Related papers: Certifiable randomness from temporal correlations
The local position invariance (LPI) is one of the three major pillars of Einstein equivalence principle, ensuring the space-time independence on the outcomes of local experiments. The LPI has been tested by measuring the gravitational…
Unpredictability, or randomness, of the outcomes of measurements made on an entangled state can be certified provided that the statistics violate a Bell inequality. In the standard Bell scenario where each party performs a single…
Developments in the field of Artificial Intelligence (AI), and particularly large language models (LLMs), have created a 'perfect storm' for observing 'sparks' of Artificial General Intelligence (AGI) that are spurious. Like simpler models,…
We develop a nonparametric extension of the sequential generalized likelihood ratio (GLR) test and corresponding time-uniform confidence sequences for the mean of a univariate distribution. By utilizing a geometric interpretation of the GLR…
The Leggett-Garg inequality (LGI) is a powerful tool for distinguishing between quantum and classical properties in studies of macroscopic systems. Applying the LGI to non-Hermitian systems with dissipation presents a fascinating…
We demonstrate violation of objective realism in quantum world using unconstrained weak measurements. Instead of limited Leggett-Garg approach with artificial bounds on the observed values, we assume two identical and indepenent weak…
Bell's inequality is established based on local realism. The violation of Bell's inequality by quantum mechanics implies either locality or realism or both are untenable. Leggett's inequality is derived based on nonlocal realism. The…
It is well known that the dependence structure for jointly Gaussian variables can be fully captured using correlations, and that the conditional dependence structure in the same way can be described using partial correlations. The partial…
Inferring linear dependence between time series is central to our understanding of natural and artificial systems. Unfortunately, the hypothesis tests that are used to determine statistically significant directed or multivariate…
A comprehensive treatment of the quantification of randomness certified device-independently by using the Hardy and Cabello-Liang-Li (CLL) nonlocality relations is provided in the two parties - two measurements per party - two outcomes per…
We present a path analysis of the condition under which the outcomes of previous observation affect the results of the measurements yet to be made. It is shown that this effect, also known as "signalling in time", occurs whenever the…
"Macrorealism" posits that a system possesses definite properties at all times and that we can discover these properties, in principle, without disturbing the system's subsequent behaviour. The Leggett-Garg inequalities are derived under…
We consider tests of Leggett-Garg's macrorealism and of macroscopic local realism, where for spacelike separated measurements the assumption of macroscopic noninvasive measurability is justified by that of macroscopic locality. We give a…
In this paper we provide an experimental illustration of Page and Wootters' quantum time mechanism that is able to describe two-time quantum correlation functions. This allows us to test a Leggett-Garg inequality, showing a violation from…
We propose an experimental programme to test Leggett--Garg-type temporal correlations in single-neuron dynamics. The goal is to distinguish between diffusive (Wiener/cable-equation) models and non-diffusive persistent stochastic models…
Correlations that cannot be reproduced with local variables certify the generation of private randomness. Usually, the violation of a Bell inequality is used to quantify the amount of randomness produced. Here, we show how private…
Separate constituents of extended systems measure proper-times on different world-lines. Relating and comparing proper-time measurements along any two such world-lines requires that common simultaneity be possible, which in turn implies…
Measures of association between cortical regions based on activity signals provide useful information for studying brain functional connectivity. Difficulties occur with signals of electric neuronal activity, where an observed signal is a…
The generation of certifiable randomness is the most fundamental information-theoretic task that meaningfully separates quantum devices from their classical counterparts. We propose a protocol for exponential certified randomness expansion…
We consider the certification of temporal quantum correlations using the pseudo-density matrix (PDM), an extension of the density matrix to the time domain, where negative eigenvalues are key indicators of temporal correlations.…