Abstract
We show how one can be led from considerations of quantum steering to Bell's theorem. We begin with Einstein's demonstration that, assuming local realism, quantum states must be in a many-to-one ("incomplete") relationship with the real physical states of the system. We then consider some simple constraints that local realism imposes on any such incomplete model of physical reality, and show they are not satisfiable. In particular, we present a very simple demonstration for the absence of a local hidden variable incomplete description of nature by steering to two ensembles, one of which contains a pair of non-orthogonal states. Historically this is not how Bell's theorem arose - there are slight and subtle differences in the arguments - but it could have been.
Highlights
In this paper we attempt a little revisionist history
For our purposes it is only important that the separation hypothesis, together with the assumption of ‘real states of real systems’ implies local realism, it potentially encompasses more
As X5 is the integral of a probability density it must be positive, in the face of this it is clear that the assumption of local realism, upon which the whole discussion is premised, must be false - this is Bell’s Theorem
Summary
In June of 1935 Einstein wrote to Schrodinger [1] bemoaning that the EPR paper [2] ‘buried in the erudition’ the simplicity of the point he was trying to make [3] In this letter he defines completeness of a state description as. In a moment we will emphasize why the choice of different (and incompatible) measurements on A was a necessary part of his argument (and amusingly he points out, contra-EPR, that he ‘doesn’t give a damn’ whether the states ΨB, ΨB are eigenfunctions of observables on B!), but first let’s note that this description of all the possible ensembles achievable in such experiments was subsequently carefully characterized by Schrodinger who, within a year, proved the quantum steering theorem [5, 6]: Theorem 1. We begin by showing that steering between two ensembles of orthogonal states for a qubit can be explained within such a local realistic theory
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