Showing papers on "Coherent information published in 2007"

An Area Law for One Dimensional Quantum Systems

Abstract: We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and present a conjecture on completely positive maps which may provide an alternate way of arriving at an area law. We also show that, for gapped, local systems, the bound on Von Neumann entropy implies a bound on R\'{e}nyi entropy for sufficiently large $\alpha<1$ and implies the ability to approximate the ground state by a matrix product state.

Quantum information cannot be completely hidden in correlations: implications for the black-hole information paradox.

Abstract: Can quantum-information theory shed light on black-hole evaporation? By entangling the in-fallen matter with an external system we show that the black-hole information paradox becomes more severe, even for cosmologically sized black holes. We rule out the possibility that the information about the in-fallen matter might hide in correlations between the Hawking radiation and the internal states of the black hole. As a consequence, either unitarity or Hawking's semiclassical predictions must break down. Any resolution of the black-hole information crisis must elucidate one of these possibilities.

Small accessible quantum information does not imply security.

Abstract: The security of quantum key distribution is typically defined in terms of the mutual information between the distributed key $S$ and the outcome of an optimal measurement applied to the adversary's system. We show that even if this so-called accessible information is small, the key $S$ might not be secure enough to be used in applications such as one-time pad encryption. This flaw is due to a locking property of the accessible information: one additional (physical) bit of information can increase the accessible information by more than one bit.

Quantum network coding

Abstract: Since quantum information is continuous, its handling is sometimes surprisingly harder than the classical counterpart. A typical example is cloning; making a copy of digital information is straightforward but it is not possible exactly for quantum information. The question in this paper is whether or not quantum network coding is possible. Its classical counterpart is another good example to show that digital information flow can be done much more efficiently than conventional (say, liquid) flow. Our answer to the question is similar to the case of cloning, namely, it is shown that quantum network coding is possible if approximation is allowed, by using a simple network model called Butterfly. In this network, there are two flow paths, s1 to t1 and s2 to t2, which shares a single bottleneck channel of capacity one. In the classical case, we can send two bits simultaneously, one for each path, in spite of the bottleneck. Our results for quantum network coding include: (i) We can send any quantum state |ψ1〉 from s1 to t1 and |ψ2〉 from s2 to t2 simultaneously with a fidelity strictly greater than 1/2. (ii) If one of |ψ1〉 and |ψ2〉 is classical, then the fidelity can be improved to 2/3. (iii) Similar improvement is also possible if |ψ1〉 and |ψ2〉 are restricted to only a finite number of (previously known) states. (iv) Several impossibility results including the general upper bound of the fidelity are also given.

Quantum Information and Entropy

Abstract: Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In view of this, we propose a new measure for the informational entropy of a quantum state that includes information in the pure states and the thermodynamic entropy. The origin of information is explained in terms of an interplay between unitary and non-unitary evolution. Such complementarity is also at the basis of the so-called interaction-free measurement.

An introduction to information theory and entropy

Abstract: information theory and entropy Tom Carter http:// ogs. sustan.edu/~ tom/information Complex Systems Summer S hool June, 2000 1 Our general topi s: } Measuring omplexity } Some probability ba kground } Basi s of information theory } Some entropy theory } The Gibbs inequality } A simple physi al example (gases) } Shannon's ommuni ation theory } Analog hannels } Appli ation to Biology (analyzing genomes) } Appli ation to Physi s (lasers) } Some other measures } Future dire tions and prospe ts } Referen es 2 The quotes } S ien e, wisdom, and ounting } Being di erent { or random } Surprise, information, and mira les } Information (and hope) } H (or S) for Entropy } Thermodynami s } Language, and putting things together } Tools

Representation of Mutual Information Via Input Estimates

Abstract: A relationship between information theory and estimation theory was recently shown for the Gaussian channel, relating the derivative of mutual information with the minimum mean-square error. This paper generalizes the link between information theory and estimation theory to arbitrary channels, giving representations of the derivative of mutual information as a function of the conditional marginal input distributions given the outputs. We illustrate the use of this representation in the efficient numerical computation of the mutual information achieved by inputs such as specific codes or natural language

Quantum capacity of dephasing channels with memory

Abstract: We show that the amount of coherent quantum information that can be reliably transmitted down a dephasing channel with memory is maximized by separable input states. In particular, we model the channel as a Markov chain or a multimode environment of oscillators. While in the first model, the maximization is achieved for the maximally mixed input state, in the latter it is convenient to exploit the presence of a decoherence-protected subspace generated by memory effects. We explicitly compute the quantum channel capacity for the first model while numerical simulations suggest a lower bound for the latter. In both cases memory effects enhance the coherent information. We present results valid for arbitrary input size.

Quantum Capacity of a dephasing channel with memory

Abstract: We show that the amount of coherent quantum information that can be reliably transmitted down a dephasing channel with memory is maximized by separable input states. In particular, we model the channel as a Markov chain or a multimode environment of oscillators. While in the first model the maximization is achieved for the maximally mixed input state, in the latter it is convenient to exploit the presence of a decoherence-protected subspace generated by memory effects. We explicitly compute the quantum channel capacity for the first model while numerical simulations suggest a lower bound for the latter. In both cases memory effects enhance the coherent information. We present results valid for arbitrary size of the input.

Exact analysis of entanglement in gapped quantum spin chains

Abstract: We investigate the entanglement properties of the valence-bond-solid states with generic integer spin $S$. Using the Schwinger boson representation of the valence-bond-solid states, the entanglement entropy, the von Neumann entropy of a subsystem, is obtained exactly and its relationship with the usual correlation function is clarified. The saturation value of the entanglement entropy, $2\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{2}(S+1)$, is derived explicitly and is interpreted in terms of the edge-state picture. The validity of our analytical results and the edge-state picture is numerically confirmed. We also propose an application of the edge state as a qubit for quantum computation.

Classical Capacities of Averaged and Compound Quantum Channels

Abstract: We determine the capacity of compound classical-quantum channels. As a consequence we obtain the capacity formula for the averaged classical-quantum channels. The capacity result for compound channels demonstrates, as in the classical setting, the existence of reliable universal classical-quantum codes in scenarios where the only a priori information about the channel used for the transmission of information is that it belongs to a given set of memoryless classical-quantum channels. Our approach is based on the universal classical approximation of the quantum relative entropy which in turn relies on the universal hypothesis testing results.

Steganographic communication with quantum information

Abstract: We introduce a scheme for steganographic communication based on a channel hidden within the quantum key distribution protocol of Bennett and Brassard. An outside observer cannot establish evidence that this communication is taking place for the simple reason that no correlations between public data and hidden information exist. Assuming an attacker guesses hidden communication is underway, we obtain a precise quantitative bound on the amount of hidden information they can acquire, and find that it is very small, less than 10-7 bits per channel use in typical experimental settings. We also calculate the capacity of the steganographic channel, including an analysis based on data available from experimental realizations of quantum protocols.

Types of quantum information

Abstract: Quantum, in contrast to classical, information theory, allows for different incompatible types (or species) of information which cannot be combined with each other. Distinguishing these incompatible types is useful in understanding the role of the two classical bits in teleportation (or one bit in one-bit teleportation), for discussing decoherence in information-theoretic terms, and for giving a proper definition, in quantum terms, of “classical information.” Various examples (some updating earlier work) are given of theorems which relate different incompatible kinds of information, and thus have no counterparts in classical information theory.

Double-control quantum interferences in a four-level atomic system.

Abstract: A new scheme is suggested to manipulate the probe transitions (and hence the optical properties of atomic vapors) via double-control destructive and constructive quantum interferences. The influence of phase coherence between the two control transitions on the probe transition is also studied. The most remarkable feature of the present scheme is that the optical properties (absorption, transparency and dispersion) of an atomic system can be manipulated using this double-control multi-pathway interferences (multiple routes to excitation). It is also shown that a four-level system will exhibit a two-level resonant absorption because the two control levels (driven by the two control fields) form a dark state (and hence a destructive quantum interference occurs between the two control transitions). However, the present four-level system will exhibit electromagnetically induced transparency to the probe field when the three lower levels (including the probe level and the two control levels) form a three-level dark state. The present scenario has potential applications in new devices (e.g. logic gates and sensitive optical switches) and new techniques (e.g. quantum coherent information storage).

Some Open Problems in Quantum Information Theory

Abstract: Some open questions in quantum information theory (QIT) are described. Most of them were presented in Ban

High-level fusion based on conceptual graphs

Abstract: Most of studies in the field of information fusion focus on the production of high-level information from low-level data. The challenge is then to fuse this high-level information to produce a global and coherent information. Another approach consists in interpreting data as high-level information and fuse it at once. Our approach relies on the use of conceptual graphs model. The model is widely used for knowledge representation. We propose to go further and use it for information fusion. Conceptual graphs model contains aggregation operators such as join and maximal join. This paper is dedicated to the extension of the maximal join operator in order to manage heterogeneous information fusion. After describing the suitability of maximal join for high-level information fusion, we present the extension that we propose. The extension relies on relaxing the equality constraint on observations and on using fusion strategies. A case study illustrates our proposition.

Random quantum codes from Gaussian ensembles and an uncertainty relation

Abstract: Using random Gaussian vectors and an information-uncertainty relation, we give a proof that the coherent information is an achievable rate for entanglement transmission through a noisy quantum channel. The codes are random subspaces selected according to the Haar measure, but distorted as a function of the sender's input density operator. Using large deviations techniques, we show that classical data transmitted in either of two Fourier-conjugate bases for the coding subspace can be decoded with low probability of error. A recently discovered information-uncertainty relation then implies that the quantum mutual information for entanglement encoded into the subspace and transmitted through the channel will be high. The monogamy of quantum correlations finally implies that the environment of the channel cannot be significantly coupled to the entanglement, and concluding, which ensures the existence of a decoding by the receiver.

Simplification of Additivity Conjecture in Quantum Information Theory

Abstract: We simplify some conjectures in quantum information theory; the additivity of minimal output entropy, the multiplicativity of maximal output p-norm and the superadditivity of convex closure of output entropy. In this paper, by using some unital extension of quantum channels, we show that proving one of these conjectures for all unital quantum channels would imply that it is also true for all quantum channels.

Quantum estimation via the minimum Kullback entropy principle

Abstract: We address quantum estimation in situations where one has at disposal data from the measurement of an incomplete set of observables and some a priori information on the state itself. By expressing the a priori information in terms of a bias toward a given state, the problem may be faced by minimizing the quantum relative entropy (Kullback entropy) with the constraint of reproducing the data. We exploit the resulting minimum Kullback entropy principle for the estimation of a quantum state from the measurement of a single observable, either from the sole mean value or from the complete probability distribution, and apply it as a tool for the estimation of weak Hamiltonian processes. Qubit and harmonic oscillator systems are analyzed in some detail.

Feedback control for communication with non-orthogonal states

Abstract: Communicating classical information with a quantum system involves the receiver making a measurement on the system so as to distinguish as well as possible the alphabet of states used by the sender. We consider the situation in which this measurement takes an appreciable time. In this case the measurement must be described by a continuous measurement process. We consider a continuous implementation of the optimal measurement for distinguishing between two non-orthogonal states, and show that feedback control can be used during this measurement to increase the rate at which the information regarding the initial preparation is obtained. We show that while the maximum obtainable increase is modest, the effect is purely quantum mechanical in the sense that the enhancement is only possible when the initial states are non-orthogonal. We find further that the enhancement in the rate of information gain is achieved at the expense of reducing the total information which the measurement can extract in the long-time limit.

The Physics of Information

Abstract: We review of the interface between (theoretical) physics and information for non-experts. The origin of information as related to the notion of entropy is described, first in the context of thermodynamics then in the context of statistical mechanics. A close examination of the foundations of statistical mechanics and the need to reconcile the probabilistic and deterministic views of the world leads us to a discussion of chaotic dynamics, where information plays a crucial role in quantifying predictability. We then discuss a variety of fundamental issues that emerge in defining information and how one must exercise care in discussing concepts such as order, disorder, and incomplete knowledge. We also discuss an alternative form of entropy and its possible relevance for nonequilibrium thermodynamics. In the final part of the paper we discuss how quantum mechanics gives rise to the very different concept of quantum information. Entirely new possibilities for information storage and computation are possible due to the massive parallel processing inherent in quantum mechanics. We also point out how entropy can be extended to apply to quantum mechanics to provide a useful measurement for quantum entanglement. Finally we make a small excursion to the interface betweeen quantum theory and general relativity, where one is confronted with an "ultimate information paradox" posed by the physics of Black Holes. In this review we have limited ourselves; not all relevant topics that touch on physics and information could be covered.

Generalized Coherent States as Preferred States of Open Quantum Systems

Abstract: We investigate the connection between quasi-classical (pointer) states and generalized coherent states (GCSs) within an algebraic approach to Markovian quantum systems (including bosons, spins, and fermions). We establish conditions for the GCS set to become most robust by relating the rate of purity loss to an invariant measure of uncertainty derived from quantum Fisher information. We find that, for damped bosonic modes, the stability of canonical coherent states is confirmed in a variety of scenarios, while for systems described by (compact) Lie algebras, stringent symmetry constraints must be obeyed for the GCS set to be preferred. The relationship between GCSs, minimum-uncertainty states, and decoherence-free subspaces is also elucidated.

Coherent communication with continuous quantum variables

Abstract: The coherent bit (cobit) channel is a resource intermediate between classical and quantum communication. It produces coherent versions of teleportation and superdense coding. We extend the cobit channel to continuous variables by providing a definition of the coherent nat (conat) channel. We construct several coherent protocols that use both a position-quadrature and a momentum-quadrature conat channel with finite squeezing. Finally, we show that the quality of squeezing diminishes through successive compositions of coherent teleportation and superdense coding.

Optimality of private quantum channels

Abstract: We addressed the question of optimality of private quantum channels. We have shown that the Shannon entropy of the classical key necessary to securely transfer the quantum information is lower bounded by the entropy exchange of the private quantum channel and the von Neumann entropy of the ciphertext state (0). Based on these bounds we have shown that decomposition of private quantum channels into orthogonal unitaries (if they exist) optimizes the entropy. For non-ancillary single-qubit PQC we have derived the optimal entropy for the arbitrary set of plaintexts. In particular, we have shown that except when the (closure of the) set of plaintexts contains all states, one bit key is sufficient. We characterized and analysed all the possible single-qubit private quantum channels for an arbitrary set of plaintexts. For the set of plaintexts consisting of all qubit states we have characterized all possible approximate private quantum channels and we have derived the relation between the security parameter and the corresponding minimal entropy.

Quantum State Transfer with Spin Chains

Abstract: The thesis covers various aspects of quantum state transfer in permanently coupled spin systems.

Fisher information and quantum–classical field theory: classical statistics similarity

Abstract: The classical statistics indication for the impossibility to derive quantum mechanics from classical mechanics is proved. The formalism of the statistical Fisher information is used. Next the Fisher information as a tool of the construction of a self-consistent field theory, which joins the quantum theory and classical field theory, is proposed.

Experimental implementation of a logical Bell state encoding

Abstract: Liquid-phase NMR is a general-purpose testbed for developing methods of coherent control relevant to quantum information processing. Here we extend these studies to the coherent control of logical qubits and in particular to the unitary gates necessary to create entanglement between logical qubits. We report an experimental implementation of a conditional logical gate between two logical qubits that are each in decoherence-free subspaces that protect the quantum information from fully correlated dephasing.

Quantum covariance, quantum Fisher information and the uncertainty principle

Abstract: In this paper the relation between quantum covariances and quantum Fisher informations are studied This study is applied to generalize a recently proved uncertainty relation based on quantum Fisher information The proof given hereconsiderably simplifies the previously proposed proofs and leads to more general inequalities

Principles of quantum computation and information volume II

Abstract: Any new textbook in quantum information has some pretty strong competition to contend with. Not only is there the classic text by Nielsen and Chuang from 2000 [1], but also John Preskill's lecture notes, available for free online [2]. Nevertheless, a proper textbook seems more enduring than online notes, and the field has progressed considerably in the seven years since Nielsen and Chuang was published. A new textbook is a great opportunity to give a snapshot of our current state of knowledge in quantum information. Therein also lies a problem: The field has expanded so much that it is impossible to cover everything at the undergraduate level. Quantum information theory is relevant to an extremely large portion of physics, from solid state and condensed matter physics to particle physics. Every discipline that has some relation to quantum mechanics is affected by our understanding of quantum information theory. Those who wish to write a book on quantum information therefore have to make some profound choices: Do you keep the ultimate aim of a quantum computer in mind, or do you focus on quantum communication and precision measurements as well? Do you describe how to build a quantum computer with all possible physical systems or do you present only the underlying principles? Do you include only the tried and tested ideas, or will you also explore more speculative directions? You don't have to take a black-or-white stance on these questions, but how you approach them will profoundly determine the character of your book. The authors of `Principles of Quantum Computation and Information (Volume II: Basic Tools and Special Topics)' have chosen to focus on the construction of quantum computers, but restrict themselves mainly to general techniques. Only in the last chapter do they explicitly address the issues that arise in the different implementations. The book is the second volume in a series, and consists of four chapters (labelled 5 to 8) called 'Quantum Information Theory', 'Decoherence', 'Quantum Error Correction', and 'First Experimental Implementations'. The first volume covers the basics of classical computation, quantum mechanics, quantum computation, and quantum communication. Chapter five starts with the density matrix formalism, and proceeds with the development of the Kraus representation, POVMs, von Neuman entropy, quantum data compression, the Holevo bound, the partial transpose criterion, and it ends with a very nice section on the various entropies that play a role in modern physics. This includes not only the thermodynamical and statistical entropy, but also the dynamical Kolmogorov–Sinai entropy, which is used in quantum chaos in chapter 6. On the whole, I think that this is a really clear and well-presented chapter. A minor drawback is that the concept of CP maps is not explained as well as it could have been, for example by relating it to the partial transpose criterion. Chapter six continues with the high standard set in chapter five, and presents a very thorough exposition of decoherence in general. It introduces the different decoherence channels, and gives truly excellent explanations of the master equation (tied in with the Kraus representation), quantum jumps, and the quantum trajectory formalism. It also has an elegant explanation for the sensitivity of Schroedinger cats to decoherence. I do miss a proper section on the fidelity of a quantum state, though. The chapter ends with two sections on quantum chaos. Since the authors are experts in this fascinating area, this is a welcome addition to the canon of topics typically covered in quantum information. Unfortunately, the section is quite hard to follow, and as a result it is a bit of a missed opportunity. There is a section on chaos in the first volume of this series, and this may provide the required background. However, for readers who posess only volume II this is of little use. Chapter seven on quantum error correction is disappointing, and I have the feeling that the authors went through the motions without a real passion for the subject matter. The chapter describes various error correction codes, including Hamming codes and CSS codes, but it is virtually silent on fault tolerance; it does not give examples of universal sets of fault tolerant gates, and it does not mention the Solovay–Kitaev theorem. Also, it does not present the stabilizer formalism. All of these are serious omissions in a textbook on quantum information theory. Chapter eight gives a rough sketch of the early simulations and implementations of quantum gates. The readers of this journal will have no trouble following this chapter, but the undergraduate in computer science or mathematics will be completely lost. Most (but not all) physics terms do get a brief explanation, but I doubt whether that is enough to keep non-physicists on board. The chapter covers NMR, cavity QED, ion traps, solid state qubits, and optical implementations of quantum communication. I would have liked to see a more bold choice for the topics covered in the last chapter. For example, whereas liquid-state NMR was an important step in the development of quantum technologies, and many current techniques were invented for it, it does no longer play a role in the design of quantum computers. It would have been better to introduce these techniques in a section on condensed matter systems. Also, as a snapshot of our current state of knowledge in quantum information, I really miss extensive sections on the one-way model of quantum computing [3] and topological quantum computing [4]. In conclusion, the second volume of 'Principles of Quantum Computation and Information' is a partial success. The first two chapters are very good, and I would happily pay £22 for these two chapters alone. However, for a text on quantum error correction the reader is better off with Nielsen and Chuang or Preskill's lecture notes. If the reader wants an overview of quantum information in specific physical systems, there are a host of review articles to choose from, which give more details and are generally more accessible. References [1]M A Nielsen and I L Chuang 2000 Quantum Computation and Quantum Information (Cambridge University Press) [2] J Preskill, http://www.theory.caltech.edu/~preskill/ph229/ [3] R Raussendorf and H J Briegel 2001 A One-Way Quantum Computer Phys. Rev. Lett. 86 5188 [4] A Yu Kitaev 2003 Fault-tolerant quantum computation by anyons Ann. Phys. 303 2

Coding theorems of classical and quantum information theory

Abstract: 1 Entropy of Elementary Information Sources 2 Stationary Information Sources 3 Communication in the Presence of Noise 4 Quantum Coding Theorems Bibliography Index.