Related papers: On Variational Expressions for Quantum Relative En…
Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy…
The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and…
The quantum relative entropy is a measure of the distinguishability of two quantum states, and it is a unifying concept in quantum information theory: many information measures such as entropy, conditional entropy, mutual information, and…
Quantum relative entropy, a quantum generalization of the renowned Kullback-Leibler divergence, serves as a fundamental measure of the distinguishability between quantum states and plays a pivotal role in quantum information science.…
The quantum relative entropy is frequently used as a distance measure between two quantum states, and inequalities relating it to other distance measures are important mathematical tools in many areas of quantum information theory. We have…
The quantum relative entropy is frequently used as a distance, or distinguishability measure between two quantum states. In this paper we study the relation between this measure and a number of other measures used for that purpose,…
The quantum Renyi relative entropies play a prominent role in quantum information theory, finding applications in characterizing error exponents and strong converse exponents for quantum hypothesis testing and quantum communication theory.…
We obtain formulas for Petz-R\'enyi and Umegaki relative entropy from the idea of distribution of a positive selfadjoint operator. Classical results on R\'enyi and Kullback-Leibler divergences are applied to obtain new results and new…
The quantum relative Renyi entropy of two density matrices was recently extended when the two do not commute, from which a conditional entropy is identified. This is here extended to the corresponding Tsallis relative entropy and to its…
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…
The relative entropy between quantum states quantifies their distinguishability. The estimation of certain relative entropies has been investigated in the literature, e.g., the von Neumann relative entropy and sandwiched R\'enyi relative…
It is well known that for pure states the relative entropy of entanglement is equal to the reduced entropy, and the closest separable state is explicitly known as well. The same holds for Renyi relative entropy per recent results. We ask…
We give a new characterization of relative entropy, also known as the Kullback-Leibler divergence. We use a number of interesting categories related to probability theory. In particular, we consider a category FinStat where an object is a…
We provide an upper bound on the quasi-relative entropy in terms of the trace distance. The bound is derived for two cases: 1) any operator monotone decreasing function and full rank mixed qubit or classical states; 2) a large class of…
The Renyi entropies constitute a family of information measures that generalizes the well-known Shannon entropy, inheriting many of its properties. They appear in the form of unconditional and conditional entropies, relative entropies or…
This paper introduces "swiveled Renyi entropies" as an alternative to the Renyi entropic quantities put forward in [Berta et al., Phys. Rev. A 91, 022333 (2015)]. What distinguishes the swiveled Renyi entropies from the prior proposal of…
We revisit the relationship between quantum separability and the sign of the relative q-entropies of composite quantum systems. The q-entropies depend on the density matrix eigenvalues p_i through the quantity omega_q = sum_i p_i^q. Renyi's…
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…
Generalizing the notion of relative entropy, the difference between a priori and a posteriori relative entropy for quantum systems is drawn. The former, known as quantum relative entropy, is associated with quantum states recognition. The…
Heisenberg's uncertainty principle has recently led to general measurement uncertainty relations for quantum systems: incompatible observables can be measured jointly or in sequence only with some unavoidable approximation, which can be…