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Discarding undesirable measurement results in Bell experiments opens the detection loophole that prevents a conclusive demonstration of nonlocality. As closing the detection loophole represents a major technical challenge for many practical Bell experiments, it is customary to assume the so-called fair sampling assumption (FSA) that, in its original form, states that the collectively postselected statistics are a fair sample of the ideal statistics. Here, we analyze the FSA from the viewpoint of causal inference: We derive a causal structure that must be present in any causal model that faithfully encapsulates the FSA. This provides an easy, intuitive, and unifying approach that includes different accepted forms of the FSA and underlines what is really assumed when using the FSA. We then show that the FSA can not only be applied in scenarios with non-ideal detectors or transmission losses, but also in ideal experiments where only parts of the correlations are postselected, e.g., when the particles' destinations are in a superposition state. Finally, we demonstrate that the FSA is also applicable in multipartite scenarios that test for (genuine) multipartite nonlocality.

Time in quantum mechanics is peculiar: it is an observable that cannot be associated to an Hermitian operator. As a consequence it is impossible to explain dynamics in an isolated system without invoking an external classical clock, a fact that becomes particularly problematic in the context of quantum gravity. An unconventional solution was pioneered by Page and Wootters (PaW) in 1983. PaW showed that dynamics can be an emergent property of the entanglement between two subsystems of a static Universe. In this work we first investigate the possibility to introduce in this framework a Hermitian time operator complement of a clock Hamiltonian having an equally-spaced energy spectrum. An Hermitian operator complement of such Hamiltonian was introduced by Pegg in 1998, who named it "Age". We show here that Age, when introduced in the PaW context, can be interpreted as a proper Hermitian time operator conjugate to a "good" clock Hamiltonian. We therefore show that, still following Pegg's formalism, it is possible to introduce in the PaW framework bounded clock Hamiltonians with an unequally-spaced energy spectrum with rational energy ratios. In this case time is described by a POVM and we demonstrate that Pegg's POVM states provide a consistent dynamical evolution of the system even if they are not orthogonal, and therefore partially un-distinguishables.

We introduce a multi-mode squeezing coefficient to characterize entanglement in $N$-partite continuous-variable systems. The coefficient relates to the squeezing of collective observables in the $2N$-dimensional phase space and can be readily extracted from the covariance matrix. Simple extensions further permit to reveal entanglement within specific partitions of a multipartite system. Applications with nonlinear observables allow for the detection of non-Gaussian entanglement.