Related papers: Quantum conditional entropy for infinite-dimension…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
In finite-dimensional quantum systems, temperature cannot be uniquely defined. This, in turn, implies that there are several ways to define entropy production in finite-dimensional quantum systems, because the classical entropy production…
The history of complementary observables and mutual unbiased bases is reviewed. A characterization is given in terms of conditional entropy of subalgebras. The concept of complementarity is extended to non-commutative subalgebras.…
Universality of quantum mechanics -- its applicability to physical systems of quite different nature and scales -- indicates that quantum behavior can be a manifestation of general mathematical properties of systems containing…
In this paper we discuss the fidelity of states in infinite dimensional systems, give an elementary proof of the infinite dimensional version of Uhlmann's theorem, and then, apply it to generalize several properties of the fidelity from…
Lieb and Ruskai's strong subadditivity theorem, which shows that the conditional mutual information must be nonnegative, is fundamental in quantum theory. It has numerous applications, such as in quantum error correction. When the mutual…
We introduce the notion of metric entropy for a nonautonomous dynamical system given by a sequence of probability spaces and a sequence of measure-preserving maps between these spaces. This notion generalizes the classical concept of metric…
As a phenomenon encompassing measurement incompatibility and Bell nonlocality, quantum contextuality is not only central to our understanding of quantum mechanics, but also an essential resource in many quantum information processing tasks.…
Thermodynamic entropy is not an entirely satisfactory measure of information of a quantum state. This entropy for an unknown pure state is zero, although repeated measurements on copies of such a pure state do communicate information. In…
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…
We propose an approach to the realization of many-body quantum state distributions inspired by combined principles of thermodynamics and mesoscopic physics. Its essence is a maximum entropy principle conditioned by conservation laws. We go…
Maximum entropy method for analytic continuation is extended by introducing quantum relative entropy. This new method is formulated in terms of matrix-valued functions and therefore invariant under arbitrary unitary transformation of input…
We introduce ways to measure information storage in quantum systems, using a recently introduced computation-theoretic model that accounts for measurement effects. The first, the quantum excess entropy, quantifies the shared information…
Quantum information measures such as the entropy and the mutual information find applications in physics, e.g., as correlation measures. Generalizing such measures based on the R\'enyi entropies is expected to enhance their scope in…
Based on the monogamy of entanglement, we develop the technique of quantum conditioning to build an {\it additive} entanglement measure: the conditional entanglement of mutual information. Its {\it operational} meaning is elaborated to be…
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…
The general framework of entropic dynamics is used to formulate a relational quantum dynamics. The main new idea is to use tools of information geometry to develop an entropic measure of the mismatch between successive configurations of a…
We consider a nontrivial class of infinite dimensional quantum channels characterized by finiteness of the Holevo capacity. Some general properties of channels of this class are described. In particular, a special sufficient condition of…
The maximum entropy principle, as applied to quantum systems, is a fundamental prescript positing that for a quantum system for which we only have partial knowledge, the maximum entropy state consistent with the partial knowledge is a…
Basic properties of the unified entropies are examined. The consideration is mainly restricted to the finite-dimensional quantum case. Bounds in terms of ensembles of quantum states are given. Both the continuity in Fannes' sense and…