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arXiv:2109.12465 · Physical Review A

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

Manushan Thenabadu, M. D. Reid

Published Jun 8, 2022• 9 citations
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Abstract

We propose delayed-choice experiments carried out with macroscopic qubits, realized as macroscopically distinct coherent states $|\ensuremath{\alpha}\ensuremath{\rangle}$ and $|\ensuremath{-}\ensuremath{\alpha}\ensuremath{\rangle}$. Quantum superpositions of $|\ensuremath{\alpha}\ensuremath{\rangle}$ and $|\ensuremath{-}\ensuremath{\alpha}\ensuremath{\rangle}$ are created via a unitary interaction $U(\ensuremath{\theta})$ 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 $\ensuremath{\phi}$. We therefore consider weak macroscopic realism (wMR), which for the system at time $t$ specifies a hidden variable ${\ensuremath{\lambda}}_{\ensuremath{\theta}}$ to determine the macroscopic qubit value, independently of $\ensuremath{\phi}$. 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 ${\ensuremath{\lambda}}_{\ensuremath{\theta}}$ without specification of the state at the level of $\ensuremath{\hbar}$. 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 ${\ensuremath{\lambda}}_{\ensuremath{\theta}}$ prior to the dynamics $U(\ensuremath{\theta})$ determining the measurement setting $\ensuremath{\theta}$. 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.

DOI
10.1103/physreva.105.062209

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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 Bell locality. We give a mapping between the Bell and Leggett-Garg experiments for microscopic qubits based on spin-1/21/21/2 eigenstates and gedanken experiments for macroscopic qubits based on two macroscopically distinct coherent states $|\ensuremath{\alpha}\ensuremath{\rangle}$ and $|\ensuremath{-}\ensuremath{\alpha}\ensuremath{\rangle}$ (as $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$). In this mapping, the unitary rotation ${U}_{\ensuremath{\theta}}$ of the Stern-Gerlach analyzer or polarizing beam splitter is realized by a local interaction $H=\mathrm{\ensuremath{\Omega}}{\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}}^{4}$ where $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{n}$ is the number of quanta. By adjusting the time of interaction, one alters the measurement setting $\ensuremath{\theta}$. We thus predict violations of Leggett-Garg and Bell inequalities in a macroscopic regime where coarse-grained measurements $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ need only discriminate between two macroscopically distinct coherent states. To interpret the violations, we distinguish between different definitions of macroscopic realism. Deterministic macroscopic local realism (dMR) assumes the system is in a state with a definite outcome ${\ensuremath{\lambda}}_{\ensuremath{\theta}}$ for the measurement $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$ prior to the unitary rotation ${U}_{\ensuremath{\theta}}$, and is negated by the violations. Weak macroscopic realism (wMR) assumes a definite outcome for systems prepared in a superposition ${\ensuremath{\psi}}_{\text{pointer}}$ of two macroscopically distinct eigenstates of $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{M}$, after the unitary rotation ${U}_{\ensuremath{\theta}}$. We find that wMR can be viewed consistently with the violations and with the predictions of quantum mechanics for two tests of wMR. A model is presented in which wMR holds and the macroscopic violations emerge over the course of the unitary dynamics occurring at both sites. Implications for the realism of the micro-macro state generated during a quantum measurement are discussed. Finally, we point out an EPR-type paradox, which demonstrates inconsistency between wMR and the completeness of quantum mechanics at a microscopic level.
The Delayed-Choice Quantum Eraser experiment is commonly interpreted as implying that in quantum mechanics a choice made at one time can influence an earlier event. We here suggest an extension of the experiment that results in a paradox when analysed in a local realist interpretation combined with backward causation (``dynamical retrocausality''). We argue that resolving the paradox requires giving up the idea that, in quantum mechanics, a choice can influence the past in this way, and that it instead requires a violation of Statistical Independence without (what most people think of as) retrocausality. Finally, we propose an implementation of the experiment that we believe to be possible with existing technology. This new experiment can distinguish between different types of hidden-variables theories in a way that Bell-type tests cannot: unlike in a Bell test, the measurement setting here is set by an earlier outcome, which makes the consistency of the backwards influence itself testable. We classify the fixed-point (consistency-enforcing) hidden-variables models of the experiment, which can reproduce quantum mechanics only if the backwards influence has no observable effect.
The delayed-choice thought experiment proposed by Wheeler has been demonstrated over the last several decades for the wave-particle duality of a single photon. The delayed-choice quantum eraser proposed by Scully and Druhl has also been intensively studied for the violation of the cause-effect relation of a single photon as well as a pair of entangled photons in an interferometric system. Here, a coherence interpretation is conducted for the nonlocal realism of the space-like separated photons observed in Phys. Rev. Lett. 84, 1 (2000). As a result, coherence solutions of the observed nonlocal fringes are deterministically derived from coincidence detection-caused selective measurements, where the resulting product-basis superposition becomes the origin of the otherwise quantum mystery of the nonlocal fringes. For this, a fixed sum-phase relation between entangled photons is a prerequisite, which cannot be explained by conventional particle nature-based quantum mechanics.
The violation of a Leggett–Garg inequality confirms the incompatibility between quantum mechanics and the combined premises (called macro-realism) of macroscopic realism (MR) and noninvasive measurability (NIM). Arguments can be given that the incompatibility arises because MR fails for systems in a superposition of macroscopically distinct states—or else, that NIM fails. In this paper, we consider a strong negation of macro-realism, involving superpositions of coherent states, where the NIM premise is replaced by Bell’s locality premise. We follow recent work and propose the validity of a subset of Einstein–Podolsky–Rosen (EPR) and Leggett–Garg premises, referred to as weak macroscopic realism (wMR). In finding consistency with wMR, we identify that the Leggett–Garg inequalities are violated because of failure of both MR and NIM, but also that both are valid in a weaker (less restrictive) sense. Weak MR is distinguished from deterministic macroscopic realism (dMR) by recognizing that a measurement involves a reversible unitary interaction that establishes the measurement setting. Weak MR posits that a predetermined value for the outcome of a measurement can be attributed to the system after the interaction, when the measurement setting is experimentally specified. An extended definition of wMR considers the “element of reality” defined by EPR for system A, where one can predict with certainty the outcome of a measurement on A by performing a measurement on system B. Weak MR posits that this element of reality exists once the unitary interaction determining the measurement setting at B has occurred. We demonstrate compatibility of systems violating Leggett–Garg inequalities with wMR but point out that dMR has been shown to be falsifiable. Other tests of wMR are proposed, the predictions of wMR agreeing with quantum mechanics. Finally, we compare wMR with macro-realism models discussed elsewhere. An argument in favour of wMR is presented: wMR resolves a potential contradiction pointed out by Leggett and Garg between failure of macro-realism and assumptions intrinsic to quantum measurement theory.
The “Delayed-choice quantum eraser” experiment is traditionally interpreted in the popular science mainstream as proof of retrocausality, while in the strict Copenhagen interpretation, it is reduced to fundamentally random post-selection. In this paper, this paradox is completely demystified within the framework of the Topological-Plexor kinematics of the vacuum. It is shown that the macroscopic chronology of events is never violated, and quantum randomness is an illusion. This illusion arises solely from ignoring the hidden fundamental 4D-metric (GAB) and the superluminal phase transfer by a Sine-Gordon soliton. In our discrete model, the impact of the Signal photon on the screen (in the past) generates a topological kink, which propagates along a 1D-chord at a velocity v4D ≫ c and deterministically “reprograms” the spinor phase of the Idler photon on the fly. The subsequent behavior of the Idler photon at the beam splitters (in the future) is not a probabilistic choice, but a rigid mechanical consequence of the Signal photon’s impact coordinate. The introduction of a macroscopic No-Signaling Theorem proves that this mechanism does not violate Special Relativity (SR). The Topological-Plexor paradigm (TPN/PPU) restores absolute causality, eliminates quantum mysticism, and paves the way for describing extreme cosmological states of matter.
We show how one may test macroscopic local realism where, differently from conventional Bell tests, all relevant measurements that lead to a violation of a Bell inequality need only distinguish between two macroscopically distinct states of the system being measured. Here, measurements give macroscopically distinct outcomes for some property of the system and do not resolve microscopically (of order $\ensuremath{\hbar}$). To obtain a quantifiable test, we define NNN-scopic local realism where the outcomes are separated by an amount $\ensuremath{\sim}N$. We show for NNN up to 20 that violations of NNN-scopic local realism are predicted for entangled systems of NNN bosons at each of two sites. We further demonstrate for arbitrarily large $\ensuremath{\alpha}$ the violation of $\ensuremath{\alpha}$-scopic local realism, for entangled superpositions of coherent states with amplitudes $\ensuremath{\sim}\phantom{\rule{1.0pt}{0ex}}\ensuremath{\alpha}$, infinitely separated in phase space, as $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\infty}$. To achieve the Bell violations, the two separated subsystems evolve dynamically according to a local nonlinear unitary interaction. The tests may be understood in two ways. First, they are macroscopic Bell tests involving spacelike separated measurement events, where the choice of measurement setting at each site corresponds to a choice between two different times of local interaction. The interaction may be seen as the unitary stage of a local measurement process. Second, the proposal is a strong version of a Leggett-Garg test of "macrorealism" that uses two trajectories, where the usual assumption of noninvasive measurability as applied to measurements at one site is replaced by that of macroscopic locality. For N=1N=1N=1, tests are feasible and give a way to demonstrate ``no classical trajectories'' without the assumption of noninvasive measurability, using instead that of locality.