Related papers: Inequalities for Quantum Entropy: A Review with Co…
A possible mechanism of time is formulated by developing an idea of time replaced by quantum correlations, with the aid of modern quantum information theory. We invent a microscopic model, where correlations of a closed system are steadily…
We give a sufficient and necessary condition for a probability measure $\mu$ on the real line to satisfy the logarithmic Sobolev inequality for convex functions. The condition is expressed in terms of the unique left-continuous and…
Entropic uncertainty relations provide an information-theoretic framework for quantifying the fundamental indeterminacy inherent in quantum mechanics. We propose more stringent quantum-memory-assisted entropic uncertainty relations for…
Holevo introduced a fidelity between quantum states that is symmetric and as effective as the trace norm in evaluating their similarity. This fidelity is bounded by a function of the trace norm, a relationship to which we will refer as…
We show that Frenkel's integral representation of the quantum relative entropy provides a natural framework to derive continuity bounds for quantum information measures. Our main general result is a dimension-independent semi-continuity…
Experimental and theoretical results about entropy limits for macroscopic and single-particle systems are reviewed. It is clarified when it is possible to speak about a quantum of entropy, given by the Boltzmann constant k, and about a…
We show that the recently formulated Equivalence Principle (EP) implies a basic cocycle condition both in Euclidean and Minkowski spaces, which holds in any dimension. This condition, that in one-dimension is sufficient to fix the…
In this paper a general definition of quantum conditional entropy for infinite-dimensional systems is given based on recent work of Holevo and Shirokov arXiv:1004.2495 devoted to quantum mutual and coherent informations in the…
We prove a limit theorem for quantum stochastic differential equations with unbounded coefficients which extends the Trotter-Kato theorem for contraction semigroups. From this theorem, general results on the convergence of approximations…
We approach the physical implications of the non-commutative nature of Complementary Observable Algebras (COA) from an information theoretic perspective. In particular, we derive a general \textit{entropic certainty principle} stating that…
In this paper, we discuss some general connections between the notions of positive map, weak majorization and entropic inequalities in the context of detection of entanglement among bipartite quantum systems. First, basing on the fact that…
We show that a relatively simple reasoning using von Neumann entropy inequalities yields a robust proof of the quantum Singleton bound for quantum error-correcting codes (QECC). For entanglement-assisted quantum error-correcting codes…
The equivalence postulate approach to quantum mechanics entails a derivation of quantum mechanics from a fundamental geometrical principle. Underlying the formalism there exists a basic cocycle condition, which is invariant under…
We study the formulation of the uncertainty principle in quantum mechanics in terms of entropic inequalities, extending results recently derived by Bialynicki-Birula [1] and Zozor et al. [2]. Those inequalities can be considered as…
Symmetries and quantum anomalies serve as powerful tools for constraining complicated quantum many-body systems, offering valuable insights into low-energy characteristics based on their ultraviolet structure. Nevertheless, their…
We investigate the universal linear inequalities that hold for the von Neumann entropies in a multi-party system, prepared in a stabiliser state. We demonstrate here that entropy vectors for stabiliser states satisfy, in addition to the…
Renyi entropy associated with spin tomograms of quantum states is shown to obey to new inequalities containing the dependence on quantum Fourier transform. The limiting inequality for the von Neumann entropy of spin quantum states and a new…
We investigate the concept of entropy in probabilistic theories more general than quantum mechanics, with particular reference to the notion of information causality recently proposed by Pawlowski et. al. (arXiv:0905.2992). We consider two…
New quantum entropic inequality for states of system of n >_ 1 qudits is obtained. The inequality has the form of quantum subadditivity condition of bipartite qudit system and coincides with this subadditivity condition for the system of…
We give response to the question: in infinite dimension states,given a state with energy bounded by E, we can write the state as a countable convex combination of pure states with energy bounded by E. We review the Alicki-Fannes-Winter…