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arXiv:2002.06208 · Physical Review Letters

Quantum Temporal Superposition: The Case of Quantum Field Theory

Laura J. Henderson, Alessio Belenchia, Esteban Castro-Ruiz, Costantino Budroni, Magdalena Zych, Časlav Brukner, Robert B. Mann

Published Sep 21, 2020• 55 citations
arXivHTMLPDF

Abstract

Quantum field theory is completely characterized by the field correlations between spacetime points. In turn, some of these can be accessed by locally coupling to the field simple quantum systems, also known as particle detectors. In this letter we consider what happens when a quantum-controlled superposition of detectors at different space-time points is used to probe the correlations of the field. We show that, due to quantum interference effects, two detectors can gain information on field correlations that would not be accessible, otherwise. This has relevant consequences for information theoretic quantities, like entanglement and mutual information harvested from the field. In particular, the quantum control allows for extraction of entanglement in scenarios where this is, otherwise, provably impossible.

DOI
10.1103/physrevlett.125.131602

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•Dec 23, 2008•4 citations
Quantum field theory is completely characterized by the field correlations between spacetime points. In turn, some of these can be accessed by locally coupling to the field simple quantum systems, also known as particle detectors. In this letter we consider what happens when a quantum-controlled superposition of detectors at different space-time points is used to probe the correlations of the field. We show that, due to quantum interference effects, two detectors can gain information on field correlations that would not be accessible, otherwise. This has relevant consequences for information theoretic quantities, like entanglement and mutual information harvested from the field. In particular, the quantum control allows for extraction of entanglement in scenarios where this is, otherwise, provably impossible.
A bstract In this paper, we explore correlation harvesting in quantum superposition, specifically focusing on the entanglement and mutual information extracted by two Unruh-DeWitt detectors interacting with a quantum field in a mass-superposed BTZ black hole spacetime. Our findings reveal that the superposed nature of spacetime induces constructive interference between the field modes that can significantly enhance the entanglement harvesting relative to a single spacetime background. In contrast to entanglement, the mutual information obtained in spacetime superposition is influenced by the proper distance between the two detectors. While the mutual information harvested in a superposed spacetime remains lower than that in a single spacetime when the proper distance between detectors is small, it exceeds that in a single spacetime for specific mass ratios as the distance increases. Notably, we find that both entanglement and mutual information harvesting reach their maxima when the final spacetime superposition state is conditioned to align with the initial spacetime state.
We discuss entanglement harvesting in the context of spacetime superposition, using Unruh-DeWitt (UDW) detectors coupled to a quantum scalar field in a background modeled as a superposition of two quotient Minkowski spaces that are not diffeomorphic to each other, based on a recent investigation [1]. Our analysis shows that the superposed nature of the spacetime induces interference effects that significantly enhance entanglement generation for both twisted and untwisted fields. In particular, the concurrence, which quantifies the harvested entanglement, achieves its maximum when the detector measurement basis for the spacetime matches the initial superposed spacetime state. Notably, for twisted fields, the region of no entanglement deviates substantially from that observed in standard Minkowski space, highlighting the influence of global spacetime structure on quantum correlations.
We consider the entanglement dynamics between two Unruh-DeWitt detectors at rest separated at a distance ddd. This simple model when analyzed properly in quantum field theory shows many interesting facets and helps to dispel some misunderstandings of entanglement dynamics. We find that there is spatial dependence of quantum entanglement in the stable regime due to the phase difference of vacuum fluctuations the two detectors experience, together with the interference of the mutual influences from the backreaction of one detector on the other. When two initially entangled detectors are still outside each other's light cone, the entanglement oscillates in time with an amplitude dependent on spatial separation ddd. When the two detectors begin to have causal contact, an interference pattern of the relative degree of entanglement (compared to those at spatial infinity) develops a parametric dependence on ddd. The detectors separated at those ddd with a stronger relative degree of entanglement enjoy longer disentanglement times. In the cases with weak coupling and large separation, the detectors always disentangle at late times. For sufficiently small ddd, the two detectors can have residual entanglement even if they initially were in a separable state, while for ddd a little larger, there could be transient entanglement created by mutual influences. However, we see no evidence of entanglement creation outside the light cone for initially separable states.
Quantum detection processes in quantum field theory (QFT) must play a key role in the description of quantum-field correlations, such as the appearance of entanglement, and of causal effects. We consider the detection in the case of a simple QFT model with a suitable interaction to exact treatment, consisting of a quantum scalar field coupled linearly to a classical scalar source. We then evaluate the response function to the field quanta of two-level pointlike quantum model detectors, and analyze the effects of the approximation adopted in standard detection theory. We show that the use of the RWA, which characterizes the Glauber detection model, leads in the detector response to nonlocal terms corresponding to an instantaneously spreading of source effects over the whole space. Other detector models, obtained with nonstandard or no application of RWA, give instead local responses to field quanta, apart from source-independent vacuum contribution linked to preexisting correlations of zero-point field.
We consider the entanglement dynamics between two Unruh-DeWitt detectors at rest separated at a distance ddd. This simple model when analyzed properly in quantum field theory shows many interesting facets and helps to dispel some misunderstandings of entanglement dynamics. We find that there is spatial dependence of quantum entanglement in the stable regime due to the phase difference of vacuum fluctuations the two detectors experience, together with the interference of the mutual influences from the backreaction of one detector on the other. When two initially entangled detectors are still outside each other's light cone, the entanglement oscillates in time with an amplitude dependent on spatial separation ddd. When the two detectors begin to have causal contact, an interference pattern of the relative degree of entanglement (compared to those at spatial infinity) develops a parametric dependence on ddd. The detectors separated at those ddd with a stronger relative degree of entanglement enjoy longer disentanglement times. In the cases with weak coupling and large separation, the detectors always disentangle at late times. For sufficiently small ddd, the two detectors can have residual entanglement even if they initially were in a separable state, while for ddd a little larger, there could be transient entanglement created by mutual influences. However, we see no evidence of entanglement creation outside the light cone for initially separable states.