Coherent information

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

Information encoding of a qubit into a multilevel environment

Abstract: I consider the interaction of a small quantum system (a qubit) with a structured environment consisting of many levels. The qubit will experience a decoherence process, which implies that part of its initial information will be encoded into correlations between system and environment. I investigate how this information is distributed on a given subset of levels as a function of its size, using the mutual information between both entities, in the spirit of the partial-information plots studied by Zurek and co-workers. In this case we can observe some differences, which arise from the fact that I am partitioning just one quantum system and not a collection of them. However, some similar features, like redundancy (in the sense that a given amount of information is shared by many subsets), which increases with the size of the environment, are also found here.

General Probabilistic Framework of Randomness

Abstract: We introduce a new mathematical framework for the probabilistic description of an experiment upon a system of any type in terms of initial information representing this system Based on the notions of an information state, an information state space and a generalized observable, this general framework covers the description of a wide range of experimental situations including those where, with respect to a system, an experiment is perturbing We prove that, to any experiment upon a system, there corresponds a unique generalized observable on a system initial information state space, which defines the probability distribution of outcomes under this experiment We specify the case where initial information on a system provides "no knowledge" for the description of an experiment Incorporating in a uniform way the basic notions of conventional probability theory and the non-commutativity aspects and the basic notions of quantum measurement theory, our framework clarifies the principle difference between Kolmogorov's model in probability theory and the statistical model of quantum theory Both models are included into our framework as particular cases We show that the phenomenon of "reduction" of a system initial information state is inherent, in general, to any non-destructive experiment and upon a system of any type Based on our general framework, we introduce the probabilistic model for the description of non-destructive experiments upon a quantum system and prove that positive bounded linear mappings on the Banach space of trace class operators, arising in the description of experiments upon a quantum system, are completely positive

Quantum measurement and information

Abstract: The operationally defined invariant information introduced by Brukner and Zeilinger is related to the problem of estimation of quantum states. It quantifies how the estimated states differ in average from the true states in the sense of Hilbert-Schmidt norm. This information evaluates the quality of the measurement and data treatment adopted. Its ultimate limitation is given by the trace of inverse of Fisher information matrix.

Quantum polar codes for arbitrary channels

Abstract: We construct a new entanglement-assisted quantum polar coding scheme which achieves the symmetric coherent information rate by synthesizing "amplitude" and "phase" channels from a given, arbitrary quantum channel. We first demonstrate the coding scheme for arbitrary quantum channels with qubit inputs, and we show that quantum data can be reliably decoded by O(N) rounds of coherent quantum successive cancellation, followed by N controlled-NOT gates (where N is the number of channel uses). We also find that the entanglement consumption rate of the code vanishes for degradable quantum channels. Finally, we extend the coding scheme to channels with multiple qubit inputs. This gives a near-explicit method for realizing one of the most striking phenomena in quantum information theory: the superactivation effect, whereby two quantum channels which individually have zero quantum capacity can have a non-zero quantum capacity when used together.

Erasable and unerasable correlations.

Abstract: We address the problem of removing correlation from sets of states while preserving as much local quantum information as possible. We prove that states obtained from universal cloning can only be decorrelated at the expense of complete erasure of local information (i.e., information about the copied state). We solve analytically the problem of decorrelation for two qubits and two qumodes (harmonic oscillators in Gaussian states), and provide sets of decorrelable states and the minimum amount of noise to be added for decorrelation.