Coherent information

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

Dynamical maps, quantum detailed balance, and the Petz recovery map

Abstract: Markovian master equations (formally known as quantum dynamical semigroups) can be used to describe the evolution of a quantum state ρ when in contact with a memoryless thermal bath. This approach has had much success in describing the dynamics of real-life open quantum systems in the laboratory. Such dynamics increase the entropy of the state ρ and the bath until both systems reach thermal equilibrium, at which point entropy production stops. Our main result is to show that the entropy production at time t is bounded by the relative entropy between the original state and the state at time 2t. The bound puts strong constraints on how quickly a state can thermalize, and we prove that the factor of 2 is tight. The proof makes use of a key physically relevant property of these dynamical semigroups, detailed balance, showing that this property is intimately connected with the field of recovery maps from quantum information theory. We envisage that the connections made here between the two fields will have further applications. We also use this connection to show that a similar relation can be derived when the fixed point is not thermal.

Determining the continuous family of quantum Fisher information from linear-response theory

Abstract: The quantum Fisher information represents a continuous family of metrics on the space of quantum states and places the fundamental limit on the accuracy of quantum state estimation. We show that the entire family of quantum Fisher information can be determined from linear-response theory through generalized covariances. We derive the generalized fluctuation-dissipation theorem that relates linear-response functions to generalized covariances and hence allows us to determine the quantum Fisher information from linear-response functions, which are experimentally measurable quantities. As an application, we examine the skew information, which is a quantum Fisher information, of a harmonic oscillator in thermal equilibrium, and show that the equality of the skew-information-based uncertainty relation holds.

On information transfer in discrete dynamical systems

Abstract: In this paper, we propose a new definition of information transfer in a discrete dynamical system. The information transfer is based on how much entropy (uncertainty) is transferred from state x to state y, as the dynamical system evolves in time. In our previous work, we had provided an axiomatic definition of information transfer where we had considered absolute entropy to define the transfer. Our new definition can be viewed as a natural generalization of directed information from information theory to dynamical systems and is based on transfer of conditional entropy. This new definition also satisfies the properties of a) zero transfer, b) transfer asymmetry and c) information conservation. We start with a definition of one-step information transfer and then generalize this definition to n-step information transfer and average information transfer over infinite time step. We also provide analytical expressions for information transfer for linear systems. Some basic examples are provided to understand the physical meaning of information transfer and how this can be used to infer causality and influence in dynamical system setting.

Review of quantum discord in bipartite and multipartite systems

Abstract: Quantum information and computation, based on quantum correlations of quantum systems, is one of the promising new fields of physics and information science. Entanglement is the key resource of quantum information processing. However, it is shown recently that quantum entanglement is not the only kind of quantum correlations useful for quantum information processing. Quantum systems without any entanglement can still be helpful for quantum information processing since unentangled systems could have another kind of quantum correlations - quantum discord. Thus, quantum discord has drawn much attention in recent years. Here, we briefly review the concepts and properties of quantum discord. Several measures of discord including the original measure of discord, relative entropy-based discord, geometric discord, global discord, Gaussian discord, are reviewed and discussed.