Alladi Ramakrishnan Hall

Quantum Correlations and the Measurement Problem

Guruprasad Kar

Indian Statistical Institute, Kolkata

The transition from classical to quantum mechanics rests on the recognition that the structure of information is not what we thought it was: there are operational, i.e., phenomenal, probabilistic correlations that lie outside the polytope of local correlations. Such correlations cannot be simulated with classical resources, which generate classical correlations represented by the points in a simplex, where the vertices of the simplex represent joint deterministic states that are the common causes of the correlations. The ‘no go’ hidden variable theorems tell us that we can’t shoe-horn phenomenal correlations outside the local polytope into a classical simplex by supposing that something has been left out of the story. The replacement of the classical simplex by the quantum convex set as the structure representing probabilistic correlations is the analogue for quantum mechanics of the replacement of Newton’s Euclidean space and time by Minkowski spacetime in special relativity. The nonclassical features of quantum mechanics, including the irreducible information loss on measurement, are generic features of correlations that lie outside the classical simplex. This paper is an elaboration of these ideas, which have their source in work by Pitowsky (J. Math. Phys. 27:1556, 1986; Math. Program. 50:395, 1991; Phys. Rev. A 77:062109, 2008), Garg and Mermin (Found. Phys. 14:1–39, 1984), Barrett (Phys. Rev. A 75:032304, 2007; Phys. Rev. A 7:022101, 2005) and others, e.g., Brunner et al. (arXiv:​1303.​2849, 2013), but the literature goes back to Boole (An Investigation of the Laws of Thought, Dover, New York, 1951). The final section looks at the measurement problem of quantum mechanics in this context. A large part of the problem is removed by seeing that the inconsistency in reconciling the entangled state at the end of a quantum measurement process with the definiteness of the macroscopic pointer reading and the definiteness of the correlated value of the measured micro-observable depends on a stipulation that is not required by the structure of the quantum possibility space. Replacing this stipulation by an alternative consistent stipulation is the first step to resolving the problem.

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