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

Abstract

We propose delayed choice experiments carried out with macroscopic qubits, realised as macroscopically-distinct coherent states $|\alpha ⟩$ and $|-\alpha ⟩$. Quantum superpositions of $|\alpha ⟩$ and $|-\alpha ⟩$ are created via a unitary interaction $U(\theta )$ based on a nonlinear Hamiltonian. Macroscopic delayed-choice experiments give a compelling reason to develop interpretations not allowing macroscopic retrocausality (MrC). We therefore consider weak macroscopic realism (wMR), which specifies a hidden variable ${\lambda }_{\theta }$ to determine the macroscopic qubit value (analogous to 'which-way' information), independent of any future measurement setting $\varphi$. Using entangled 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 ${\lambda }_{\theta }$ without specification of the state at the level of $\hslash$, where fringes manifest. We then demonstrate violations of a delayed-choice Leggett-Garg inequality, and of the dimension witness inequality applied to the Wheeler-Chaves-Lemos-Pienaar experiment, where measurements need only distinguish the macroscopic qubit states. This negates all two-dimensional non-retrocausal models, thereby suggesting MrC. However, one can interpret consistently with wMR, thus avoiding MrC, by noting extra dimensions, and by noting that the violations require further unitary dynamics $U$ for each system. The violations are then explained as failure of deterministic macroscopic realism (dMR), which specifies validity of ${\lambda }_{\theta }$ prior to the dynamics $U(\theta )$ determining the measurement setting $\theta$. Finally, although there is consistency with wMR for macroscopic observations, we demonstrate EPR paradoxes at a microscopic level.

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• A macroscopic quantum three-box paradox: finding consistency with weak macroscopic realism
• Quantum observable's reality erasure with spacelike-separated operations
• Violation of Diagonal Non-Invasiveness: A Hallmark of Non-Classical Memory Effects
• Correlating Local Quantum Reality with Causally Disconnected Choices
• Forward-backward stochastic simulations: Q-based model for measurement and Bell-nonlocality consistent with weak local realistic premises