISBN:
- 9780198768609
- eISBN:
- 9780191822353
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198768609.003.0001
- Subject:
- Physics, Atomic, Laser, and Optical Physics, Particle Physics / Astrophysics / Cosmology
This chapter gives a short introduction to the field of quantum information. Although the chapter is self-contained, it cannot hope to cover the totality of what is now a large and active field of ...
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This chapter gives a short introduction to the field of quantum information. Although the chapter is self-contained, it cannot hope to cover the totality of what is now a large and active field of research. Rather, the aim is to give a taster of the subject to whet the appetite of the reader. More complete introductions may be found in any of a now large collection of books and review papers devoted to the topic.Less
This chapter gives a short introduction to the field of quantum information. Although the chapter is self-contained, it cannot hope to cover the totality of what is now a large and active field of research. Rather, the aim is to give a taster of the subject to whet the appetite of the reader. More complete introductions may be found in any of a now large collection of books and review papers devoted to the topic.
Vlatko Vedral
- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0007
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
The Mach–Zehnder interferometer experiment described earlier shows why and how quantum mechanics is different from classical mechanics. A photon sent through a beam splitter behaves like a particle ...
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The Mach–Zehnder interferometer experiment described earlier shows why and how quantum mechanics is different from classical mechanics. A photon sent through a beam splitter behaves like a particle when it is observed by only one of the two detectors. When two beam splitters are used, the photon “interferes with itself” and behaves like a wave. This is the so-called wave-particle duality of quantum mechanics which leads to quantum entanglement. This chapter discusses quantum superpositions when two or more particles are present. Understanding and analysing entanglement is one of the most interesting directions in the field of quantum information. First, a historical background of quantum entanglement is given, followed by a discussion on Bell's inequalities, separable states that do not violate Bell's inequalities, pure states that violate Bell's inequalities, mixed states that do not violate Bell's inequalities, and entanglement in second quantisation.Less
The Mach–Zehnder interferometer experiment described earlier shows why and how quantum mechanics is different from classical mechanics. A photon sent through a beam splitter behaves like a particle when it is observed by only one of the two detectors. When two beam splitters are used, the photon “interferes with itself” and behaves like a wave. This is the so-called wave-particle duality of quantum mechanics which leads to quantum entanglement. This chapter discusses quantum superpositions when two or more particles are present. Understanding and analysing entanglement is one of the most interesting directions in the field of quantum information. First, a historical background of quantum entanglement is given, followed by a discussion on Bell's inequalities, separable states that do not violate Bell's inequalities, pure states that violate Bell's inequalities, mixed states that do not violate Bell's inequalities, and entanglement in second quantisation.
T. Monz, P. Schindler, D. Nigg, and R. Blatt
- Published in print:
- 2014
- Published Online:
- September 2014
- ISBN:
- 9780199681181
- eISBN:
- 9780191761454
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199681181.003.0013
- Subject:
- Physics, Condensed Matter Physics / Materials
This chapter discusses ion-trap-based quantum computation. Itexplains why ion traps constitute the most advanced quantum information processors to date.
This chapter discusses ion-trap-based quantum computation. Itexplains why ion traps constitute the most advanced quantum information processors to date.
P. Bertet, F. R. Ong, M. Boissonneault, A. Bolduc, F. Mallet, A. C. Doherty, A. Blais, D. Vion, and D. Esteve
- Published in print:
- 2012
- Published Online:
- September 2012
- ISBN:
- 9780199691388
- eISBN:
- 9780191742255
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199691388.003.0001
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics
This chapter investigates the coupling of a two-level system to a nonlinear resonator, one of the simplest extensions to the well-known Jaynes–Cummings model. In the experiment, the two-level system ...
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This chapter investigates the coupling of a two-level system to a nonlinear resonator, one of the simplest extensions to the well-known Jaynes–Cummings model. In the experiment, the two-level system is a superconducting transmon qubit, and the resonator is a coplanar resonator with a Kerr nonlinearity induced by a Josephson junction. Effects arising from the resonator nonlinearity (bistability, parametric amplification, squeezing) qualitatively modify the dispersive qubit-resonator coupling. This makes it possible to design a qubit readout which has both a high fidelity and the potential of being QND. Motivated by fundamental and practical issues concerning the quantum limit of such a measurement, the chapter also studies spectroscopically the quantum back action exerted by the intraresonator field onto the qubit. Qualitative agreement is obtained with analytical results and quantitative agreement with numerical simulations.Less
This chapter investigates the coupling of a two-level system to a nonlinear resonator, one of the simplest extensions to the well-known Jaynes–Cummings model. In the experiment, the two-level system is a superconducting transmon qubit, and the resonator is a coplanar resonator with a Kerr nonlinearity induced by a Josephson junction. Effects arising from the resonator nonlinearity (bistability, parametric amplification, squeezing) qualitatively modify the dispersive qubit-resonator coupling. This makes it possible to design a qubit readout which has both a high fidelity and the potential of being QND. Motivated by fundamental and practical issues concerning the quantum limit of such a measurement, the chapter also studies spectroscopically the quantum back action exerted by the intraresonator field onto the qubit. Qualitative agreement is obtained with analytical results and quantitative agreement with numerical simulations.
Christopher C. Gerry and Kimberley M. Bruno
- Published in print:
- 2013
- Published Online:
- May 2013
- ISBN:
- 9780199666560
- eISBN:
- 9780191748646
- Item type:
- chapter
- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199666560.003.0006
- Subject:
- Physics, Atomic, Laser, and Optical Physics
This chapter discusses quantum information science (QIS), quantum key distribution (QKD), and quantum teleportation. The new field of QIS encompasses several overlapping subdisciplines: quantum ...
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This chapter discusses quantum information science (QIS), quantum key distribution (QKD), and quantum teleportation. The new field of QIS encompasses several overlapping subdisciplines: quantum computing, quantum key distribution (also known as quantum cryptography), and quantum metrology (the measurement of small parameters and weak forces with ultra-high precision). In QIS, bits of information are encoded in quantum states, which themselves can be in superposition states and/or entanglement states. Generically, the 0 and 1 quantum bits are represented as qubits (quantum bits). QKD, or quantum cryptography, is a completely secure method of secret communication, and will remain so even if a quantum computer becomes available. Quantum teleportation is one of the more exotic features to have emerged from the field of QIS. It refers to the ability to transfer an unknown quantum state from one location to another, possibly very distant, location by using quantum entanglement.Less
This chapter discusses quantum information science (QIS), quantum key distribution (QKD), and quantum teleportation. The new field of QIS encompasses several overlapping subdisciplines: quantum computing, quantum key distribution (also known as quantum cryptography), and quantum metrology (the measurement of small parameters and weak forces with ultra-high precision). In QIS, bits of information are encoded in quantum states, which themselves can be in superposition states and/or entanglement states. Generically, the 0 and 1 quantum bits are represented as qubits (quantum bits). QKD, or quantum cryptography, is a completely secure method of secret communication, and will remain so even if a quantum computer becomes available. Quantum teleportation is one of the more exotic features to have emerged from the field of QIS. It refers to the ability to transfer an unknown quantum state from one location to another, possibly very distant, location by using quantum entanglement.
