A bstract The CPT invariant vacuum states of a scalar field in de Sitter space, called α -vacua, are not unique. We explore the α -vacua from the quantum information perspective by a pair of static Unruh-DeWitt (UDW) detectors coupled to a scalar field with either monopole or dipole coupling, which are in time-like zero separation or space-like antipodal separation. The analytical form of the reduced final state of the UDW detector is derived. We study the entanglement harvesting and quantum discord of the reduced state, which characterize the quantum entanglement and quantum correlation of the underlying α -vacua, respectively. Our results imply that the quantum entanglement gravitated by de Sitter gravity behaves quite differently for time-like and space-like separations. It experiences “sudden death” for the former and grows for the latter as the measuring time or the value of α increases. This demonstrates the nonlocal nature of quantum entanglement. For the quantum discord, we find no “sudden death” behavior, and it experiences superhorizon suppression, which explains the superhorizon decoherence in the inflationary universe scenario. Overall, the time-like or space-like quantum entanglement and correlation behave differently on their dependence of α , measuring time and spectral gaps, with details discussed in this work.
A bstract The CPT invariant vacuum states of a scalar field in de Sitter space, called α -vacua, are not unique. We explore the α -vacua from the quantum information perspective by a pair of static Unruh-DeWitt (UDW) detectors coupled to a scalar field with either monopole or dipole coupling, which are in time-like zero separation or space-like antipodal separation. The analytical form of the reduced final state of the UDW detector is derived. We study the entanglement harvesting and quantum discord of the reduced state, which characterize the quantum entanglement and quantum correlation of the underlying α -vacua, respectively. Our results imply that the quantum entanglement gravitated by de Sitter gravity behaves quite differently for time-like and space-like separations. It experiences “sudden death” for the former and grows for the latter as the measuring time or the value of α increases. This demonstrates the nonlocal nature of quantum entanglement. For the quantum discord, we find no “sudden death” behavior, and it experiences superhorizon suppression, which explains the superhorizon decoherence in the inflationary universe scenario. Overall, the time-like or space-like quantum entanglement and correlation behave differently on their dependence of α , measuring time and spectral gaps, with details discussed in this work.
Abstract We examine in (2+1)-dimensional anti-de Sitter (AdS) space the phenomena of entanglement harvesting — the process in which a pair of detectors (two-level atoms) extract entanglement from a quantum field through local interactions with the field. We begin by reviewing the Unruh-DeWitt detector and its interaction with a real scalar field in the vacuum state, as well as the entanglement harvesting protocol in general. We then examine how the entanglement harvested by a pair of such detectors depends on their spacetime trajectory, separation, spacetime curvature, and boundary conditions satisfied by the field. The harvested entanglement is interpreted as an indicator of field entanglement between the localized regions where the detectors interact with the field, and thus this investigation allows us to probe indirectly the entanglement structure of the AdS vacuum. We find an island of separability for specific values of the detectors’ energy gap and separation at intermediate values of the AdS length for which entanglement harvesting is not possible; an analogous phenomena is observed in AdS4, to which we compare and contrast our results. In the process we examine how the transition probability of a single detector, as a proxy for local fluctuations of the field, depends on spacetime curvature, its location in AdS space, and boundary conditions satisfied by the field.
We study correlations between two Unruh--DeWitt detectors coupled to a massless scalar field confined inside a cylindrical cavity through entanglement negativity, mutual information and quantum discord measures. The entanglement negativity follows the free space behavior for small energy gaps and small separation, while it gets enhanced for large energy gap as the off-axis detector reach cavity boundary. The entanglement island, where negativity is nonzero, gets extended for large energy gaps as compared to free space and the detectors can get entangled for large separations when one of them is placed near cavity boundary. In contrast, quantum mutual information and quantum discord remain nonzero over a substantially broader parameter range, including regions in which the negativity has vanished. However, these correlations are suppressed inside the cavity as compared to the free space correlations. Therefore, boundary conditions can selectively reshape the structure of harvested correlations in quantum field theory.
Black holes, as characterized by the Hawking effect and Bekenstein-Hawking entropy, can be treated as a compact object carrying nontrivial quantum information obscured behind the event horizon. This quantum information, while hidden behind the event horizon, can be indirectly probed through the black hole’s interactions with surrounding quantum fields. In this paper, we investigate how the quantum nature of a black-hole influences the correlations harvested by a pair of static Unruh-DeWitt (UDW) detectors. To provide a comprehensive analysis, we employ various correlation measures: concurrence, quantum discord, and the violation of Bell’s inequality, thereby shedding light on the quantum nature of the black hole as perceived by local probes. By treating the black hole as a tidally deformable thermal body under the quantum fluctuation of the mediator fields, as observed by Goldberger and Rothstein [; ] and Biggs and Maldacena [], we employ a post-Newtonian effective field theory (PN-EFT) to derive the final states of the two UDW probes analytically. A key advantage of our approach is the ability to analytically derive all these correlation measures without encountering the complicated Matsubara sum of infinite thermal poles, as in the conventional approach based on quantum fields in curved spacetime. By tuning the relative strengths in the action of PN-EFT, we can extract the effects of the black hole on the entanglement harvesting, quantum correlation, and nonlocality bound of the UDW probe systems. Furthermore, our PN-EFT approach can be extended in future studies to include backreaction on black holes by accounting for higher-order PN corrections.
A bstract The effect of black holes on entanglement harvesting has been of considerable interest over the past decade. Research involving stationary Unruh-DeWitt (UDW) detectors near a (2+1)-dimensional Bañados-Teitelboim-Zanelli (BTZ) black hole has uncovered phenomena such as entanglement shadows, entanglement amplification through black hole rotation, and differences between bipartite and tripartite entanglement. For a (1+1)-dimensional Schwarzschild black hole, it has been shown that two infalling UDW detectors can harvest entanglement from the scalar quantum vacuum even when separated by an event horizon. In this paper, we calculate the mutual information between two UDW detectors coupled to a massless quantum scalar field, with the detectors starting at rest and falling radially into a non-rotating (2+1)-dimensional BTZ black hole. The trajectory of the detectors includes regions where both detectors are switched on outside of the horizon; where one detector is switched on inside of the horizon while the other switches on outside; and where both detectors switch on inside of the horizon. We investigate different black hole masses, detector energy gaps, widths and temporal separations of the detector switching functions, and field boundary conditions. We find that black holes — even the simplest kind having constant curvature — significantly affect the correlation properties of quantum fields in the vacuum state. These correlations, both outside and inside the horizon, can be mapped out by infalling detectors.
One consequence of the cosmic censorship conjecture is that any topological structure will ultimately collapse to within the horizons of a set of black holes, and as a result, an external classical observer will be unable to probe it. However, a single two-level quantum system [Unruh–DeWitt (UDW) detector] that remains outside of the horizon has been shown to distinguish between a black hole and its associated geon counterpart via its different response rates. Here, we extend this investigation of the quantum vacuum outside of an ℝP2 geon by considering the entanglement structure of the vacuum state of a quantum scalar field in this spacetime, and how this differs from its Banados–Teitelboim–Zanelli (BTZ) black hole counterpart. Employing the entanglement harvesting protocol, where field entanglement is swapped to a pair of UDW detectors, we find that the classically hidden topology of the geon can have an appreciable difference in the amount of entanglement harvested in the two spacetimes for sufficiently small mass. In this regime, we find that detectors with a small energy gap harvest more entanglement in the BTZ spacetime; however, as the energy gap increases, the detectors harvest more entanglement in a geon spacetime. The energy gap at the crossover is dependent on the black hole mass, occurring at lower values for lower masses. This also impacts the size of the entanglement shadow, the region near the horizon where the detectors cannot harvest entanglement. Small gap detectors experience a larger entanglement shadow in a geon spacetime, whereas for large gap detectors, the shadow is larger in a BTZ spacetime.
This thesis is focused on using a pair of Unruh-DeWitt detectors, which interact locally with a quantum field, to gain information about properties of the field and the underlying spacetime. \n \nFirst, we consider a massless scalar field with a bandlimit, a hard ultraviolet cutoff. We show that that when UDW detectors interact with a bandlimited field, they are able to become entangled over larger distances then would be expected in the case of no cutoff. The bandlimit introduces some non locality into the interaction, which boosts the nonlocal correlations between the detectors. This boost in entanglement could, in principle, be used to put a lower bound . \n \nThen we study the affect of a quantum controlled switch to the entanglement harvesting protocol. This switch will control when the detectors interact with the quantum scalar field and can allow for them to each couple to the field in a superposition of two times. We show that when a detector interacts with a field at a superposition of times, its transition probability is reduced compared to what it interacted at a mixture of times. This in turn increases the entanglement harvested by a pair of detectors, which can even violate no-go theorems. \n \nNext, we turn our attention to (2+1)-dimensional AdS spacetime. We map out a large amount of the parameter space, tuning both detector and spacetime properties. Most interestingly, we find an "island of seprability" in the parameter space, which occurs at a relatively small Ads length. When the detectors' properties fall in the "island of seprablity", they cannot become entangled through local interactions with the field; however for a good range of parameters around the island, they can. \n \nWe then apply the entanglement harvesting protocol to a black hole spacetime, specifically the BTZ black hole. We find an entanglement "death zone" which marks the point where entanglement harvesting is no longer possible as two detectors with fixed proper separation approach the horizon. \n \nFinally, we make a change to the detector model itself. We consider the the center of mass degree of freedom of the detectors to be quantum, and so will it coherently delocalize over the course of the interaction with the quantum field. We find that this delocalization inhibits entanglement harvesting, and it is only in the limit of very heavy and very sharply localized detectors that we recover the case of a pair of UDW detectors classical center center of mass.