Related papers: Inequalities for nonnegative numbers and informati…
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…
The monogamy of quantum entanglement captures the property of limitation in the distribution of entanglement. Various monogamy relations exist for different entanglement measures that are important in quantum information processing. Our…
Shannon's entropy power inequality (EPI) can be viewed as a statement of concavity of an entropic function of a continuous random variable under a scaled addition rule: $$f(\sqrt{a}\,X + \sqrt{1-a}\,Y) \ge a f(X) + (1-a) f(Y) \quad \forall…
The nonextensive statistics based on the $q$-entropy $S_q=-\frac{\sum_{i=1}^v(p_i-p_i^q)}{1-q}$ has been so far applied to systems in which the $q$ value is uniformly distributed. For the systems containing different $q$'s, the…
We present a problem relating measurements and information theory in spin foam models. In the three dimensional case of quantum gravity we can compute probabilities of spin network graphs and study the behaviour of the Shannon entropy…
The probability representation of quantum mechanics including propagators and tomograms of quantum states of the universe and its application to quantum gravity and cosmology are reviewed. The minisuperspaces modeled by oscillator, free…
It is argued that the factorization of compound probability over subsystems is a consequence of the existence of thermodynamic equilibrium in the composite system having Tsallis entropy. So it should be respected by all exact calculations…
Uncertainty relations based on information theory for both discrete and continuous distribution functions are briefly reviewed. We extend these results to account for (differential) R\'{e}nyi entropy and its related entropy power. This…
We demonstrate that the Renyi-2 entropy provides a natural measure of information for any multimode Gaussian state of quantum harmonic systems, operationally linked to the phase-space Shannon sampling entropy of the Wigner distribution of…
The tomographic approach to quantum mechanics is revisited as a direct tool to investigate violation of Bell-like inequalities. Since quantum tomograms are well defined probability distributions, the tomographic approach is emphasized to be…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
Strong subadditivity inequality for a three-particle composite system is an important inequality in quantum information theory which can be studied via a four-particle entangled state. We use two three-level atoms in $\Lambda$ configuration…
Using joint Shannon entropy, we propose an inequality for a four-level system, which is satisfied in any non-contextual realist hidden variable model. We show that this entropic inequality is violated by quantum mechanics for a range of…
We study the $p$-R\'{e}nyi entropy power inequality with a weight factor $t$ on two independent continuous random variables $X$ and $Y$. The extension essentially relies on a modulation on the sharp Young's inequality due to Bobkov and…
Information theory has become an increasingly important research field to better understand quantum mechanics. Noteworthy, it covers both foundational and applied perspectives, also offering a common technical language to study a variety of…
Bell inequalities constitute a key tool in quantum information theory: they not only allow one to reveal nonlocality in composite quantum systems, but, more importantly, they can be used to certify relevant properties thereof. We provide a…
Review of tomographic probability representation of quantum states is presented both for oscillator systems with continious variables and spin--systems with discrete variables. New entropic--information inequalities are obtained for…
We provide a simple physical interpretation, in the context of the second law of thermodynamics, to the information inequality (a.k.a. the Gibbs' inequality, which is also equivalent to the log-sum inequality), asserting that the relative…
Quantum information refers to the distinctive information-processing properties of quantum systems, which arise when information is stored in or retrieved from nonorthogonal quantum states. More information is required to prepare an…
This paper is generally concerned with understanding how the uncertainty principle arises in formulations of quantum mechanics, such as the decoherent histories approach, whose central goal is the assignment of probabilities to histories.…