Macroscopic delayed choice and retrocausality: Quantum eraser, Leggett-Garg, and dimension witness tests with cat states

We propose delayed-choice experiments carried out with macroscopic qubits, realized as macroscopically distinct coherent states |??) and | ??? ??). Quantum superpositions of |??) and | ??? ??) are created via a unitary interaction U(??) based on a nonlinear Hamiltonian, in analogy with polarizing beam splitters used in photonic experiments. Macroscopic delayed-choice experiments give a compelling reason to develop interpretations not allowing macroscopic retrocausality: This would otherwise suggest changes to the macroscopic qubit value based on a future measurement setting ??. We therefore consider weak macroscopic realism (wMR), which for the system at time t specifies a hidden variable ???? to determine the macroscopic qubit value, independently of ??. Using entangled cat states, we demonstrate a quantum eraser where the choice to measure a which-way or wave-type property is delayed. Consistency with wMR is possible, if we interpret the macroscopic qubit value to be determined by ???? without specification of the state at the level of h??. We then demonstrate violations of a delayed-choice Leggett-Garg inequality, and of the Wheeler-Chaves-Lemos-Pienaar dimension witness inequality, for the macroscopic qubits. This negates all two-dimensional nonretrocausal wMR models. However, one can interpret consistently with wMR, thus avoiding conclusions of macroscopic retrocausality, by noting extra dimensions, and that violations require further unitary dynamics U after t. The violations are then explained as failure of deterministic macroscopic realism, which specifies the validity of ???? prior to the dynamics U(??) determining the measurement setting ??. Finally, although there is consistency with wMR for macroscopic observations, Einstein-Podolsky-Rosen???type paradoxes pointing to the incompleteness of quantum mechanics exist at a microscopic level, based on fringe distributions.

Automated summary

This study proposes delayed-choice experiments with macroscopic qubits and investigates the implications of macroscopic retrocausality. The results demonstrate that the retrocausal behavior can be explained and avoided through extra dimensions and additional unitary dynamics. However, Einstein-Podolsky-Rosen type paradoxes pointing to the incompleteness of quantum mechanics still exist at the microscopic level.