Bipartite Leggett-Garg and macroscopic Bell inequality violations using cat states: distinguishing weak and deterministic macroscopic realism

Abstract: We consider tests of Leggett-Garg's macrorealism and of macroscopic local realism, where for spacelike separated measurements the assumption of macroscopic noninvasive measurability is justified by that of macroscopic locality. We give a mapping between the Bell and Leggett-Garg experiments for microscopic qubits based on spin $1/2$ eigenstates and gedanken experiments for macroscopic qubits based on two macroscopically distinct coherent states (cat states). In this mapping, the unitary rotation of the Stern-Gerlach analyzer is realized by an interaction $H=\Omega\hat{n}^{4}$ where $\hat{n}$ is the number of quanta. By adjusting the time of interaction, one alters the measurement setting. We thus predict violations of Leggett-Garg and Bell inequalities in a macroscopic regime where coarse-grained measurements $\hat{M}$ need only discriminate between two macroscopically distinct coherent states. To interpret the violations, we distinguish between subtly different definitions of macroscopic realism. Deterministic macroscopic local realism (dMR) assumes a definite outcome for the measurement $\hat{M}$ prior to the unitary rotation created by the analyser, and is negated by the violations. Weak macroscopic realism (wMR) assumes a definite outcome for systems prepared in a superposition $\psi_{pointer}$ of two macroscopically-distinct eigenstates of $\hat{M}$, after the unitary rotation. We find that wMR can be viewed as consistent with the violations. A model is presented, in which wMR holds, and for which the macroscopic violations emerge over the course of the unitary dynamics. Finally, we point out an EPR-type paradox, that a weak macro-realistic description for the system prior to the measurement $\hat{M}$ is inconsistent with the completeness of quantum mechanics.