A central principle of consistent histories quantum theory, the requirement that quantum descriptions be based upon a single framework (or family), is employed to show that there is no conflict between consistent histories and a no-hidden-variables theorem of Bell, and Kochen and Specker, contrary to a recent claim by Bassi and Ghirardi. The argument makes use of “truth functionals” defined on ...

Recently we proposed a hybrid architecture for quantum computing based on stationary and flying qubits: the repeat-until-success (RUS) quantum computing scheme. The scheme is largely implementation independent. Despite the incompleteness theorem for optical Bell-state measurements in any linear optics set-up, it allows for the implementation of a deterministic entangling gate between distant qu...

Many seemingly paradoxical effects are known in the predictions for outcomes of measurements made on preand post-selected quantum systems. A class of such effects, which we call “logical preand post-selection paradoxes”, bear a striking resemblance to proofs of the Bell-Kochen-Specker theorem, which suggests that they demonstrate the contextuality of quantum mechanics. Despite the apparent simi...

Many seemingly paradoxical effects are known in the predictions for outcomes of measurements made on preand post-selected quantum systems. A class of such effects, which we call “logical preand post-selection paradoxes”, bear a striking resemblance to proofs of the Bell-Kochen-Specker theorem, which suggests that they demonstrate the contextuality of quantum mechanics. Despite the apparent simi...

The functor taking global elements of Boolean algebras in the topos ShB of sheaves on a complete Boolean algebra B is shown to preserve and reflect injectivity as well as completeness. This is then used to derive a result of Bell on the Boolean Ultrafilter Theorem in B-valued set theory and to prove that (i) the category of complete Boolean algebras and complete homomorphisms has no non-trivial...

The Kochen-Specker theorem shows the incompatibility of noncontextual hidden variable theories with quantum mechanics. Quantum contextuality is a more general concept than quantum non-locality which is quite well tested in experiments using Bell inequalities. Within neutron interferometry we performed an experimental test of the Kochen-Specker theorem with an inequality, which identifies quantu...

where the al , a2 , . . . are positive integers . We show in § 1 that, for "almost all" ~, G(B,,) increases rapidly with n (Theorem 1) . In § 2, we prove that ~ is a Liouville number (i .e . B,, < Bell-1-1 for arbitrary E > 0 and an infinity of 7a) if G(B„) is bounded for all n (Theorem 2) ; and, in fact, there are Liouville numbers with bounded G(B„) . If the denominators a,,+1 are bounded or ...

Stochastic resonance occurs when noise improves how a nonlinear system performs. This paper presents two general stochastic-resonance theorems for threshold neurons that process noisy Bernoulli input sequences. The performance measure is Shannon mutual information. The theorems show that small amounts of independent additive noise can increase the mutual information of threshold neurons if the ...

Usually the ‘hidden variables’ of Bell’s theorem are supposed to describe the pair of Bell particles. Here a semantic shift is proposed, namely to attach the hidden variables to a stochastic medium or field in which the particles move. It appears that under certain conditions one of the premises of Bell’s theorem, namely ‘measurement independence’, is not satisfied for such ‘backgroundbased’ th...

We seem to be surrounded by bell curves—curves more formally known as normal distributions, or Gaussian distributions. All manner of things appear to be distributed normally: people’s heights, sizes of snowflakes, errors in measurements, lifetimes of lightbulbs, IQ scores, weights of loaves of bread, and so on. I argue that the standard explanation for why such quantities are normally distribut...