Related papers: Compatibility and noncontextuality for sequential …
The measurement process is taken into account in the dynamics of trapped ions prepared in nonclassical motional states. The induced decoherence is shown to manifest itself both in the inhibition of the internal population dynamics and in a…
We propose a class of incompatibility measures for quantum observables based on quantifying the effect of a measurement of one observable on the statistics of the outcomes of another. Specifically, for a pair of observables $A$ and $B$ with…
The existence of incompatible measurements, epitomized by Heisenberg's uncertainty principle, is one of the distinctive features of quantum theory. So far, quantum incompatibility has been studied for measurements that test the preparation…
We report an inconsistency found in probability theory (also referred to as measure-theoretic probability). For probability measures induced by real-valued random variables, we deduce an "equality" such that one side of the "equality" is a…
In the presence of weak overall correlation, it may be useful to investigate if the correlation is significantly and substantially more pronounced over a subpopulation. Two different testing procedures are compared. Both are based on the…
Finding a set of empirical criteria fulfilled by any theory satisfying the generalized notion of noncontextuality is a challenging task of both operational and foundational importance. This work presents a methodology for constructing the…
The uncertainty relations, pioneered by Werner Heisenberg nearly 90 years ago, set a fundamental limitation on the joint measurability of complementary observables. This limitation has long been a subject of debate, which has been reignited…
Here is considered a specific detection loophole, that is relevant not only to testing of quantum nonlocality, but also to some other applications of quantum computations and communications. It is described by a simple affine relation…
This work applies a quantitative metric well-known to the data assimilation community to a new context in order to capture the relative representativeness of non-simultaneous or non-co-located observations and quantify how these…
The fact that there are quantum observables without a simultaneous measurement is one of the fundamental characteristics of quantum mechanics. In this work we expand the concept of joint measurability to all kinds of possible measurement…
The quantum measurement incompatibility is a distinctive feature of quantum mechanics. We investigate the incompatibility of a set of general measurements and classify the incompatibility by the hierarchy of compatibilities of its subsets.…
We derive two classes of multi-mode Bell inequalities under local realistic assumptions, which are violated only by the entangled states negative under partial transposition in accordance with the Peres conjecture. Remarkably, the failure…
Given a finite collection of probability measures defined on subsets of a measurable space, how can we determine if they are compatible, in the sense that they can be realized as conditional distributions of a single probability measure on…
It is well known that when two or more quantum measurements suffer from imperfections they may lose their incompatibility. For a quantum system of finite dimension d we study the incompatibility of all projective measurements subjected to…
Handling object interaction is a fundamental challenge in practical multi-object tracking, even for simple interactive effects such as one object temporarily occluding another. We formalize the problem of occlusion in tracking with two…
Weak values are quantities accessed through quantum experiments involving weak measurements and post-selection. It has been shown that 'anomalous' weak values (those lying beyond the eigenvalue range of the corresponding operator) defy…
In the conventional formulation, it is broadly accepted that simultaneous measurability and commutativity of observables are equivalent. However, several objections have been claimed that there are cases in which even nowhere commuting…
This is a review devoted to the complementarity-contextuality interplay with connection to the Bell inequalities. Starting discussion with complementarity, we point out to contextuality as its seed. {\it Bohr-contextuality} is dependence of…
A suggestion for an observational test of the difference between quantum mechanics and noncontextual hidden variables theories requires the measurement of a product of two commuting observables without measuring either observable…
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…