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Weak versus deterministic macroscopic realism

M. D. Reid, M. Thenabadu

Abstract: We construct a mapping of Bell and bipartite Leggett-Garg experiments for microscopic qubits onto a gedanken experiment for macroscopic qubits based on two macroscopically distinct coherent states. This provides an unusual situation where the dichotomic measurements (and associated hidden variables) involved in the Bell tests need only discriminate between two macroscopically distinct states of a system i.e. correspond to coarse-grained measurements that do not specify values to a level of precision of order $\sim\hbar$. Violations of macro-realism and macroscopic local realism are predicted. We show how one may obtain consistency with a weak form of macroscopic realism (wMR): that for a system prepared in a superposition of macroscopically distinct pointer eigenstates, the outcome of the coarse-grained pointer measurement $\hat{M}$ is predetermined. Macroscopic realism does not however hold in a deterministic fashion, where one assumes the predetermination of outcomes prior to the unitary rotations that define the choice of measurement setting in the Bell experiment. We illustrate an analogy with the Einstein-Podolsky-Rosen (EPR) argument, showing how wMR can be regarded as inconsistent with the completeness of quantum mechanics.

Submitted to arXiv on 23 Jan. 2021