Showing papers on "Coherent information published in 2010"
TL;DR: An operational framework, using information-preserving structures, to classify all the kinds of information that can be perfectly preserved by quantum dynamics, and proves that every perfectly preserved code has the same structure as a matrix algebra, and that preserved information can always be corrected.
Abstract: Quantum systems carry information. Quantum theory supports at least two distinct kinds of information (classical and quantum), and a variety of different ways to encode and preserve information in physical systems. A system’s ability to carry information is constrained and defined by the noise in its dynamics. This paper introduces an operational framework, using information-preserving structures, to classify all the kinds of information that
can be perfectly (i.e., with zero error) preserved by quantum dynamics. We prove that every perfectly preserved
code has the same structure as a matrix algebra, and that preserved information can always be corrected.We also
classify distinct operational criteria for preservation (e.g., “noiseless,” “unitarily correctible,” etc.) and introduce two natural criteria for measurement-stabilized and unconditionally preserved codes. Finally, for several of these operational criteria, we present efficient (polynomial in the state-space dimension) algorithms to find all of a channel’s information-preserving structures.
125 citations
TL;DR: An entropic measure of information is proposed for any physical theory that admits systems, states and measurements and is proved a coding theorem for some theories that is analogous to the quantum and classical settings, providing us with an appealing operational interpretation.
Abstract: Information plays an important role in our understanding of the physical world. Hence we propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical worlds, our measure reduces to the von Neumann and Shannon entropies, respectively. It can even be used in a quantum or classical setting where we are only allowed to perform a limited set of operations. In a world that admits superstrong correlations in the form of non-local boxes, our measure can be used to analyze protocols such as superstrong random access encodings and the violation of 'information causality'. However, we also show that in such a world no entropic measure can exhibit all the properties we commonly accept in a quantum setting. For example, there exists no 'reasonable' measure of conditional entropy that is subadditive. Finally, we prove a coding theorem for some theories that is analogous to the quantum and classical settings, providing us with an appealing operational interpretation.
119 citations
TL;DR: A mathematical transition from the Fisher information of classical statistics to the matrix formalism of quantum theory, where the monotonicity is the main requirement, and several quantum versions parametrized by a function.
Abstract: The subject of this paper is a mathematical transition from the Fisher information of classical statistics to the matrix formalism of quantum theory. If the monotonicity is the main requirement, then there are several quantum versions parametrized by a function. In physical applications the minimal is the most popular. There is a one-to-one correspondence between Fisher informations (called also monotone metrics) and abstract covariances. The skew information and the chi-square-divergence are treated here as particular cases.
106 citations
TL;DR: A pair of entanglement-breaking channels are given that can be perfectly discriminated by means of an adaptive strategy that requires just two channel evaluations, but for which no nonadaptive strategy can give a perfect discrimination using any finite number of channel evaluations.
Abstract: We provide a simple example that illustrates the advantage of adaptive over nonadaptive strategies for quantum channel discrimination. In particular, we give a pair of entanglement-breaking channels that can be perfectly discriminated by means of an adaptive strategy that requires just two channel evaluations, but for which no nonadaptive strategy can give a perfect discrimination using any finite number of channel evaluations.
105 citations
TL;DR: A nonclassicality criterion derived from quantum Fisher information is found, which shows that this is true for linear detection schemes but false for nonlinear schemes.
Abstract: We examine whether metrological resolution beyond coherent states is a nonclassical effect. We show that this is true for linear detection schemes but false for nonlinear schemes, and propose a very simple experimental setup to test it. We find a nonclassicality criterion derived from quantum Fisher information.
92 citations
26 Oct 2010
TL;DR: The evaluation shows that the framework can lead to acceptable performance in an ad-hoc retrieval task, and the potential of the framework for three active challenges in information retrieval, namely, interaction, novelty and diversity is discussed.
Abstract: The probabilistic formalism of quantum physics is said to provide a sound basis for building a principled information retrieval framework. Such a framework can be based on the notion of information need vector spaces where events, such as document relevance or observed user interactions, correspond to subspaces. As in quantum theory, a probability distribution over these subspaces is defined through weighted sets of state vectors (density operators), and used to represent the current view of the retrieval system on the user information need. Tensor spaces can be used to capture different aspects of information needs. Our evaluation shows that the framework can lead to acceptable performance in an ad-hoc retrieval task. Going beyond this, we discuss the potential of the framework for three active challenges in information retrieval, namely, interaction, novelty and diversity.
84 citations
TL;DR: In this paper, the authors study quantum Darwinism, the redundant recording of information about the preferred states of a decohering system by its environment, for an object illuminated by a blackbody.
Abstract: We study quantum Darwinism---the redundant recording of information about the preferred states of a decohering system by its environment---for an object illuminated by a blackbody. In the cases of point-source and isotropic illumination, we calculate the quantum mutual information between the object and its photon environment. We demonstrate that this realistic model exhibits fast and extensive proliferation of information about the object into the environment and results in redundancies orders of magnitude larger than the exactly soluble models considered to date.
83 citations
Book•
26 Apr 2010TL;DR: A new and exciting approach to the basics of quantum theory, this undergraduate textbook contains extensive discussions of conceptual puzzles and over 800 exercises and problems as discussed by the authors, which gives a broad view of quantum theories by emphasizing dynamical evolution, and exploring conceptual and foundational issues.
Abstract: A new and exciting approach to the basics of quantum theory, this undergraduate textbook contains extensive discussions of conceptual puzzles and over 800 exercises and problems. Beginning with three elementary 'qubit' systems, the book develops the formalism of quantum theory, addresses questions of measurement and distinguishability, and explores the dynamics of quantum systems. In addition to the standard topics covered in other textbooks, it also covers communication and measurement, quantum entanglement, entropy and thermodynamics, and quantum information processing. This textbook gives a broad view of quantum theory by emphasizing dynamical evolution, and exploring conceptual and foundational issues. It focuses on contemporary topics, including measurement, time evolution, open systems, quantum entanglement, and the role of information.
78 citations
TL;DR: The results demonstrate that Quantum Darwinism is robust with respect to nonideal initial states of the environment: the environment almost always acquires redundant information about the system but its rate of acquisition can be reduced.
Abstract: Quantum Darwinism provides an information-theoretic framework for the emergence of the objective, classical world from the quantum substrate. The key to this emergence is the proliferation of redundant information throughout the environment where observers can then intercept it. We study this process for a purely decohering interaction when the environment, $\mathcal{E}$, is in a nonideal (e.g., mixed) initial state. In the case of good decoherence, that is, after the pointer states have been unambiguously selected, the mutual information between the system, $\mathcal{S}$, and an environment fragment, $\mathcal{F}$, is given solely by $\mathcal{F}$'s entropy increase. This demonstrates that the environment's capacity for recording the state of $\mathcal{S}$ is directly related to its ability to increase its entropy. Environments that remain nearly invariant under the interaction with $\mathcal{S}$, either because they have a large initial entropy or a misaligned initial state, therefore have a diminished ability to acquire information. To elucidate the concept of good decoherence, we show that, when decoherence is not complete, the deviation of the mutual information from $\mathcal{F}$'s entropy change is quantified by the quantum discord, i.e., the excess mutual information between $\mathcal{S}$ and $\mathcal{F}$ is information regarding the initial coherence between pointer states of $\mathcal{S}$. In addition to illustrating these results with a single-qubit system interacting with a multiqubit environment, we find scaling relations for the redundancy of information acquired by the environment that display a universal behavior independent of the initial state of $\mathcal{S}$. Our results demonstrate that Quantum Darwinism is robust with respect to nonideal initial states of the environment: the environment almost always acquires redundant information about the system but its rate of acquisition can be reduced.
77 citations
TL;DR: Using strong subadditivity of entropy, it is proved that the Holevo quantity is not larger than an exchange entropy, which implies an upper bound for coherent information.
Abstract: The mutual information between the sender of a classical message encoded in quantum carriers and a receiver is fundamentally limited by the Holevo quantity. Using strong subadditivity of entropy, we prove that the Holevo quantity is not larger than an exchange entropy. This implies an upper bound for coherent information. Moreover, restricting our attention to classical information, we bound the transmission distance between probability distributions by their entropic distance, which is a concave function of their Hellinger distance.
75 citations
TL;DR: In this article, an experimentally accessible criterion has been proposed to measure the degree of non-Gaussianity of quantum states based on the conditional entropy of the state with a Gaussian reference.
Abstract: Non-Gaussian states and processes are useful resources in quantum information with continuous variables. An experimentally accessible criterion has been proposed to measure the degree of non-Gaussianity of quantum states based on the conditional entropy of the state with a Gaussian reference. Here we adopt such a criterion to characterize an important class of nonclassical states: single-photon-added coherent states. Our studies demonstrate the reliability and sensitivity of this measure and use it to quantify how detrimental is the role of experimental imperfections in our implementation.
Posted Content•
Abstract: I study the mutual information between spatial subsystems in a variety of scale invariant quantum field theories. While it is derived from the bare entanglement entropy, the mutual information offers a more refined probe of the entanglement structure of quantum field theories because it remains finite in the continuum limit. I argue that the mutual information has certain universal singularities that are a manifestation of the idea of "entanglement per scale". Moreover, I propose a method, based on an ansatz for higher dimensional twist operators, to compute the entanglement entropy, Renyi entropy, and mutual information in a general quantum field theory. The relevance of these results to the search for renormalization group monotones, to holographic duality, and to entanglement based simulation methods for many body systems are all discussed.
01 Jan 2010
TL;DR: This chapter reviews the basic definitions and properties of entropy in both classical and quantum information theory and discusses Shannon entropy, a key concept of classical information theory.
Abstract: Entropy is a key concept of quantum information theory. It measures how much uncertainty there is in the state of a physical system. In this chapter we review the basic definitions and properties of entropy in both classical and quantum information theory. In places the chapter contains rather detailed and lengthy mathematical arguments. On a first reading these sections may be read lightly and returned to later for reference purposes. Shannon entropy The key concept of classical information theory is the Shannon entropy . Suppose we learn the value of a random variable X . The Shannon entropy of X quantifies how much information we gain, on average, when we learn the value of X . An alternative view is that the entropy of X measures the amount of uncertainty about X before we learn its value. These two views are complementary; we can view the entropy either as a measure of our uncertainty before we learn the value of X , or as a measure of how much information we have gained after we learn the value of X . Intuitively, the information content of a random variable should not depend on the labels attached to the different values that may be taken by the random variable. For example, we expect that a random variable taking the values ‘heads’ and ‘tails’ with respective probabilities ¼ and ¾ contains the same amount of information as a random variable that takes the values 0 and 1 with respective probabilities ¼ and ¾.
TL;DR: It is proved that, regardless of the protecting Hamiltonian, there exists a perturbed evolution thatnecessitates a final error correcting step for the state of the memory to be read, and depart from the usual Markovian approximation for a thermal bath by concen-trating on models for which part of the evolution can be calculated exactly.
Abstract: The ability to protect quantum information from the effect of noise is one of the majorgoals of quantum information processing. In this article, we study limitations on theasymptotic stability of quantum information stored in passive N-qubit systems. Weconsider the effect of small imperfections in the implementation of the protecting Hamil-tonian in the form of perturbations or weak coupling to a ground state environment.We thus depart from the usual Markovian approximation for a thermal bath by concen-trating on models for which part of the evolution can be calculated exactly. We provethat, regardless of the protecting Hamiltonian, there exists a perturbed evolution thatnecessitates a final error correcting step for the state of the memory to be read. Suchan error correction step is shown to require a finite error threshold, the lack thereofbeing exemplified by the 3D XZ-compass model [1]. We go on to present explicit weakHamiltonian perturbations which destroy the logical information stored in the 2D toriccode in a time O(log(N)).
01 Jan 2010
TL;DR: In this article, the authors studied the properties of quantum mutual information and coherent information in the infinite-dimensional case, and their properties were studied in detail, and an upper bound for the coherent information was obtained.
Abstract: The paper is devoted to the study of quantum mutual information and coherent information, two important characteristics of a quantum communication channel. Appropriate definitions of these quantities in the infinite-dimensional case are given, and their properties are studied in detail. Basic identities relating the quantum mutual information and coherent information of a pair of complementary channels are proved. An unexpected continuity property of the quantum mutual information and coherent information, following from the above identities, is observed. An upper bound for the coherent information is obtained.
TL;DR: Based on a canonical joint purification which encodes the system, apparatus, and environment as well as their interplay, several basic relations involving various entropies arising from the most general quantum measurements are established.
Abstract: The information transfer in the system-apparatus-environment trio is of fundamental importance for both the theory and practice of quantum information. Based on a canonical joint purification which encodes the system, apparatus, and environment as well as their interplay, we establish several basic relations involving various entropies arising from the most general quantum measurements. Some celebrated results concerning entropy change and information-disturbance tradeoff are recaptured as particular cases in a unified framework of information conservation.
TL;DR: A new logical system to reason about the information carried by a complex system composed of several parts is proposed, based on an extension of epistemic logic with operators for “group knowledge” and further extended with atomic sentences describing the results of “joint observations”.
Abstract: In this paper we give a logical analysis of both classical and quantum correlations. We propose a new logical system to reason about the information carried by a complex system composed of several parts. Our formalism is based on an extension of epistemic logic with operators for “group knowledge” (the logic GEL), further extended with atomic sentences describing the results of “joint observations” (the logic LCK). As models we introduce correlation models, as a generalization of the standard representation of epistemic models as vector models. We give sound and complete axiomatizations for our logics, and we use this setting to investigate the relationship between the information carried by each of the parts of a complex system and the information carried by the whole system. In particular we distinguish between the “distributed information”, obtainable by simply pooling together all the information that can be separately observed in any of the parts, and “correlated information”, obtainable only by doing joint observations of the parts (and pooling together the results). Our formalism throws a new light on the difference between classical and quantum information and gives rise to an informational-logical characterization of the notion of “quantum entanglement”.
IBM1
TL;DR: What is known about the various capacities of a quantum channel is summarized, including a discussion of the relevant additivity questions, to give some indication of potentially interesting directions for future research.
Abstract: A quantum communication channel can be put to many uses: it can transmit classical information, private classical information, or quantum information. It can be used alone, with shared entanglement, or together with other channels. For each of these settings there is a capacity that quantifies a channel's potential for communication. In this short review, I summarize what is known about the various capacities of a quantum channel, including a discussion of the relevant additivity questions. I also give some indication of potentially interesting directions for future research.
TL;DR: This work considers a special form of state discrimination in which after the measurement the authors are given additional information that may help us identify the state, and shows that for the corresponding classical state discrimination problems with postmeasurement information such a reduction is impossible.
Abstract: We consider a special form of state discrimination in which after the measurement we are given additional information that may help us identify the state. This task plays a central role in the analysis of quantum cryptographic protocols in the noisy-storage model, where the identity of the state corresponds to a certain bit string, and the additional information is typically a choice of encoding that is initially unknown to the cheating party. We first provide simple optimality conditions for measurements for any such problem and show upper and lower bounds on the success probability. For a certain class of problems, we furthermore provide tight bounds on how useful postmeasurement information can be. In particular, we show that for this class finding the optimal measurement for the task of state discrimination with postmeasurement information does in fact reduce to solving a different problem of state discrimination without such information. However, we show that for the corresponding classical state discrimination problems with postmeasurement information such a reduction is impossible, by relating the success probability to the violation of Bell inequalities. This suggests the usefulness of postmeasurement information as another feature that distinguishes the classical from a quantum world.
TL;DR: In this paper, it is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal horizons, and the path integral quantization and quantum randomness can be derived by considering information loss of fields or particles crossing Rindler horizons for accelerating observers.
Abstract: It is suggested that quantum mechanics is not fundamental but emerges from classical information theory applied to causal horizons. The path integral quantization and quantum randomness can be derived by considering information loss of fields or particles crossing Rindler horizons for accelerating observers. This implies that information is one of the fundamental roots of all physical phenomena. The connection between this theory and Verlinde's entropic gravity theory is also investigated.
TL;DR: A theoretical framework for quantifying information processing in a quantum dynamical system that combines tools from dynamical systems theory, information theory, quantum mechanics, and computation theory is reviewed.
Abstract: Nature intrinsically computes. It has been suggested that the entire universe is a computer, in particular, a quantum computer. To corroborate this idea we require tools to quantify the information processing. Here we review a theoretical framework for quantifying information processing in a quantum dynamical system. So-called intrinsic quantum computation combines tools from dynamical systems theory, information theory, quantum mechanics, and computation theory. We will review how far the framework has been developed and what some of the main open questions are. On the basis of this framework we discuss upper and lower bounds for intrinsic information storage in a quantum dynamical system.
TL;DR: In this article, a quantum expectation value under the assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1≤N<+∞) was derived and it was shown that von Neumann's theory cannot depict our physical world with a violation factor that grows exponentially with the number of particles.
Abstract: The theoretical formalism of the implementation of the Deutsch-Jozsa algorithm relies on von Neumann’s theory. We try to investigate whether von Neumann’s theory meet our physical world. We derive a proposition concerning a quantum expectation value under the assumption of the existence of the orientation of reference frames in N spin-1/2 systems (1≤N<+∞). This assumption intuitively depictures our physical world. However, the quantum predictions within the formalism of von Neumann’s projective measurement violate the proposition with a magnitude that grows exponentially with the number of particles. Therefore, von Neumann’s theory cannot depicture our physical world with a violation factor that grows exponentially with the number of particles. Hence, von Neumann’s theory cannot meet the Deutsch-Jozsa algorithm. We propose the solution of the problem. Our solution is equivalent to changing Planck’s constant (ℏ) to new constant ( \(\hbar/\sqrt{2}\) ). It may be that a new type of the quantum theory early approaches Newton’s theory in the macroscopic scale than the old quantum theory does so.
TL;DR: Wave front detection, which allows for registering the direction of the incoming wave flux at a given position, can be used to reconstruct the mutual coherence function when combined with some techniques previously developed for quantum information processing.
Abstract: Light is a major carrier of information about the world around us, from the microcosmos to the macrocosmos. The present methods of detection are sensitive both to robust features, such as intensity, or polarization, and to more subtle effects, such as correlations. Here we show how wave front detection, which allows for registering the direction of the incoming wave flux at a given position, can be used to reconstruct the mutual coherence function when combined with some techniques previously developed for quantum information processing.
TL;DR: A two-step deterministic remote state preparation protocol for an arbitrary quhit with the aid of a three-particle Greenberger—Horne—Zeilinger state is presented, showing that only single-particles von Neumann measurements, local operations, and classical communication are necessary.
Abstract: We present a two-step deterministic remote state preparation protocol for an arbitrary quhit with the aid of a three-particle Greenberger—Horne—Zeilinger state. Generalization of this protocol for higher-dimensional Hilbert space systems among three parties is also given. We show that only single-particle von Neumann measurements, local operations, and classical communication are necessary. Moreover, since the overall information of the quantum state can be divided into two different pieces, which may be at different locations, this protocol may be useful in the quantum information field.
TL;DR: The kinetic energy decomposition for both stationary and nonstationary states is demonstrated and the dequantization procedure is employed to shed light on the nature of kinetic energy functionals.
TL;DR: The location of quantum information in various subsets of the qudit carriers of an additive graph code is discussed using a collection of operators on the coding space which form the information group, which represents the input information through an encoding operation constructed as an explicit quantum circuit.
Abstract: The location of quantum information in various subsets of the qudit carriers of an additive graph code is discussed using a collection of operators on the coding space which form what we call the information group. It represents the input information through an encoding operation constructed as an explicit quantum circuit. Partial traces of these operators down to a particular subset of carriers provide an isomorphism of a subgroup of the information group, and this gives a precise characterization of what kinds of information they contain. All carriers are assumed to have the same dimension $D$, an arbitrary integer greater than 1.
TL;DR: In this article, the authors present some preliminary theoretical and numerical explorations concerning the properties of the Helstrom bound in binary (or multibinary) communication involving non-Poissonian or nonlinear coherent states.
Abstract: Part of the difficulties in implementing communication in quantum information stems from the fragility of Schrodinger's cat-like superpositions. A recent experiment in quantum optics by Cook et al (2007 Nature 446 774) has proved the feasibility of a feedback-mediated quantum measurement for discriminating between optical coherent states under photodetection. Minimizing the error in receiver measurement over all possible POVMs leads to the so-called quantum error probability or 'Helstrom bound', and CMG measurements validate the theoretical prediction by Helstrom, Dolinar and Geremia concerning this bound. In this work, we present some preliminary theoretical and numerical explorations concerning the properties of the Helstrom bound in binary (or multibinary) communication involving non-Poissonian or nonlinear coherent states.
TL;DR: It is proposed that regular- and Z-DNA are equivalent to the alternative words chosen from an alphabet to maintain the equilibrium of an information transmission system.
Abstract: We discuss the possibility of a relativistic relationship between information and entropy, closely analogous to the classical Maxwell electro-magnetic wave equations. Inherent to the analysis is the description of information as residing in points of non-analyticity; yet ultimately also exhibiting a distributed characteristic: additionally analogous, therefore, to the wave-particle duality of light. At cosmological scales our vector differential equations predict conservation of information in black holes, whereas regular- and Z-DNA molecules correspond to helical solutions at microscopic levels. We further propose that regular- and Z-DNA are equivalent to the alternative words chosen from an alphabet to maintain the equilibrium of an information transmission system.