Showing papers on "Coherent information published in 2006"

Quantum state merging and negative information

Abstract: We consider a quantum state shared between many distant locations, and define a quantum information processing primitive, state merging, that optimally merges the state into one location. As announced in [Horodecki, Oppenheim, Winter, Nature 436, 673 (2005)], the optimal entanglement cost of this task is the conditional entropy if classical communication is free. Since this quantity can be negative, and the state merging rate measures partial quantum information, we find that quantum information can be negative. The classical communication rate also has a minimum rate: a certain quantum mutual information. State merging enabled one to solve a number of open problems: distributed quantum data compression, quantum coding with side information at the decoder and sender, multi-party entanglement of assistance, and the capacity of the quantum multiple access channel. It also provides an operational proof of strong subadditivity. Here, we give precise definitions and prove these results rigorously.

Quantum Darwinism: Entanglement, branches, and the emergent classicality of redundantly stored quantum information

Abstract: We lay a comprehensive foundation for the study of redundant information storage in decoherence processes. Redundancy has been proposed as a prerequisite for objectivity, the defining property of classical objects. We consider two ensembles of states for a model universe consisting of one system and many environments: the first consisting of arbitrary states, and the second consisting of "singly branching" states consistent with a simple decoherence model. Typical states from the random ensemble do not store information about the system redundantly, but information stored in branching states has a redundancy proportional to the environment's size. We compute the specific redundancy for a wide range of model universes, and fit the results to a simple first-principles theory. Our results show that the presence of redundancy divides information about the system into three parts: classical (redundant); purely quantum; and the borderline, undifferentiated or "nonredundant," information.

Quantum mutual information and the one-time pad

Abstract: Alice and Bob share a correlated composite quantum system AB. If AB is used as the key for a one-time pad cryptographic system, we show that the maximum amount of information that Alice can send securely to Bob is the quantum mutual information of AB.

Quantum uncertainty of mixed states based on skew information

Abstract: The uncertainty of a mixed state has two quite different origins: classical mixing and quantum randomness. While the classical aspect (mixedness) is significantly quantified by the von Neumann entropy, it seems that we still do not have a well accepted measure of quantum uncertainty. In terms of the skew information introduced by Wigner and Yanase in 1963 in the context of quantum measurements, we will propose an intrinsic measure for synthesizing quantum uncertainty of a mixed state and investigate its fundamental properties. We illustrate how it arises naturally from a naive hidden-variable approach to entanglement and how it exhibits a simple relation to the notion of negativity, which is an entanglement monotone introduced quite recently. We further show that it has a dramatic nonextensive feature resembling the probability law relating operations of two events. This measure of quantum uncertainty provides an alternative quantity complementary to the von Neumann entropy for studying mixedness and quantum correlations.

Dialogue Concerning Two Views on Quantum Coherence: Factist and Fictionist

Abstract: A controversy that has arisen many times over in disparate contexts is whether quantum coherences between eigenstates of certain quantities are fact or fiction. We present a pedagogical introduction to the debate in the form of a hypothetical dialogue between proponents from each of the two camps: a factist and a fictionist. A resolution of the debate can be achieved, we argue, by recognizing that quantum states do not only contain information about the intrinsic properties of a system but about its extrinsic properties as well, that is, about its relation to other systems external to it. Specifically, the coherent quantum state of the factist is the appropriate description of the relation of the system to one reference frame, while the incoherent quantum state of the fictionist is the appropriate description of the relation of the system to another, uncorrelated, reference frame. The two views, we conclude, are alternative but equally valid paradigms of description.

The structure of physics

Abstract: Preface by the Editors Preface 1985 On Weizsacker's Philosophy of Physics (by H. Lyre) Chapter 1: Introduction. 1.1. The Question. 1.2. Outline Part I: The Unity of Physics Chapter 2: The System of theories. 2.1. Preliminary. 2.2. Classical point mechanics. 2.3. Mathematical forms of the Laws of Nature. 2.4. Chemistry. 2.5. Thermodynamics. 2.6. Field theories. 2.7. Non-Euclidan geometry and semantical consistency. 2.8. The relativity problem. 2.9. Special theory of relativity. 2.10. General theory of relativity. 2.11. Quantum theory, historical. 2.12. Quantum theory, plan of reconstruction. Chapter 3: Probability and abstract quantum theory. 3.1. Probability and experience. 3.2. The classical concept of probability. 3.3. Empirical determination of probabilities. 3.4. Second quantization. 3.5. Methodical: reconstruction of abstract quantum theory. 3.6. Reconstruction via probabilities and the lattice of propositions. Chapter 4: Quantum theory and space-time. 4.1. Concrete quantum theory. 4.2. Reconstruction of quantum theory via variable alternatives. 4.3. Space and time. Chapter 5: Models of particles and interaction. 5.1. Open questions. 5.2. Representations in tensor space. 5.3. Quasi-particles in rigid coordinate spaces. 5.4. Model of quantum electrodynamics. 5.5. Elementary particles. 5.6. General theory of relativity. Chapter 6: Cosmology and particle physics (by Th. Gornitz). 6.1. Quantum theory of abstract binary alternatives and cosmology. 6.2. Ur-theoretical vacuum and particle states. 6.4. Outlook. Part II: Time and Information Chapter 7: Irreversibility and entropy. 7.1. Irreversibility as problem. 7.2. A model of irreversible processes. 7.3. Documents. 7.4. Cosmology and the theory of relativity. Chapter 8: Information and evolution. 8.1. The systematic place of the chapter. 8.2. What is information? 8.3. What is evolution? 8.4. Information and probability. 8.5. Evolution as growth of potential information. 8.6. Pragmaticinformation: novelty and confirmation. 8.7. Biological preliminaries to logic. Part III: On the Interpretation of Physics Chapter 9: The problem of the interpretation of quantum theory. 9.1. About the history of the interpretation. 9.2. The semantical consistency of quantum theory. 9.3. Paradoxa and alternatives. Chapter 10: The stream of information. 10.1. The quest for substance. 10.2. The stream of information in quantum theory. 10.3. Mind and form. Chapter 11: Beyond quantum theory. 11.1. Crossing the frontier. 11.2. Facticity of the future. 11.3. Possibility of the past. 11.4. Comprehensive present. 11.5. Beyond physics. Chapter 12: In the language of philosophers. 12.1. Exposition. 12.2. Philosophy of science. 12.3. Physics. 12.4. Metaphysics. References Index

Description of multidimensional tunnelling with the help of coupled coherent states guided by classical Hamiltonians with quantum corrections

Abstract: The recently developed coupled coherent states theory is applied to direct full dimensional simulation of tunneling in multidimensional systems. The approach is shown to work well for both symmetric and asymmetric tunneling in up to 20 dimensions. We show that the efficiency of the technique is largely due to the use of quantum averaged potentials to guide a moving basis of coherent states.

Experimental demonstration of coherent state estimation with minimal disturbance.

Abstract: We investigate the optimal trade-off between information gained about an unknown coherent state and the state disturbance caused by the measurement process. We propose several optical schemes that can enable this task, and we implement one of them, a scheme that relies on only linear optics and homodyne detection. Experimentally we reach near optimal performance, limited only by detection inefficiencies. In addition, we show that such a scheme can be used to enhance the transmission fidelity of a class of noisy channels.

Information Theory and Thermodynamics

Abstract: . A communication theory for a transmitter broadcasting to many receivers presented. In this case, energetic considerations cannot neglected as in Shannon theory. It is shown that, when energy is assigned to the information bit, information theory complies with classical thermodynamic and is part of it. To provide a thermodynamic theory of communication it is necessary to define equilibrium for informatics systems that are not in thermal equilibrium and to calculate temperature, heat, and entropy with accordance to Clausius inequality. It shown that for a binary file, the temperature is proportional to the bit energy and that information is thermodynamic entropy. Equilibrium exists in random files that cannot compressed. Thermodynamic bounds on the computing power of a physical device, and the maximum information that an antenna can broadcast are calculated. Keywords. Information theory, Thermodynamics, Entropy. JEL. C62.

An application of the Lieb-Thirring inequality in quantum information theory

Abstract: Quantum information theory has generated several interesting conjectures involving products of completely positive maps on matrix algebras, also known as quantum channels. In particular it is conjectured that the minimal entropy output state from a product channel is always a product state. We show how the Lieb-Thirring inequality can be used to prove this conjecture for one special case, namely when one of the components of the product channel is of the type known as a diagonal channel.

Information Gain versus State Disturbance for a Single Qubit

Abstract: The trade-off between the information gain and the state disturbance is derived for quantum operations on a single qubit prepared in a uniformly distributed pure state. The derivation is valid for a class of measures quantifying the state disturbance and the information gain which satisfy certain invariance conditions. This class includes in particular the Shannon entropy versus the operation fidelity. The central role in the derivation is played by efficient quantum operations, which leave the system in a pure output state for any measurement outcome. It is pointed out that the optimality of efficient quantum operations among those inducing a given operator-valued measure is related to Davies' characterization of convex invariant functions on hermitian operators.

Cross-Kerr-based information transfer processes

Abstract: The realization of nonclassical states is an important task for many applications of quantum information processing. Usually, properly tailored interactions, different from goal to goal, are considered in order to accomplish specific tasks within the general framework of quantum state engineering. In this paper, we remark on the flexibility of a cross-Kerr nonlinear coupling in hybrid systems as an important ingredient in the engineering of nonclassical states. The general scenario we consider is the implementation of high cross-Kerr nonlinearity in cavity-quantum electrodynamics. In this context, we discuss the possibility of performing entanglement transfer and swapping between matter qubits and light fields initially prepared in separable coherent states. The recently introduced concept of entanglement reciprocation is also considered and shown to be possible with our scheme. We reinterpret some of our results in terms of applications of a generalized Ising interaction to systems of different nature.

Fisher Information of Wavefunctions: Classical and Quantum

Abstract: A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces parametric rank-one projections which may be viewed as density operators, and we can talk about its quantum Fisher information. Among many versions of quantum Fisher information, there are two prominent ones. The first, defined via a quantum score function, was introduced by Helstrom in 1967 and is well known. The second, defined via the square root of the density operator, has its origin in the skew information introduced by Wigner and Yanase in 1963 and remains relatively unnoticed. This study is devoted to investigating the relationships between the classical Fisher information and these two versions of quantum Fisher information for wavefunctions. It is shown that the two versions of quantum Fisher information differ by a factor 2 and that they dominate the classical Fisher information. The non-coincidence of these two versions of quantum Fisher information may be interpreted as a manifestation of quantum discord. We further calculate the difference between the Helstrom quantum Fisher information and the classical Fisher information, and show that it is precisely the instantaneous phase fluctuation of the wavefunctions.

A bound on the mutual information, and properties of entropy reduction, for quantum channels with inefficient measurements

Abstract: The Holevo bound is a bound on the mutual information for a given quantum encoding. In 1996 Schumacher, Westmoreland, and Wootters [Phys. Rev. Lett. 76, 3452 (1996)] derived a bound that reduces to the Holevo bound for complete measurements, but that is tighter for incomplete measurements. The most general quantum operations may be both incomplete and inefficient. Here we show that the bound derived by SWW can be further extended to obtain one that is yet again tighter for inefficient measurements. This allows us, in addition, to obtain a generalization of a bound derived by Hall, and to show that the average reduction in the von Neumann entropy during a quantum operation is concave in the initial state, for all quantum operations. This is a quantum version of the concavity of the mutual information. We also show that both this average entropy reduction and the mutual information for pure state ensembles, are Schur concave for unitarily covariant measurements; that is, for these measurements, information ...

Quantumness of ensemble from no-broadcasting principle

Abstract: Quantum information, though not precisely defined, is a fundamental concept of quantum information theory which predicts many fascinating phenomena and provides new physical resources. A basic problem is to recognize the features of quantum systems responsible for those phenomena. One of these important features is that non-commuting quantum states cannot be broadcast: two copies cannot be obtained out of a single copy, not even reproduced marginally on separate systems. We focus on the difference in information content between one copy and two copies, which is a basic manifestation of the gap between quantum and classical information. We show that if the chosen information measure is the Holevo quantity, the difference between the information content of one copy and two copies is zero if and only if the states can be broadcast. We propose a new approach in defining measures of quantumness of ensembles based on the difference in information content between the original ensemble and the ensemble of duplicated states. We comment on the permanence property of quantum states and the recently introduced superbroadcasting operation. We also provide an appendix where we discuss the status of quantum information in quantum physics, based on the so-called isomorphism principle.

Information and the Brukner-Zeilinger Interpretation of Quantum Mechanics: A Critical Investigation

Abstract: In Brukner and Zeilinger's interpretation of quantum mechanics, information is introduced as the most fundamental notion and the finiteness of information is considered as an essential feature of quantum systems. They also define a new measure of information which is inherently different from the Shannon information and try to show that the latter is not useful in defining the information content in a quantum object. Here, we show that there are serious problems in their approach which make their efforts unsatisfactory. The finiteness of information does not explain how objective results appear in experiments and what an instantaneous change in the so-called information vector (or catalog of knowledge) really means during the measurement. On the other hand, Brukner and Zeilinger's definition of a new measure of information may lose its significance, when the spin measurement of an elementary system is treated realistically. Hence, the sum of the individual measures of information may not be a conserved value in real experiments.

Asymptotic entanglement manipulation of bipartite pure states

Abstract: Entanglement of pure states of bipartite quantum systems has been shown to have a unique measure in terms of the von Neumann entropy of the reduced states of either of its subsystems. The measure is established under entanglement manipulation of an asymptotically large number of copies of the states. In this paper, different asymptotic measures of entanglement assigned to arbitrary sequences of bipartite pure states are shown to coincide only when the sequence is information stable, in terms of the quantum spectral information rates of the sequence of subsystem states. Additional bounds on the optimal rates of entanglement manipulation protocols in quantum information are also presented, including bounds given by generalizations of the coherent information and the relative entropy of entanglement.

Can one build a quantum hard drive? A no-go theorem for storing quantum information in equilibrium systems

Abstract: We prove a no-go theorem for storing quantum information in equilibrium systems. Namely, quantum information cannot be stored in a system with time-independent Hamiltonian interacting with heat bath of temperature $T>0$ during time that grows with the number of used qubits. We prove it by showing, that storing quantum information for macroscopic time would imply existence of perpetuum mobile of the second kind. The general results are illustrated by the Kitaev model of quantum memory. In contrast, classical information can be stored in equilibrium states for arbitrary long times. We show how it is possible via phase-transition type phenomena. Our result shows that there is a fundamental difference between quantum and classical information in {\it physical} terms.

Quantum information conversion between matter and light representations

Abstract: Structures and methods allow: transfer of quantum information represented using the states of light (160) to a representation using the states of matter systems (120); transfer of quantum information represented by the states of matter systems (120) to a representation using the states of light (134); and error resistant encoding of quantum information using entangled states of matter and light to minimize errors.

Dynamic statistical information theory

Abstract: In recent years we extended Shannon static statistical information theory to dynamic processes and established a Shannon dynamic statistical information theory, whose core is the evolution law of dynamic entropy and dynamic information. We also proposed a corresponding Boltzmman dynamic statistical information theory. Based on the fact that the state variable evolution equation of respective dynamic systems, i.e. Fokker-Planck equation and Liouville diffusion equation can be regarded as their information symbol evolution equation, we derived the nonlinear evolution equations of Shannon dynamic entropy density and dynamic information density and the nonlinear evolution equations of Boltzmann dynamic entropy density and dynamic information density, that describe respectively the evolution law of dynamic entropy and dynamic information. The evolution equations of these two kinds of dynamic entropies and dynamic informations show in unison that the time rate of change of dynamic entropy densities is caused by their drift, diffusion and production in state variable space inside the systems and coordinate space in the transmission processes; and that the time rate of change of dynamic information densities originates from their drift, diffusion and dissipation in state variable space inside the systems and coordinate space in the transmission processes. Entropy and information have been combined with the state and its law of motion of the systems. Furthermore we presented the formulas of two kinds of entropy production rates and information dissipation rates, the expressions of two kinds of drift information flows and diffusion information flows. We proved that two kinds of information dissipation rates (or the decrease rates of the total information) were equal to their corresponding entropy produc-tion rates (or the increase rates of the total entropy) in the same dynamic system. We obtained the formulas of two kinds of dynamic mutual informations and dynamic channel capacities reflecting the dynamic dissipation characteristics in the transmission processes, which change into their maximum—the present static mutual information and static channel capacity under the limit case where the proportion of channel length to informa-tion transmission rate approaches to zero. All these unified and rigorous theoretical for-mulas and results are derived from the evolution equations of dynamic information and dynamic entropy without adding any extra assumption. In this review, we give an overview on the above main ideas, methods and results, and discuss the similarity and difference between two kinds of dynamic statistical information theories.

A General Information Theoretical Proof for the Second Law of Thermodynamics

Abstract: We show that the conservation and the non-additivity of the information, together with the additivity of the entropy make the entropy increase in an isolated system. The collapse of the entangled quantum state offers an example of the information non-additivity. Nevertheless, the later is also true in other fields, in which the interaction information is important. Examples are classical statistical mechanics, social statistics and financial processes. The second law of thermodynamics is thus proven in its most general form. It is exactly true, not only in quantum and classical physics but also in other processes, in which the information is conservative and non-additive.

Aligning spatial frames through quantum channels

Abstract: We review the optimal protocols for aligning spatial frames using quantum systems. The communication problem addressed here concerns a type of information that cannot be digitalized. Asher Peres referred to it as "unspeakable information." We comment on his contribution to this subject and give a brief account of his scientific interaction with the authors.

Some Issues in Quantum Information Theory

Abstract: Quantum information theory is a new interdisciplinary research field related to quantum mechanics, computer science, information theory, and applied mathematics. It provides completely new paradigms to do information processing tasks by employing the principles of quantum mechanics. In this review, we first survey some of the significant advances in quantum information theory in the last twenty years. We then focus mainly on two special subjects: discrimination of quantum objects and transformations between entanglements. More specifically, we first discuss discrimination of quantum states and quantum apparatus in both global and local settings. Secondly, we present systematical characterizations and equivalence relations of several interesting entanglement transformation phenomena, namely entanglement catalysis, multiple-copy entanglement transformation, and partial entanglement recovery.

Coordinating quantum agents' perspectives: convex operational theories, quantum information, and quantum foundations

Abstract: In this paper, I propose a project of enlisting quantum information science as a source of task-oriented axioms for use in the investigation of operational theories in a general framework capable of encompassing quantum mechanics, classical theory, and more. Whatever else they may be, quantum states of systems are compendia of probabilities for the outcomes of possible operations we may perform on the systems: ``operational theories.'' I discuss appropriate general frameworks for such theories, in which convexity plays a key role. Such frameworks are appropriate for investigating what things look like from an ``inside view,'' i.e. for describing perspectival information that one subsystem of the world can have about another. Understanding how such views can combine, and whether an overall ``geometric'' picture (``outside view'') coordinating them all can be had, even if this picture is very different in nature from the structure of the perspectives within it, is the key to understanding whether we may be able to achieve a unified, ``objective'' physical view in which quantum mechanics is the appropriate description for certain perspectives, or whether quantum mechanics is truly telling us we must go beyond this ``geometric'' conception of physics. The nature of information, its flow and processing, as seen from various operational persepectives, is likely to be key to understanding whether and how such coordination and unification can be achieved.

Introduction to the study of entropy in Quantum Games

Abstract: The present work is an introductory study about entropy its properties and its role in quantum information theory. In a next work, we will use these results to the analysis of a quantum game described by a density operator and with its entropy equal to von Neumann's.