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In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the…
One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…
In 1985, Leggett and Garg put forward the concept of macroscopic realism (macrorealism) and, in analogy to Bell's theorem, derived a necessary condition in terms of inequalities, which are now known as the Leggett-Garg inequalities. In this…
We investigate the presence of memory in the sequential measurement statistics of an open quantum system, as witnessed by the departure from the quantum regression theorem (QRT), that is, the possibility to predict multitime probabilities…
Leggett Garg inequalities (LGIs) provide an elegant way for probing the incompatibility between the notion of macrorealism and quantum mechanics. For unitary dynamics, the optimal quantum violation of a LGI is constrained by the L\"uders…
Although approaches for handling missing data from longitudinal studies are well-developed when the patterns of missingness are monotone, fewer methods are available for non-monotone missingness. Moreover, the conventional missing at random…
The study of quantum correlations within relativistic spacetimes, and the consequences of relativistic causality on information processing using such correlations, has gained much attention in recent years. In this paper, we establish a…
According to the dominant view, time in perceptual decision making is used for integrating new sensory evidence. Based on a probabilistic framework, we investigated the alternative hypothesis that time is used for gradually refining an…
Nonlinear quantum dynamics is often invoked in models trying to bridge the gap between the quantum micro-world and the classical macro-world. Such endeavors, however, encounter challenges at the nexus with relativity. In 1989 Nicolas Gisin…
In quantum theory we refer to the probability of finding a particle between positions $x$ and $x+dx$ at the instant $t$, although we have no capacity of predicting exactly when the detection occurs. In this work, first we present an…
We analyze statistical consequences of a conjecture that there exists a fundamental (indivisible) quant of time. We study particle dynamics with discrete time. We show that a quantum-like interference pattern could appear as a statistical…
The no-signaling constraints state that the probability distribution of the outputs of any subset of parties is independent of the inputs of the complementary set; here we re-examine these to see how they arise from relativistic causality.…
Nonlocality and quantum entanglement constitute two special features of quantum systems of paramount importance in quantum information theory (QIT). Essentially regarded as identical or equivalent for many years, they constitute different…
We have developed in the previous works a statistical model of quantum fluctuation based on a chaotic deviation from infinitesimal stationary action which is constrained by the principle of Locality to have a unique exponential distribution…
The dynamics of complex systems, from financial markets to the brain, can be monitored in terms of multiple time series of activity of the constituent units, such as stocks or neurons respectively. While the main focus of time series…
We show how one may test macroscopic local realism where, different from conventional Bell tests, all relevant measurements need only distinguish between two macroscopically distinct states of the system being measured. Here, measurements…
We investigate non-Markovianity measure using two-time correlation functions for open quantum systems. We define non-Markovianity measure as the difference between the exact two-time correlation function and the one obtained in the Markov…
We explore quantum nonlocality in one of the simplest bipartite scenarios. Several new facet-defining Bell inequalities for the {[3 3 3] [3 3 3]} scenario are obtained with their quantum violations analyzed in details. Surprisingly, all…
We provide a general description of the phenomenon of entanglement in bipartite systems, as it manifests in micro and macro physical systems, as well as in human cognitive processes. We do so by observing that when genuine coincidence…
In the two-user Gaussian interference channel with Gaussian inputs and treating interference as noise (TIN), improper complex signals can be beneficial if time-sharing is not allowed or if only the data rates are averaged over several…