Related papers: Quantum weighted entropy and its properties
In quantum field theory it is generally known that the energy density may be negative at a given point in spacetime. A number of papers have shown that there is a restriction on this energy density which is called a quantum inequality (QI).…
We consider three von Neumann entropy inequalities: subadditivity; Pinsker's inequality for relative entropy; and the monotonicity of relative entropy. For these we state conditions for equality, and we prove some new error bounds away from…
We give new upper and lower bounds on the concavity of quantum entropy. Comparisons are given with other results in the literature.
Regarding the strange properties of quantum entropy and entanglement, e.g., the negative quantum conditional entropy, we revisited the foundations of quantum entropy, namely, von Neumann entropy, and raised the new method of quantum…
We propose a new measure of relative incompatibility for a quantum system with respect to two non-commuting observables, and call it quantumness of relative incompatibility. In case of a classical state, order of observation is…
We extend algorithmic information theory to quantum mechanics, taking a universal semicomputable density matrix (``universal probability'') as a starting point, and define complexity (an operator) as its negative logarithm. A number of…
Since the beginning of quantum mechanics, many puzzling phenomena which distinguish the quantum from the classical world, have appeared such as complementarity, entanglement or contextuality. All of these phenomena are based on the…
Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…
Some of the important inequalities associated with quantum entropy are immediate algebraic consequences of the Hansen-Pedersen-Jensen inequality. A general argument is given using matrix perspectives of operator convex functions. A matrix…
The basic features of a quantum field theory which is Poincar\'e invariant, gauge invariant, finite and unitary to all orders of perturbation theory are reviewed. Quantum gravity is finite and unitary to all orders of perturbation theory.…
The properties of an alternative definition of quantum entropy, based on Wigner functions, are discussed. Such definition emerges naturally from the Wigner representation of quantum mechanics, and can easily quantify the amount of…
Quantum relative entropy $D(\rho\|\sigma)\defeq\Tr \rho (\log \rho- \log \sigma)$ plays an important role in quantum information and related fields. However, there are many quantum analogues of relative entropy. In this paper, we…
Brascamp-Lieb inequalities are entropy inequalities which have a dual formulation as generalized Young inequalities. In this work, we introduce a fully quantum version of this duality, relating quantum relative entropy inequalities to…
We discuss the notion of hidden correlations in classical and quantum indivisible systems along with such characteristics of the correlations as the mutual information and conditional information corresponding to the entropic subadditivity…
A framework for categorizing entropic measures of nonclassical correlations in bipartite quantum states is presented. The measures are based on the difference between a quantum entropic quantity and the corresponding classical quantity…
We introduce the notion of reduced relative quantum entropy and prove that it is convex. This result is then used to give a simplified proof of a theorem of Lieb and Seiringer.
The Araki-Lieb inequality is commonly used to calculate the entropy of subsystems when they are initially in pure states as this forces the entropy of the two subsystems to be equal after the complete system evolves. Then, it is easy to…
We investigate the interaction of the gravitational field with a quantum particle. First, we give the proof of the equality of the inertial and the gravitational mass for the nonrelativistic quantum particle, independently of the…
Without imposing the trapping boundary conditions and only from within the very definition of area it is shown that the loop quantization of area manifests an unexpected degeneracy in area eigenvalues. This could lead to a deeper…
We introduce an axiomatic approach for characterizing quantum conditional entropy. Our approach relies on two physically motivated axioms: monotonicity under conditional majorization and additivity. We show that these two axioms provide…