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arXiv:2505.15716

Detector Based Evaluation of Extractable Entanglement in Flat spacetime

Hiromasa Tajima, Riku Yoshimoto, Nemoto, Ryo, Yuki Osawa

Published May 21, 2025• 0 citations
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Abstract

Entanglement entropy (EE) is widely used to quantify quantum correlations in field theory, with the well-known result in two-dimensional conformal field theory (CFT) predicting a logarithmic divergence with the ultraviolet (UV) cutoff. However, this expression lacks operational meaning: it remains unclear how much of the entanglement is physically extractable via local measurements. In this work, we investigate the operationally accessible entanglement by employing a pair of Unruh-DeWitt detectors, each interacting with complementary regions of a quantum field. We derive an upper bound on the entanglement that can be harvested by such detectors and show that it scales as a double logarithm with respect to the UV cutoff-significantly weaker than the single-logarithmic divergence of the standard CFT result. This work provides an operational perspective on field-theoretic entanglement and sets fundamental limits on its extractability.

DOI
10.48550/arxiv.2505.15716

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Entanglement entropy (EE) is widely used to quantify quantum correlations in field theory, with the well-known result in two-dimensional conformal field theory (CFT) predicting a logarithmic divergence with the ultraviolet (UV) cutoff. However, this expression lacks operational meaning: it remains unclear how much of the entanglement is physically extractable via local measurements. In this work, we investigate the operationally accessible entanglement by employing a pair of Unruh-DeWitt detectors, each interacting with complementary regions of a quantum field. We derive an upper bound on the entanglement that can be harvested by such detectors and show that it scales as a double logarithm with respect to the UV cutoff-significantly weaker than the single-logarithmic divergence of the standard CFT result. This work provides an operational perspective on field-theoretic entanglement and sets fundamental limits on its extractability.
We analyze correlations between pairs of detectors quadratically coupled to real and complex scalar bosonic fields in 3+1 dimensions. This is a first step toward studying the entanglement structure of the fermionic vacuum through the entanglement harvesting protocol. We find that, while a single quadratically coupled Unruh-DeWitt presents no divergences, when one considers pairs of detectors there emerge persistent divergences (not regularizable via smooth switching or smearing) in the entanglement they acquire \nfrom the field. These divergences were not anticipated in previous studies. We characterize the divergences, discuss whether a suitable regularization can allow for fair comparison of the entanglement harvesting ability of the quadratic and the linear couplings, and finally find a UV-safe quantifier of harvested correlations.
We study entanglement harvesting in general ddd-dimensional conformal field theories using pointlike Unruh-DeWitt detectors coupled to scalar primary operators. This extends standard harvesting protocols beyond free fields to interacting conformal theories and arbitrary spatial dimensions. We find that increasing the operator scaling dimension suppresses both negativity and mutual information, reflecting the faster decay of correlations. For holographic CFTs, we show that bulk effective field theory enables a separation between field-harvested and communication-mediated entanglement. We also derive asymptotic, closed-form approximations that agree well with numerical results.
Quantum gravity in a finite region of spacetime is conjectured to be dual to a conformal field theory (CFT) deformed by the irrelevant operator TT[over ¯]. We test this conjecture with entanglement entropy, which is sensitive to ultraviolet physics on the boundary, while also probing the bulk geometry. We find that the entanglement entropy for an entangling surface consisting of two antipodal points on a sphere is finite and precisely matches the Ryu-Takayanagi formula applied to a finite region consistent with the conjecture of McGough et al. We also consider a one-parameter family of conical entropies, which are finite and verify a conjecture due to Dong. Since ultraviolet divergences are local, we conclude that the TT[over ¯] deformation acts as an ultraviolet cutoff on the entanglement entropy. Our results support the conjecture that the TT[over ¯]-deformed CFT is the holographic dual of a finite region of spacetime.
We analyze correlations between pairs of particle detectors quadratically coupled to a real scalar field. We find that, while a single quadratically coupled detector presents no divergences, when one considers pairs of detectors, there emerge unanticipated persistent divergences (not regularizable via smooth switching or smearing) in the entanglement they acquire from the field. We have characterized such divergences, discussed whether a suitable regularization can allow for fair comparison of the entanglement harvesting ability of the quadratic and the linear couplings, and finally found a UV-safe quantifier of harvested correlations. Our results are relevant to future studies of the entanglement structure of the fermionic vacuum.
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.
A bstract The entanglement entropy of spacetime regions A in odd-dimensional conformal field theories (CFTs) contains a universal constant term, (−1)d−12 F(A) {\left(-1\right)}^{\frac{d-1}{2}}\ F(A) (−1)2d−1​ F(A) − 1 d − 1 2 F A . This quantity can be robustly defined by considering the mutual information of pairs of slightly deformed versions of A . In the case of general three-dimensional CFTs, F ( A ) is positive definite and bounded below by the round disk result, F ( A ) ≥ F 0 ≡ F ( ∂A = 𝕊 1 ). Additionally, strong evidence has been provided that for every region A , F ( A ) /F 0 is maximized, within the space of CFT 3 ’s, by the free scalar field result. In this paper we show that while F ( A ) remains a local minimum around F 0 ≡ F ( ∂A = 𝕊 3 ) for small deformations of the spherical entangling surface, it can take values of arbitrarily large magnitude with either sign for more general regions, and hence it is neither upper- nor lower-bounded in general CFT 5 ’s. We argue that an analogous conjecture regarding the extremization of F ( A ) /F 0 for general regions within the space of theories fails in d = 5. We instead analyze the viability of the weaker bound, F ϵ /F 0 ≤ F ϵ /F 0 | free scalar , ∀CFT 5 for general small geometric deformations of the spherical entangling surface. This is equivalent to a general constraint involving the stress-tensor two-point function C T and the Euclidean partition function on the sphere, namely, C T /F 0 ≤ C T /F 0 | free scalar ≈ 0 . 314, which we show to hold for all known CFT 5 ’s. We also comment on possible extensions of this result to higher dimensions.