No-Signalling Is Equivalent To Free Choice of Measurements

No-Signalling is a fundamental constraint on the probabilistic predictions made by physical theories. It is usually justified in terms of the constraints imposed by special relativity. However, this justification is not as clear-cut as is usually supposed. We shall give a different perspective on this condition by showing an equivalence between No-Signalling and Lambda Independence, or "free choice of measurements", a condition on hidden-variable theories which is needed to make no-go theorems such as Bell's theorem non-trivial. More precisely, we shall show that a probability table describing measurement outcomes is No-Signalling if and only if it can be realized by a Lambda-Independent hidden-variable theory of a particular canonical form, in which the hidden variables correspond to non-contextual deterministic predictions of measurement outcomes. The key proviso which avoids contradiction with Bell's theorem is that we consider hidden-variable theories with signed probability measures over the hidden variables - i.e. negative probabilities. Negative probabilities have often been discussed in the literature on quantum mechanics. We use a result proved previously in "The Sheaf-theoretic Structure of Locality and Contextuality" by Abramsky and Brandenburger, which shows that they give rise to, and indeed characterize, the entire class of No-Signalling behaviours. In the present paper, we put this result in a broader context, which reveals the surprising consequence that the No-Signalling condition is equivalent to the apparently completely different notion of free choice of measurements.Comment: In Proceedings QPL 2013, arXiv:1412.791

Time asymmetries in quantum cosmology and the searching for boundary conditions to the Wheeler-DeWitt equation

The paper addresses the quantization of minisuperspace cosmological models by studying a possible solution to the problem of time and time asymmetries in quantum cosmology. Since General Relativity does not have a privileged time variable of the newtonian type, it is necessary, in order to have a dynamical evolution, to select a physical clock. This choice yields, in the proposed approach, to the breaking of the so called clock-reversal invariance of the theory which is clearly distinguished from the well known motion-reversal invariance of both classical and quantum mechanics. In the light of this new perspective, the problem of imposing proper boundary conditions on the space of solutions of the Wheeler-DeWitt equation is reformulated. The symmetry-breaking formalism of previous papers is analyzed and a clarification of it is proposed in order to satisfy the requirements of the new interpretation.Comment: 25 pages, 1 figur

A canonical space-time state space model: state and parameter estimation

The maximum likelihood estimation of a dynamic spatiotemporal model is introduced, centred around the inclusion of a prior arbitrary spatiotemporal neighborhood description. The neighborhood description defines a specific parameterization of the state transition matrix, chosen on the basis of prior knowledge about the system. The model used is inspired by the spatiotemporal ARMA (STARMA) model, but the representation used is based on the standard state-space model. The inclusion of the neighborhood into an expectation-maximization based joint state and parameter estimation algorithm allows for accurate characterization of the spatiotemporal model. The process of including the neighborhood, and the effect it has on the maximum likelihood parameter estimate is described and demonstrated in this paper

On the 'Reality' of Observable Properties

This note contains some initial work on attempting to bring recent developments in the foundations of quantum mechanics concerning the nature of the wavefunction within the scope of more logical and structural methods. A first step involves generalising and reformulating a criterion for the reality of the wavefunction proposed by Harrigan & Spekkens, which was central to the PBR theorem. The resulting criterion has several advantages, including the avoidance of certain technical difficulties relating to sets of measure zero. By considering the 'reality' not of the wavefunction but of the observable properties of any ontological physical theory a novel characterisation of non-locality and contextuality is found. Secondly, a careful analysis of preparation independence, one of the key assumptions of the PBR theorem, leads to an analogy with Bell locality, and thence to a proposal to weaken it to an assumption of `no-preparation-signalling' in analogy with no-signalling. This amounts to introducing non-local correlations in the joint ontic state, which is, at least, consistent with the Bell and Kochen-Specker theorems. The question of whether the PBR result can be strengthened to hold under this relaxed assumption is therefore posed.Comment: 8 pages, re-written with new section

Quantum Systems based upon Galois Fields: from Sub-quantum to Super-quantum Correlations

In this talk we describe our recent work on discrete quantum theory based on Galois fields. In particular, we discuss how discrete quantum theory sheds new light on the foundations of quantum theory and we review an explicit model of super-quantum correlations we have constructed in this context. We also discuss the larger questions of the origins and foundations of quantum theory, as well as the relevance of super-quantum theory for the quantum theory of gravity.Comment: 22 pages LaTeX. Uses ws-procs975x65.cls. Contribution to the Proceedings of the Conference in Honour of the 90th Birthday of Freeman Dyson, 26-29 August 2013, Institute of Advanced Studies at the Nanyang Technological University, Singapore. Talk presented by Takeuch

Some Mutant Forms of Quantum Mechanics

We construct a `mutant' form of quantum mechanics on a vector space over the finite Galois field GF(q). We find that the correlations in our model do not violate the Clauser-Horne-Shimony-Holt (CHSH) version of Bell's inequality, despite the fact that the predictions of this discretized quantum mechanics cannot be reproduced with any hidden variable theory. An alternative `mutation' is also suggested.Comment: 5 pages aipproc, 1 pdf figure. Talk presented by Takeuchi at QTRF6, June 11, 2012, V\"axj\"o, Swede

A proposal for a first class conversion formalism based on the symmetries of the Wess-Zumino terms

We propose a new procedure to embed second class systems by introducing Wess-Zumino (WZ) fields in order to unveil hidden symmetries existent in the models. This formalism is based on the direct imposition that the new Hamiltonian must be invariant by gauge-symmetry transformations. An interesting feature in this approach is the possibility to find a representation for the WZ fields in a convenient way, which leads to preserve the gauge symmetry in the original phase space. Consequently, the gauge-invariant Hamiltonian can be written only in terms of the original phase-space variables. In this situation, the WZ variables are only auxiliary tools that permit to reveal the hidden symmetries present in the original second class model. We apply this formalism to important physical models: the reduced-SU(2) Skyrme model, the Chern-Simons-Proca quantum mechanics and the chiral bosons field theory. In all these systems, the gauge-invariant Hamiltonians are derived in a very simple way.Comment: Revised version. Title changed for Gauging by symmetries. To appear in IJMP