Related papers: Simple state preparation for contextuality tests w…
In this sequence of papers, noncommutative analysis is used to give a consistent axiomatic approach to a unified conceptual foundation of classical and quantum physics. The present Part I defines the concepts of observables, states and…
In quantum physics the term `contextual' can be used in more than one way. One usage, here called `Bell contextual' since the idea goes back to Bell, is that if $A$, $B$ and $C$ are three quantum observables, with $A$ compatible (i.e.,…
We present a way of experimentally determining the concurrence in terms of the expectation values of local observables for arbitrary multipartite pure states. In stead of the joint measurements on two copies of a state in the experiment for…
We consider a protocol to perform the optimal quantum state discrimination of $N$ linearly independent non-orthogonal pure quantum states and present a computational code. Through the extension of the original Hilbert space, it is possible…
The uncertainty relation is one of the key ingredients of quantum theory. Despite the great efforts devoted to this subject, most of the variance-based uncertainty relations are state-dependent and suffering from the triviality problem of…
For a quantum particle with a single degree of freedom, we derive preparational sum and product uncertainty relations satisfied by $N$ linear combinations of position and momentum observables. The state-independent bounds depend on their…
The noncontextuality of quantum mechanics can be directly tested by measuring two entangled particles with more than two outcomes per particle. The two associated contexts are "interlinked" by common observables.
We show that partial transposition for pure and mixed two-particle states in a discrete $N$-dimensional Hilbert space is equivalent to a change in sign of a "momentum-like" variable of one of the particles in the Wigner function for the…
When you measure an observable, A, in Quantum Mechanics, the state of the system changes. This, in turn, affects the quantum-mechanical uncertainty in some non-commuting observable, B. The standard Uncertainty Relation puts a lower bound on…
We consider high-dimensional estimation problems where the number of parameters diverges with the sample size. General conditions are established for consistency, uniqueness, and asymptotic normality in both unpenalized and penalized…
The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables.…
In this article, we study the problem of comparing mixed quantum states: given $n$ unknown mixed quantum states, can one determine whether they are identical or not with an unambiguous quantum measurement? We first study universal…
In this paper, we consider the problem of testing independence in high-dimensional settings with missing data. Building upon a recently proposed Kendall-based statistic, we introduce two new modifications specifically designed to…
We consider the problem of certification of arbitrary ensembles of pure states and projective measurements solely from the experimental statistics in the prepare-and-measure scenario assuming the upper bound on the dimension of the Hilbert…
The problem of measuring conditional dependence between two random phenomena arises when a third one (a confounder) has a potential influence on the amount of information between them. A typical issue in this challenging problem is the…
The Klyachko inequality is an inequality for the probabiities of the values of five observables of a spin-1 particle, which is satisfied by any noncontextual assignment of values to this set of observables, but is violated by the…
Measurement error in the observed values of the variables can greatly change the output of various causal discovery methods. This problem has received much attention in multiple fields, but it is not clear to what extent the causal model…
In the Contextuality-by-Default theory random variables representing measurement outcomes are labeled contextually, i.e., not only by what they measure but also under what conditions (in what contexts) the measurements are made, including…
By probabilistic means, the concept of contextuality is extended so that it can be used in non-ideal situations. An inequality is presented, which at least in principle enables a test to discard non-contextual hidden-variable models at low…
It is well known that the effect of quantum nonlocality, as witnessed by violation of a Bell inequality, can be observed even when relaxing the assumption of measurement independence, i.e. allowing for the source to be partially correlated…