How Einstein and/or Schr\"odinger should have discovered Bell's Theorem in 1936

TL;DR

This paper demonstrates how considerations of quantum steering and local realism could have led Einstein and Schrödinger to discover Bell's theorem in 1936, highlighting a different historical pathway to understanding quantum nonlocality.

Contribution

It provides a novel derivation of Bell's theorem from quantum steering and local realism constraints, predating the original 1964 formulation.

Findings

Quantum steering leads to constraints incompatible with local realism.

A simple demonstration shows the impossibility of local hidden variables with non-orthogonal states.

The approach offers an alternative historical perspective on Bell's theorem's discovery.

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.