Coherent information

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

Estimating the output entropy of a tensor product of two quantum channels

Abstract: For a class of bipartite quantum states, we find a nontrivial lower bound on the entropy gain resulting from the action of a tensor product of the identity channel with an arbitrary channel. We use the obtained result to bound the output entropy of the tensor product of a dephasing channel with an arbitrary channel from below. We characterize phase-damping channels that are particular cases of dephasing channels.

Quantum rate distortion, reverse Shannon theorems, and source-channel separation

Abstract: We derive quantum counterparts of two key theorems of classical information theory, namely, the rate distortion theorem and the source-channel separation theorem. The rate-distortion theorem gives the ultimate limits on lossy data compression, and the source-channel separation theorem implies that a two-stage protocol consisting of compression and channel coding is optimal for transmitting a memoryless source over a memoryless channel. In spite of their importance in the classical domain, there has been surprisingly little work in these areas for quantum information theory. In the present paper, we prove that the quantum rate distortion function is given in terms of the regularized entanglement of purification. We also determine a single-letter expression for the entanglement-assisted quantum rate distortion function, and we prove that it serves as a lower bound on the unassisted quantum rate distortion function. This implies that the unassisted quantum rate distortion function is non-negative and generally not equal to the coherent information between the source and distorted output (in spite of Barnum's conjecture that the coherent information would be relevant here). Moreover, we prove several quantum source-channel separation theorems. The strongest of these are in the entanglement-assisted setting, in which we establish a necessary and sufficient codition for transmitting a memoryless source over a memoryless quantum channel up to a given distortion.

Information theory and energy spectra.

Abstract: We examine the possibility of inferring energy spectra and their concomitant eigenstates on the basis of incomplete information concerning the system's ground state. In addition, the possibility of considering, as prior information, the expectation values of a partially unknown Hamiltonian also is examined and shown to be feasible.

Universal quantum uncertainty relations between nonergodicity and loss of information

Abstract: We establish uncertainty relations between information loss in general open quantum systems and the amount of nonergodicity of the corresponding dynamics. The relations hold for arbitrary quantum systems interacting with an arbitrary quantum environment. The elements of the uncertainty relations are quantified via distance measures on the space of quantum density matrices. The relations hold for arbitrary distance measures satisfying a set of intuitively satisfactory axioms. The relations show that as the nonergodicity of the dynamics increases, the lower bound on information loss decreases, which validates the belief that nonergodicity plays an important role in preserving information of quantum states undergoing lossy evolution. We also consider a model of a central qubit interacting with a fermionic thermal bath and derive its reduced dynamics to subsequently investigate the information loss and nonergodicity in such dynamics. We comment on the ``minimal'' situations that saturate the uncertainty relations.