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 |α and | − α . Quantum superpositions of |α and | − α are created via a unitary interaction U (θ) based on a nonlinear Hamiltonian, in analogy with polarising beam splitters used in photonic experiments. 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 λ θ to determine the macroscopic qubit value (analogous to 'which-way' information), independent of any future measurement setting φ. 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 λ θ without specification of the state at the level of order , 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 conclusions of 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 λ θ prior to the dynamics U (θ) determining the measurement setting θ. Finally, although there is consistency with wMR for macroscopic observations, we demonstrate Einstein-Podolsky-Rosen-type paradoxes at a microscopic level, based on fringe distributions.

A quantum phase-space equivalence leads to hidden causal loops in a model for measurement consistent with macroscopic realism

“…The incompleteness of quantum mechanics to describe the state of the cat system is shown by the reduced variances in x and p for the trajectories conditioned on the final measurement outcome. The objective field model therefore provides a resolution of Einstein-Podolsky-Rosen-type paradoxes that argue for the completion of quantum mechanics, based on the validity of macroscopic realism [42,79,108]. A resolution of similar related paradoxes may also be possible.…”

“…The subtle distinction between weak macroscopic realism and deterministic macroscopic realism is explained in Refs. [42,79,108,116].…”

“…The outcome of the measurement x is either x 1 or x 2 . The macroscopic realism model postulates that the system in the macroscopic state |ψ m can be ascribed a definite value for the final outcome of the amplified measurement, which we call the pointer measurement [42,79,90,91]. The value of λ is then either x 1 or x 2 , indicating the two final possible amplified outcomes.…”