Related papers: Generalized measurements for Bell tests in differe…
The problem of binary hypothesis testing between two probability measures is considered. New sharp bounds are derived for the best achievable error probability of such tests based on independent and identically distributed observations.…
Incompatibility of observables, or measurements, is one of the key features of quantum mechanics, related, among other concepts, to Heisenberg's uncertainty relations and Bell nonlocality. In this manuscript we show, however, that even…
We show that by taking into account randomness of realization of experimental contexts it is possible to construct common Kolmogorov space for data collected for these contexts, although they can be incompatible. We call such a construction…
The empirical proof of Bell inequality violations was a landmark moment for research into quantum foundations. It commits us to a universe without strict relativistic locality or requires that we escape through a potential loophole like…
Proposals for Bell inequality tests on systems restricted by superselection rules often require operations that are difficult to implement in practice. In this paper, we derive a new Bell inequality, where pairs of states are used to…
Bell inequalities rely on an assumption that the probabilities of adopting configurations of hidden variables describing a system prior to measurement are independent of the choice of measured physical property, also known as measurement…
We formally prove the existence of an enduring incongruence pervading a widespread interpretation of the Bell inequality and explain how to rationally avoid it with a natural assumption justified by explicit reference to a mathematical…
Proofs of Bell's theorem and the data analysis used to show its violation have commonly assumed a spatially stationary underlying process. However, it has been shown recently that the appropriate Bell's inequality holds identically for…
Certifying maximal quantum randomness without assumptions about system dimension remains a pivotal challenge for secure communication and foundational studies. Here, we introduce a generalized framework to directly certify maximal…
By taking into account that all real measurements are performed successively, during time, it is concluded that the violation of the Bell's inequalities in the Nature does not refute (even in an ideally perfect experiment) the theories…
Unavoidable disturbance caused by a quantum measurement implies that the realizable subsequent measurements are getting limited after one performs some measurement. The obvious general limitation that one cannot circumvent by sequential or…
It is shown that the Bell inequalities are closely related to the triangle inequalities involving distance functions amongst pairs of random variables with values $\left\{ 0,1\right\} $. A hidden variables model may be defined as a mapping…
We present Bell tests for optical continuous variable systems, combining both hybrid measurements (i.e. measuring both particle and wave aspects of light) and heralded amplifiers. We discuss two types of schemes, in which the amplifier is…
We derive a multipartite generalized Bell inequality which involves the entire range of settings for each of the local observers. Especially, it is applied to show non-local behavior of a six-qubit mixture of Greenberger-Horne-Zeilinger…
Bell measurements, entailing the projection onto one of the Bell states, play a key role in quantum information and communication, where the outcome of a variety of protocols crucially depends on the success probability of such…
We study the compatibility of measurements on finite-dimensional compact convex state space in the framework of general probabilistic theory. Our main emphasis is on formulation of necessary and sufficient conditions for two-outcome…
In a recent article [Phys. Rev. A 111, 022204 (2025)], Genovese and Piacentini analyzed recent experiments measuring what they call "the entire Bell-CHSH parameter". They claimed those experiments may have implications for interpreting…
We consider dynamics of hidden variables for measurements in a generalized bell-type model for a single spin using natural assumptions. The evolution of the system, which can be expressed as dynamic chaos is studied. The equilibrium state…
We introduce Bell inequalities based on covariance, one of the most common measures of correlation. Explicit examples are discussed, and violations in quantum theory are demonstrated. A crucial feature of these covariance Bell inequalities…
In randomized experiments, treatment and control groups should be roughly the same--balanced--in their distributions of pretreatment variables. But how nearly so? Can descriptive comparisons meaningfully be paired with significance tests?…