Related papers: Necessary and sufficient condition for quantum sta…
Physical entities are ultimately (re)constructed from elementary yes/no events, in particular clicks in detectors or measurement devices recording quanta. Recently, the interpretation of certain such clicks has given rise to unfounded…
This article comprehensively explores matrices and their prerequisites for achieving positive semidefiniteness. The study delves into a series of theorems concerning pure quantum states in the context of weighted graphs. The main objective…
When comparing quantum states to each other, it is possible to obtain an unambiguous answer, indicating that the states are definitely different, already after a single measurement. In this paper we investigate comparison of coherent…
We address the problem of testing the dimensionality of classical and quantum systems in a `black-box' scenario. We develop a general formalism for tackling this problem. This allows us to derive lower bounds on the classical dimension…
Quantum contextuality, where measurement outcomes depend on the measurement context, implies a failure of classical realism in quantum systems. As recently shown, the transition between measurement contexts can be mapped onto the path that…
Quantum contextuality is the key concept which explains the fact that the result of a measurement is not independent of the context in which it is found. It is observed to be an intrinsic feature, i.e., neither entanglement nor spatial…
We discuss representations and colorings of orthogonality hypergraphs in terms of their two-valued states interpretable as classical truth assignments. Such hypergraphs, if they allow for a faithful orthogonal representation, have quantum…
We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…
The actual gate performed on, say, a qubit in a quantum computer may depend, not just on the actual laser pulses and voltages we programmed to implement the gate, but on its {\em context} as well. For example, it may depend on what gate has…
The standard method to check for the independence of two real-valued random variables -- demonstrating that the bivariate joint distribution factors into the product of its marginals -- is both necessary and sufficient. Here we present a…
When observations must come from incompatible devices and cannot be produced by compatible devices? This question motivates two integer valued quantifications of incompatibility, called incompatibility dimension and compatibility dimension.…
We introduce a new notion of a sufficient subalgebra for quantum states: a subalgebra is 2- sufficient for a pair of states $\{\rho_0,\rho_1\}$ if it contains all Bayes optimal tests of $\rho_0$ against $\rho_1$. In classical statistics,…
We present quantum complexity lower and upper bounds for independent set problems in graphs. In particular, we give quantum algorithms for computing a maximal and a maximum independent set in a graph. We present applications of these…
Partial Boolean algebra underlies the quantum logic as an important tool for quantum contextuality. We propose the notion atom graphs to reveal the graph structure of partial Boolean algebra for finite dimensional quantum systems by proving…
Device-independent self-testing allows to uniquely characterize the quantum state shared by untrusted parties (up to local isometries) by simply inspecting their correlations, and requiring only minimal assumptions, namely a no-signaling…
We propose to detect quantum entanglement by a condition of local measurments. We find that this condition can detect efficiently the pure entangled states for both discrete and continuous variable systems. It does not depend on…
We propose a simple test of quantumness which can decide whether for the given set of accessible experimental data the classical model is insufficient. Take two observables $ A,B$ such that for any state $\psi$ their mean values satisfy…
Contextuality is a signature of operational nonclassicality in the outcome statistics of an experiment. This notion of nonclassicality applies to a breadth of physical phenomena. Here, we establish its relation to two fundamental…
It is nowadays accepted that truly quantum correlations can exist even in the absence of entanglement. For the case of symmetric states, a physically trivial unitary transformation can alter a quantum state from entangled to separable and…
Non Gaussian states and processes are useful resources in quantum information with continuous variables. An experimentally accessible criterion has been proposed to measure the degree of non Gaussianity of quantum states, based on the…