Interpreting the macroscopic pointer by analysing the elements of reality of a Schrödinger cat

Abstract

We examine Einstein–Podolsky–Rosen’s (EPR) steering nonlocality for two realisable Schrödinger cat-type states where a meso/macroscopic system (called the ‘cat’-system) is entangled with a microscopic spin- system. We follow EPR’s argument and derive the predictions for ‘elements of reality’ that would exist to describe the cat-system, under the assumption of EPR’s local realism. By showing that those predictions cannot be replicated by any local quantum state description of the cat-system, we demonstrate the EPR-steering of the cat-system. For large cat-systems, we find that a local hidden state model is near-satisfied, meaning that a local quantum state description exists (for the cat) whose predictions differ from those of the elements of reality by a vanishingly small amount. For such a local hidden state model, the EPR-steering of the cat vanishes, and the cat-system can be regarded as being in a mixture of ‘dead’ and ‘alive’ states despite it being entangled with the spin system. We therefore propose that a rigorous signature of the Schrödinger cat-type paradox is the EPR-steering of the cat-system and provide two experimental signatures. This leads to a hybrid quantum/classical interpretation of the macroscopic pointer of a measurement device and suggests that many Schrödinger cat-type paradoxes may be explained by microscopic nonlocality.