Coherent information

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

Entropic Information & Black Hole: Black Hole Information Entropy The Missing Link

Abstract: Understanding the ‘Area Law,’ in regards to the black hole entropy, based on an underlying fundamental theory has been one of the goals pursued by all models of quantum gravity. In black hole thermodynamics, black hole entropy is a measure of uncertainty or lack of information about the actual internal configuration of the system. The Bekenstein bound corresponds to the interpretation in terms of bits of information of a given physical system down to the quantum level. However, at present, it is not known which microstates are counted by the entropy of black holes. Here, i show that the new formulation of entropic information approach, based on the bit of information gives an explanation of information processes involved in calculating entropy on missing information from black holes as well as down to the quantum level. Moreover, this formulation of entropic information constitutes a new coherent global mathematical framework candidate to be the Grand Unification Theory; with information as the ultimate building block of universe.

Quantum control of the geometric phase in exact analytical solution using ultra-short strong pulses

Abstract: In the present paper, we study the geometric phase by considering a model that closely describes a realistic experimental scenario. We present an active way to control and quench the variation of the geometric phase using ultra-short strong pulses for a two-level quantum system with an exact analytical solution, i.e. beyond the rotating wave approximation. In particular, we study the variation of the geometric phase with a few cycles pulse and a smooth phase jump over a finite time intervals. The control of the variation rate of the geometric phase is obtained by acting on the shape of the phase transient and other parameters of the considered system. These features make two-level systems incorporated in ultra-short, of-resonant and gradually changing phase good candidates for implementation of schemes for the quantum computation and the coherent information processing.

Quantum Codes from Neural Networks

Abstract: We examine the usefulness of applying neural networks as a variational state ansatz for many-body quantum systems in the context of quantum information-processing tasks. In the neural network state ansatz, the complex amplitude function of a quantum state is computed by a neural network. The resulting multipartite entanglement structure captured by this ansatz has proven rich enough to describe the ground states and unitary dynamics of various physical systems of interest. In the present paper, we initiate the study of neural network states in quantum information-processing tasks. We demonstrate that neural network states are capable of efficiently representing quantum codes for quantum information transmission and quantum error correction, supplying further evidence for the usefulness of neural network states to describe multipartite entanglement. In particular, we show the following main results: a) Neural network states yield quantum codes with a high coherent information for two important quantum channels, the generalized amplitude damping channel and the dephrasure channel. These codes outperform all other known codes for these channels, and cannot be found using a direct parametrization of the quantum state. b) For the depolarizing channel, the neural network state ansatz reliably finds the best known codes given by repetition codes. c) Neural network states can be used to represent absolutely maximally entangled states, a special type of quantum error-correcting codes. In all three cases, the neural network state ansatz provides an efficient and versatile means as a variational parametrization of these highly entangled states.

Symmetry, order, entropy and information

Abstract: Conditions of applicability of the laws established for thermodynamic entropy do not necessarily fit to the entropy defined for information. Therefore, one must handle carefully the informational conclusions derived by mathematical analogies from the laws that hold for thermodynamic entropy. Entropy, and the arrow of its change are closely related to the arrows of the change of symmetry and of orderliness. Symmetry and order are interpreted in different ways in statistical thermodynamics, in symmetrology, and in evolution; and their relation to each other is also equivocal. Evolution is meant quite different in statistical physics and in philosophical terms. Which of the different interpretations can be transferred to the description of information? Entropy, introduced by Shannon on mathematical analogy borrowed from thermodynamics, is a mean to characterise information. One is looking for a possibly most general information theory. Generality of the sought theory can be qualified by its applicability to all (or at least the more) kinds of information. However, I express doubts, whether entropy is a property to characterise all kinds of information. Entropy plays an important role in information theory. This concept has been borrowed from physics, more precisely from thermodynamics, and applied to information by certain formal analogies. Several authors, having contributed to the FIS discussion and published papers in the periodical Entropy, emphasized the also existing differences in contrast to the analogies. Since the relations of entropy - as applied in information theory - to symmetry are taken from its physical origin, there is worth to take a glance at the ambiguous meaning of this term in physics in its relation to order and symmetry, respectively.

Non-Commutative Blahut-Arimoto Algorithms

Abstract: We generalize alternating optimization algorithms of Blahut-Arimoto type to the quantum setting. In particular, we give iterative algorithms to compute the mutual information of quantum channels, the Holevo quantity of classical-quantum channels, the coherent information of less noisy quantum channels, and the thermodynamic capacity of quantum channels. Our convergence analysis is based on quantum entropy inequalities and leads to a priori additive $\varepsilon$-approximations after $\mathcal{O}\left(\varepsilon^{-1}\log N\right)$ iterations, where $N$ denotes the input dimension of the channel. We complement our analysis with an a posteriori stopping criterion which allows us to terminate the algorithm after significantly fewer iterations compared to the a priori criterion in numerical examples. Finally, we discuss heuristics to accelerate the convergence.