Related papers: Exact characterizations for quantum conditional mu…
Incremental information, as measured by the quantum entropy, is increasing when two ensembles are united. This result was proved by Lieb and Ruskai, and it is the foundation for the proof of strong subadditivity of quantum entropy. We…
Given an unknown quantum state distributed over two systems, we determine how much quantum communication is needed to transfer the full state to one system. This communication measures the "partial information" one system needs conditioned…
The relative entropy is a principal measure of distinguishability in quantum information theory, with its most important property being that it is non-increasing with respect to noisy quantum operations. Here, we establish a remainder term…
We present a quantum information theory that allows for the consistent description of quantum entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices, rather than probability…
The fundamental goal of information theory is to characterize complex operational tasks using efficiently computable information quantities, Shannon's capacity formula being the prime example of this. However, many tasks in quantum…
It is observed that the entropy reduction (the information gain in the initial terminology) of an efficient (ideal or pure) quantum measurement coincides with the generalized quantum mutual information of a q-c channel mapping an a priori…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
Many quantum information measures can be written as an optimization of the quantum relative entropy between sets of states. For example, the relative entropy of entanglement of a state is the minimum relative entropy to the set of separable…
Information theory establishes the fundamental limits on data transmission, storage, and processing. Quantum information theory unites information theoretic ideas with an accurate quantum-mechanical description of reality to give a more…
Several important measures of quantum correlations of a state of a finite-dimensional composite system are defined as linear combinations of marginal entropies of this state. This paper is devoted to the infinite-dimensional generalizations…
We review with a tutorial scope the information theory foundations of quantum statistical physics. Only a small proportion of the variables that characterize a system at the microscopic scale can be controlled, for both practical and…
We give two strengthenings of an inequality for the quantum conditional mutual information of a tripartite quantum state recently proved by Fawzi and Renner, connecting it with the ability to reconstruct the state from its bipartite…
Information-theoretic quantities like entropy and mutual information have found numerous uses in machine learning. It is well known that there is a strong connection between these entropic quantities and submodularity since entropy over a…
The fact that the quantum relative entropy is non-increasing with respect to quantum physical evolutions lies at the core of many optimality theorems in quantum information theory and has applications in other areas of physics. In this…
The work is devoted to study of quantum mutual information and coherent information -- the two important characteristics of quantum communication channel. Appropriate definitions of these quantities in the infinite-dimensional case are…
In quantum error correction, the Petz map serves as a perfect recovery map when the Knill-Laflamme conditions are satisfied. Notably, while perfect recovery is generally infeasible for most quantum channels of finite dimension, the Petz map…
Mutual information is used as a purely geometrical regularization of entanglement entropy applicable to any QFT. A coefficient in the mutual information between concentric circular entangling surfaces gives a precise universal prescription…
We characterize mutual information as the unique map on ordered pairs of random variables satisfying a set of axioms similar to those of Faddeev's characterization of the Shannon entropy. There is a new axiom in our characterization however…
Quantum conditional entropies play a fundamental role in quantum information theory. In quantum key distribution, they are exploited to obtain reliable lower bounds on the secret-key rates in the finite-size regime, against collective…
We study a proper definition of R\'enyi mutual information (RMI) in quantum field theory as defined via the Petz R\'enyi relative entropy. Unlike the standard definition, the RMI we compute is a genuine measure of correlations between…