Classical and Quantum Structures

L. A. Lugiato, A. Gatti, K.I. Petsas

Shashaank Khanna, Matthew F. Pusey, Roger Colbeck

In his seminal paper, Bell [Physics Physique Fizika 1, 195 (1964)] considers the correlations that result from space-like separated measurements on a pair of entangled particles. He uses relativity theory to motivate the Bell causal structure, then shows the existence of quantum correlations that cannot be explained classically within this causal structure. Classical explanations of such quantum correlations are possible in alternative causal structures, for instance, those that allow superluminal causal influences, but, as shown in [New Journal of Physics 17 033002 (2015)], all such alternative explanations require fine tuning (causation without correlation). Here we discuss the existence of spurious quantum correlations --- correlations that look quantum in one causal structure, but have a natural classical explanation in another. More precisely, there are causal structures that admit non-classical quantum correlations, but for which the same correlations have a classical explanation in another causal structure without fine tuning. The realisation in the other causal structure can also be achieved without breaking any natural constraints on the causal structure that follow from relativity theory. However, similarly to non-classical quantum correlations in the Bell causal structure, we find other causal structures with non-classical quantum correlations that do not have a classical causal explanation in any alternative causal structure without fine tuning.

Giuseppe Marmo, G. Scolarici, Alberto Simoni +1 more

According to Dirac, fundamental laws of Classical Mechanics should be recovered by means of an "appropriate limit" of Quantum Mechanics. In the same spirit it is reasonable to enquire about the fundamental geometric structures of Classical Mechanics which will survive the appropriate limit of Quantum Mechanics. This is the case for the symplectic structure. On the contrary, such geometric structures as the metric tensor and the complex structure, which are necessary for the formulation of the Quantum theory, may not survive the Classical limit, being not relevant in the Classical theory. Here we discuss the Classical limit of those geometric structures mainly in the Ehrenfest and Heisenberg pictures, i.e. at the level of observables rather than at the level of states. A brief discussion of the fate of the complex structure in the Quantum-Classical transition in the Schrödinger picture is also mentioned.

L.A. Lugiato, A. Gatti, K.I. Petsas

Ruth E. Kastner, J. Jeknić-Dugić, George Jaroszkiewicz

Shashaank Khanna, Matthew Pusey, Roger Colbeck

The discovery of Bell that there exist quantum correlations that cannot be reproduced classically is one of the most important in the foundations of quantum mechanics, as well as having practical implications. Bell's result was originally proven in a simple bipartite causal structure, but analogous results have also been shown in further causal structures. Here we study the only causal structure with six or fewer nodes in which the question of whether or not there exist quantum correlations that cannot be achieved classically was open. In this causal structure we show that such quantum correlations exist using a method that involves imposing additional restrictions on the correlations. This hence completes the picture of which causal structures of up to six nodes support non-classical quantum correlations. We also provide further illustrations of our method using other causal structures.