Related papers: Max- Relative Entropy of Entanglement, alias Log R…
Two new relative entropy quantities, called the min- and max-relative entropies, are introduced and their properties are investigated. The well-known min- and max- entropies, introduced by Renner, are obtained from these. We define a new…
We show that an entanglement measure called relative entropy of entanglement satisfies a strong continuity condition. If two states are close to each other then so are their entanglements per particle pair in this measure. It follows in…
The operational characterization of quantum coherence is the corner stone in the development of resource theory of coherence. We introduce a new coherence quantifier based on max-relative entropy. We prove that max-relative entropy of…
Special approximation technique for analysis of different characteristics of states of multipartite infinite-dimensional quantum systems is proposed and applied to study of the relative entropy of entanglement and its regularisation. We…
We introduce variants of relative entropy of entanglement based on the optimal distinguishability from unentangled states by means of restricted measurements. In this way, we are able to prove that the standard regularized entropy of…
The precise one-shot characterisation of operational tasks in classical and quantum information theory relies on different forms of smooth entropic quantities. A particularly important connection is between the hypothesis testing relative…
Maximal correlation is a measure of correlation for bipartite distributions. This measure has two intriguing features: (1) it is monotone under local stochastic maps; (2) it gives the same number when computed on i.i.d. copies of a pair of…
We prove that the relative entropy of entanglement is additive when \emph{at least one of the two states} belongs to some specific class. We show that these classes include bipartite pure, maximally correlated, GHZ, Bell diagonal,…
The entanglement entropy of a subsystem of a quantum system is expressed, in the replica approach, through analytic continuation with respect to n of the trace of the n-th power of the reduced density matrix. This trace can be thought of as…
We present the modified relative entropy of entanglement for multi-party systems by a given relative density matrix which is spanned by a linear combination of the direct products of so-called basis of relative density matrices and reduced…
We investigate the properties of three entanglement measures that quantify the statistical distinguishability of a given state with the closest disentangled state that has the same reductions as the primary state. In particular, we…
As two of the most important entanglement measures--the entanglement of formation and the entanglement of distillation--have so far been limited to bipartite settings, the study of other entanglement measures for multipartite systems…
We provide a versatile upper bound on the number of maximally entangled qubits, or private bits, shared by two parties via a generic adaptive communication protocol over a quantum network when the use of classical communication is not…
A criterion of local continuity of the relative entropy of resource -- the relative entropy distance to the set of free states -- is obtained. Several basic corollaries of this criterion are presented. Applications to the relative entropy…
Generalized entropies and relative entropies are the subject of active research. Similar to the standard relative entropy, the relative $q$-entropy is generally unbounded for $q>1$. Upper bounds on the quantum relative $q$-entropy in terms…
We review studies of entanglement entropy in systems with quenched randomness, concentrating on universal behavior at strongly random quantum critical points. The disorder-averaged entanglement entropy provides insight into the quantum…
The relative entropy of entanglement $E_R$ is defined as the distance of a multi-partite quantum state from the set of separable states as measured by the quantum relative entropy. We show that this optimisation is always achieved, i.e. any…
In the quest of completely describing entanglement in the general case of a finite number of parties sharing a physical system of finite dimensional Hilbert space a new entanglement magnitude is introduced for its pure and mixed states:…
Quantifying entanglement for multipartite quantum state is a crucial task in many aspects of quantum information theory. Among all the entanglement measures, relative entropy of entanglement $E_{R}$ is an outstanding quantity due to its…
We study systematically resource measures of coherence and entanglement based on R\'enyi relative entropies, which include the logarithmic robustness of coherence, geometric coherence, and conventional relative entropy of coherence together…