Related papers: Limitations on entropic Bell inequalities
Mathematical inequalities, combined with atomic-physics sum rules, enable one to derive lower and upper bounds for the Rosseland and/or Planck mean opacities. The resulting constraints must be satisfied, either for pure elements or…
Some bounds on the entropic informational quantities related to a quantum continual measurement are obtained and the time dependencies of these quantities are studied.
We define a general notion of entropy in elementary, algebraic terms. Based on that, weak forms of a scalar product and a distance measure are derived. We give basic properties of these quantities, generalize the Cauchy-Schwarz inequality,…
We present an analysis of the structure of Bell inequalities, mainly for the case of N qubits with two observables each. We show that these inequalities are related to Hadamard matrices and define Bell polynomials (in one variable) as an…
Recently it was shown that if a given state fulfils the reduction criterion it must also satisfy the known entropic inequalities. Now the questions arises whether on the assumption that stronger criteria based on positive but not completely…
Assumed data streams from a delayed choice gedanken experiment must satisfy a Bell's identity independently of locality assumptions. The violation of Bell's inequality by assumed correlations of identical form among these data streams…
Based on a geometrical argument introduced by Zukowski, a new multisetting Bell inequality is derived, for the scenario in which many parties make measurements on two-level systems. This generalizes and unifies some previous results.…
The characterization of a quantum system can be complicated by non-ideal measurement processes. In many systems, the underlying physical measurement is only sensitive to a single fixed state, complementary outcomes are inferred by…
Generalized versions of the entropic (Hirschman-Beckner) and support (Elad-Bruckstein) uncertainty principle are presented for frames representations. Moreover, a sharpened version of the support inequality has been obtained by introducing…
We construct a wide class of bounded continuous variables observables that lead to violations of Bell inequalities for the EPR state and give an intuitive Wigner function explanation how to predetermine which operators won't ever exceed the…
In most Bell tests, the measurement settings are specially chosen so that the maximal quantum violations of the Bell inequalities can be detected, or at least, the violations are strong enough to be observed. Such choices can usually…
Bell inequality is a mathematical inequality derived using the assumptions of locality and realism. Its violation guarantees the existence of quantum correlations in a quantum state. Bell inequality acts as an entanglement witness in the…
A parametrization of density matrices of $d$ dimensions in terms of the raising $J_+$ and lowering $J_-$ angular momentum operators is established together with an implicit connection with the generalized Bloch-GellMann parameters. A…
This note provides some new inequalities and approximations for beta distributions, including tail inequalities, exponential inequalities of Hoeffding and Bernstein type, Gaussian inequalities and approximations.
The possibility of stating the second law of thermodynamics in terms of the increasing behaviour of a physical property establishes a connection between that branch of physics and the theory of algebraic inequalities. We use this connection…
In this paper we prove exponential inequalities (also called Bernstein's inequality) for fractional martingales. As an immediate corollary, we will discuss weak law of large numbers for fractional martingales under divergence assumption on…
Using the monotonity of relative entropy of composite quantum systems we obtain new entropic inequalities for arbitrary density matrices of single qudit states. Example of qutrit state inequalities and the "qubit portrait" bound for the…
We present bipartite Bell-type inequalities which allow the two partners to use some non-local resource. Such inequality can only be violated if the parties use a resource which is more non-local than the one permitted by the inequality. We…
In a quantum system, there may be many density matrices associated with a state on an algebra of observables. For each density matrix, one can compute its entropy. These are in general different. Therefore one reaches the remarkable…
We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an…