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arXiv:2111.09347

The Quantum Eraser Paradox

Colm P. Bracken, Jonte R. Hance, Sabine Hossenfelder

Published Nov 17, 2021• 0 citations
arXivHTMLPDF

Abstract

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.

DOI
10.48550/arxiv.2111.09347

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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.
Delayed-choice and quantum eraser experiments are frequently interpreted as implying retrocausal effects, in which present measurement decisions influence past physical events. This paper develops an Observer-First Interpretation (OFI) in which quantum states are treated as observer-relative informational constructs constrained by evidence accessibility and record availability. Within this framework, delayed-choice phenomena do not involve backward-in-time physical influence, but instead arise from conditional informational updates applied to measurement records that were never globally fixed. Temporal paradoxes emerge only when observer-relative state assignments are illegitimately promoted to observer-independent histories. The proposed interpretation preserves causal ordering, respects relativistic constraints, and reproduces all standard quantum predictions without modifying the formalism of quantum mechanics.
I discuss the delayed choice quantum eraser experiment by drawing an analogy to a Bell-type measurement and giving a straightforward account in standard quantum mechanics. The delayed choice quantum eraser experiment turns out to resemble a Bell-type scenario in which the resolution of the paradox is rather trivial, and so there really is no mystery. At first glance, the experiment suggests that measurements on one part of an entangled photon pair (the idler) can be employed to control whether the measurement outcome of the other part of the photon pair (the signal) produces interference fringes at a screen after being sent through a double slit. Significantly, the choice whether there is interference or not can be made long after the signal photon encounters the screen. The results of the experiment have been alleged to invoke some sort of backwards in time influence. I argue that this issue can be eliminated by taking into proper account the role of the signal photon. Likewise, in the de Broglie–Bohm picture the trajectories of the particle can be given a well-defined description at any instant of time during the experiment. Thus, it is again clear that there is no need to resort to any kind of backwards in time influence. Quanta 2019; 8: 44-56.
I discuss the delayed choice quantum eraser experiment (DCQE) by drawing an analogy to a Bell-type measurement and giving a straightforward account in standard quantum mechanics. The delayed choice quantum eraser experiment turns out to resemble a Bell-type scenario in which the paradox's resolution is rather trivial, and so there really is no mystery. At first glance, the experiment suggests that measurements on one part of an entangled photon pair (the idler) can be employed to control whether the measurement outcome of the other part of the photon pair (the signal) produces interference fringes at a screen after being sent through a double slit. Significantly, the choice whether there is interference or not can be made long after the signal photon encounters the screen. The results of the experiment have been alleged to invoke some sort of 'backwards in time influence'. I argue that this issue can be eliminated by taking into proper account the role of the signal photon. Likewise, in the de Broglie-Bohm picture the particle's trajectories can be given a well-defined description at any instant of time during the experiment. Thus, it is again clear that there is no need to resort to any kind of 'backwards in time influence'.
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 ttt 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 UUU after ttt. 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.
Ever since the proposal of delayed choice quantum erasure and subsequent realization in the experiment by Kim et al., the interpretation and implications of delayed-choice experiments have remained a subject of intense foundational debate. This paper resolves the apparent paradox attached to the experiment using standard quantum mechanics. Using an extended Mach-Zehnder interferometer which captures every operational feature of the original experiment, we show that choosing between which-path and erasure detectors is simply a choice of measurement bases, which does not rewrite a photon's past. Furthermore, by mapping the experiment to a two-way Stern-Gerlach framework, we prove that quantum erasure is an expected result of measuring entangled states, not a physical anomaly. Ultimately, through a pedagogical game, we illustrate that the illusion of retrocausality arises from asking illegitimate questions, and that a forward-in-time description is entirely sufficient to explain the logic.
Abstract The delayed-choice quantum eraser has long been a subject of controversy, and has been looked at as being incomprehensible to having retro-causal effect in time. Here the delayed-choice quantum eraser is theoretically analyzed using standard quantum mechanics. Employing a Mach–Zehnder interferometer, instead of a conventional two-slit interference, brings in surprising clarity. Some common mistakes in interpreting the experiment are pointed out. It is demonstrated that in the delayed mode there is no which-way information present after the particle is registered on the screen or the final detectors, contrary to popular belief. However, it is shown that another kind of path information is present even after the particle is registered in the final detectors. The registered particle can be used to predict the results of certain yet to be made measurements on the which-way detector. This novel correlation can be tested in a careful experiment. It is consequently argued that there is no big mystery in the experiment, and no retro-causal effect whatsoever.