Let X be an arbitrary nonempty set and a lattice of subsets of X such that φ, X∈ . ( ) is the algebra generated by and ( ) denotes those nonnegative, finite, finitely additive measures μ on ( ). I( ) denotes the subset of ( ) of nontrivial zeroone valued measures. Associated with μ ∈ I( ) (or Iσ ( )) are the outer measures μ′ and μ′′ considered in detail. In addition, measurability conditions a...

It is well known that jointly measurable observables cannot lead to a violation of any Bell inequality--independent of the state and the measurements chosen at the other site. In this Letter we prove the converse: every pair of incompatible quantum observables enables the violation of a Bell inequality and therefore must remain incompatible within any other no-signaling theory. While in the cas...

An error in the proof of data-dependent tail bounds on generalization presented Hellström and Durisi (2020) is identified, a correction proposed. Furthermore, we note that absolute continuity requirements need to be strengthened avoid measurability issues.

Abstract It is well known that in gauge theories, the spin (and orbital angular momentum) of gauge particles is not gauge invariant, although the helicity is; neither are the canonical momentum and canonical angular momentum of charged particles. However, the simple appeal of these concepts has motivated repeated attempts to resurrect them as physical descriptions of gauge systems. In particula...