Related papers: High-dimensional Bell test for a continuous variab…
We show that arbitrary functions of continuous variables, e.g. position and momentum, can be used to generate tests that distinguish quantum theory from local hidden variable theories. By optimising these functions, we obtain more robust…
We consider a multiphoton Bell-type inequality to study nonlocality in four-mode continuous variable systems, which goes beyond two-photon states and can be applied to mixed as well as states with fluctuating photon number. We apply the…
Estimation of the high-dimensional banded covariance matrix is widely used in multivariate statistical analysis. To ensure the validity of estimation, we aim to test the hypothesis that the covariance matrix is banded with a certain…
We present an extension to the robust phase estimation protocol, which can identify incorrect results that would otherwise lie outside the expected statistical range. Robust phase estimation is increasingly a method of choice for…
We derive ``Bell inequalities'' in four dimensional phase space and prove the following ``three marginal theorem'' for phase space densities $\rho(\overrightarrow{q},\overrightarrow{p})$, thus settling a long standing conjecture : ``there…
We consider testing the equality of two high-dimensional covariance matrices by carrying out a multi-level thresholding procedure, which is designed to detect sparse and faint differences between the covariances. A novel U-statistic…
We have theoretically investigated the possibility of using any of several continuous-variable Bell-type inequalities - for which the dichotomic measurements are achieved with coarse-grained quadrature (homodyne) measurements - in a…
We propose Bell inequalities for discrete or continuous quantum systems which test the compatibility of quantum physics with an interpretation in terms of deterministic hidden-variable theories. The wave function collapse that occurs in a…
We show that the detection efficiencies required for closing the detection loophole in Bell tests can be significantly lowered using quantum systems of dimension larger than two. We introduce a series of asymmetric Bell tests for which an…
This paper studies the problem of high-dimensional multiple testing and sparse recovery from the perspective of sequential analysis. In this setting, the probability of error is a function of the dimension of the problem. A simple…
In its vast majority entanglement verification is examined either in the complete characterized or totally device independent scenario. The assumptions imposed by these extreme cases are often either too weak or strong for real experiments.…
By extending the usual two-mode squeezing operator $S_{2}=\exp [ i\lambda (Q_{1}P_{2}+Q_{2}P_{1}) ] $ to the three-mode squeezing operator $S_{3}=\exp {i\lambda [ Q_{1}(P_{2}+P_{3}) +Q_{2}(P_{1}+P_{3}) +Q_{3}(P_{1}+P_{2}) ]} $, we obtain…
We propose a whole family of physical states that yield a violation of the Bell CHSH inequality arbitrarily close to its maximum value, when using quadrature phase homodyne detection. This result is based on a new binning process called…
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…
Recent work has shown that the hidden states of large language models contain signals useful for uncertainty estimation and hallucination detection, motivating a growing interest in efficient probe-based approaches. Yet it remains unclear…
When separated measurements on entangled quantum systems are performed, the theory predicts correlations that cannot be explained by any classical mechanism: communication is excluded because the signal should travel faster than light;…
Self-testing was originally introduced as a device-independent method of certification of entangled quantum states and local measurements performed on them. Recently, in [F. Baccari \textit{et al.}, arXiv:2003.02285] the notion of state…
We consider bipartite quantum systems characterized by a continuous angular variable \theta \in [-\pi, \pi[, representing, for instance, the position of a particle on a circle. We show how to reveal non-locality on this type of system using…
We propose a feasible optical setup allowing for a loophole-free Bell test with efficient homodyne detection. A non-gaussian entangled state is generated from a two-mode squeezed vacuum by subtracting a single photon from each mode, using…
In the high dimensional regression analysis when the number of predictors is much larger than the sample size, an important question is to select the important variable which are relevant to the response variable of interest. Variable…