Typical local measurements in generalised probabilistic theories: emergence of quantum bipartite correlations

What singles out quantum mechanics as the fundamental theory of Nature? Here we study local measurements in generalised probabilistic theories (GPTs) and investigate how observational limitations affect the production of correlations. We find that if only a subset of typical local measurements can be made then all the bipartite correlations produced in a GPT can be simulated to a high degree of accuracy by quantum mechanics. Our result makes use of a generalisation of Dvoretzky's theorem for GPTs. The tripartite correlations can go beyond those exhibited by quantum mechanics, however.Comment: 5 pages, 1 figure v2: more details in the proof of the main resul

All multipartite Bell correlation inequalities for two dichotomic observables per site

We construct a set of 2^(2^n) independent Bell correlation inequalities for n-partite systems with two dichotomic observables each, which is complete in the sense that the inequalities are satisfied if and only if the correlations considered allow a local classical model. All these inequalities can be summarized in a single, albeit non-linear inequality. We show that quantum correlations satisfy this condition provided the state has positive partial transpose with respect to any grouping of the n systems into two subsystems. We also provide an efficient algorithm for finding the maximal quantum mechanical violation of each inequality, and show that the maximum is always attained for the generalized GHZ state.Comment: 11 pages, REVTe

Quantum value indefiniteness

The indeterministic outcome of a measurement of an individual quantum is certified by the impossibility of the simultaneous, definite, deterministic pre-existence of all conceivable observables from physical conditions of that quantum alone. We discuss possible interpretations and consequences for quantum oracles.Comment: 19 pages, 2 tables, 2 figures; contribution to PC0

Forward–backward SDEs with distributional coefficients

Forward–backward stochastic differential equations (FBSDEs) have attracted significant attention since they were introduced, due to their wide range of applications, from solving non-linear PDEs to pricing American-type options. Here, we consider two new classes of multidimensional FBSDEs with distributional coefficients (elements of a Sobolev space with negative order). We introduce a suitable notion of solution and show its existence and in certain cases its uniqueness. Moreover we establish a link with PDE theory via a non-linear Feynman–Kac formula. The associated semi-linear parabolic PDE is the same for both FBSDEs, also involves distributional coefficients and has not previously been investigated

Strong solutions of Tsirel’son’s equation in discrete time taking values in compact spaces with semigroup action

Under the assumption that the infinite product of the evolution process converges almost surely, the set of strong solutions is characterized by a compact space T, which may be regarded as the set of possible initial states. More precisely, any strong solution may be represented as the result of a uniquely specified element of T acted by the infinite product of the evolution process