Coherent information

About: Coherent information is a research topic. Over the lifetime, 1225 publications have been published within this topic receiving 46672 citations.

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.

Error Thresholds for Arbitrary Pauli Noise

Abstract: The error threshold of a one-parameter family of quantum channels is defined as the largest noise level such that the quantum capacity of the channel remains positive. This in turn guarantees the existence of a quantum error correction code for noise modeled by that channel. Discretizing the single-qubit errors leads to the important family of Pauli quantum channels; curiously, multipartite entangled states can increase the threshold of these channels beyond the so-called hashing bound, an effect termed superadditivity of coherent information. In this work, we divide the simplex of Pauli channels into one-parameter families and compute numerical lower bounds on their error thresholds. We find substantial increases of error thresholds relative to the hashing bound for large regions in the Pauli simplex corresponding to biased noise, which is a realistic noise model in promising quantum computing architectures. The error thresholds are computed on the family of graph states, a special type of stabilizer state. In order to determine the coherent information of a graph state, we devise an algorithm that exploits the symmetries of the underlying graph resulting in a substantial computational speed-up. This algorithm uses tools from computational group theory and allows us to consider symmetric graph states on a large number of vertices. Our algorithm works particularly well for repetition codes and concatenated repetition codes (or cat codes), for which our results provide the first comprehensive study of superadditivity for arbitrary Pauli channels. In addition, we identify a novel family of quantum codes based on tree graphs. The error thresholds of these tree graph states outperform repetition and cat codes in large regions of the Pauli simplex, and hence form a new code family with desirable error correction properties.

Information Theory for Quantum Systems

Abstract: Basic concepts and results of physical information theory are presented. The entropy defect and Shannon’s measure of information are introduced and the entropy defect principle is formulated for both quasiclassical and consistently quantum description of a physical system. Results related to ideal physical information channels are discussed. The entropy defect and the amount of information coincide in the quasiclassical case, but the latter quantity is, in general, smaller than the former in quantum case due to the quantum-mechanical irreversibility of measurement. The physical meaning of both quantities is analyzed in connection with Gibbs paradox and the maximum work obtainable from a non-equilibrium system. Indirect (generalized) vs. direct (von Neumann’s) quantum measurements are considered. It is shown that in any separable infinite-dimensional Hilbert space direct and indirect quantum measurements yield equal maximum information.

Nonequilibrium quantum impurities: from entropy production to information theory.

Abstract: Nonequilibrium steady-state currents, unlike their equilibrium counterparts, continuously dissipate energy into their physical surroundings leading to entropy production and time-reversal symmetry breaking. This Letter discusses these issues in the context of quantum impurity models. We use simple thermodynamic arguments to define the rate of entropy production sigma and show that sigma has a simple information-theoretic interpretation in terms of nonequilibrium distribution functions. This allows us to show that the entropy production is strictly positive for any nonequilibrium steady state. We conclude by applying these ideas to the resonance level model and the Kondo model.