Lectures on entanglement in quantum field theory

Casini, Horacio; Huerta, Marina

doi:10.48550/arxiv.2201.13310

Cited by 10 publications

(16 citation statements)

References 99 publications

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“…Theories with gauge symmetries including quantum gravity do not always admit local gauge-invariant operators and therefore the gauge-invariant Hilbert space does not admit a natural tensor product structure. For gauge theories, this issue was discussed in [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and has been summarized recently in [17]. This lack of factorization of the Hilbert space is due to the presence of a centre of the algebra of operators.…”

Section: Introductionmentioning

confidence: 99%

Entanglement entropy of gravitational edge modes

David

Mukherjee

2022

J. High Energ. Phys.

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We consider the linearised graviton in 4d Minkowski space and decompose it into tensor spherical harmonics and fix the gauge. The Gauss law of gravity implies that certain radial components of the Riemann tensor of the graviton on the sphere labels the superselection sectors for the graviton. We show that among these 6 normal components of the Riemann tensor, 2 are related locally to the algebra of gauge-invariant operators in the sphere. From the two-point function of these components of the Riemann tensor on S2 we compute the logarithmic coefficient of the entanglement entropy of these superselection sectors across a spherical entangling surface. For sectors labelled by each of the two components of the Riemann tensor these coefficients are equal and their total contribution is given by $$ -\frac{16}{3} $$ − 16 3 . We observe that this coefficient coincides with that extracted from the edge partition function of the massless spin-2 field on the 4-sphere when written in terms of its Harish-Chandra character. As a preliminary step, we also evaluate the logarithmic coefficient of the entanglement entropy from the superselection sectors labelled by the radial component of the electric field of the U(1) theory in even d dimensions. We show that this agrees with the corresponding coefficient of the edge Harish-Chandra character of the massless spin-1 field on Sd.

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Section: Introductionmentioning

confidence: 99%

Entanglement entropy of gravitational edge modes

David

Mukherjee

2022

J. High Energ. Phys.

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“…We quote here the pioneering work by [21,22,23,24,25] who have been able to show, by using the techniques of the Algebraic Quantum Field Theory, that even free fields lead to a violation of the CHSH inequality. This important result is taken as a strong confirmation of the fact that the phenomenon of entanglement in Quantum Field Theory is believed to be more severe than in Quantum Mechanics, a property often underlined in the extensive literature on the so-called entanglement entropy, a fundamental quantity in order to quantify the degree of entanglement of a very large class of systems, see [26,27,28,29] for recent overview on this matter.…”

Section: Introductionmentioning

confidence: 70%

Remarks on the Clauser-Horne-Shimony-Holt inequality in relativistic quantum field theory

Peruzzo¹,

Sorella²

2022

Preprint

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We present an investigation of the CHSH inequality within a relativistic quantum field theory model built up with a pair of free massive scalar fields (ϕA, ϕB) where, as it is customary, the indices (A, B) refer to Alice and Bob, respectively. A set of bounded Hermitian operators is introduced by making use of the Weyl operators. A CHSH type correlator is constructed and evaluated in the Fock vacuum by means of the canonical quantization. Although the observed violation of the CHSH inequality turns out to be rather small as compared to Tsirelson's bound of Quantum Mechanics, the model can be employed for the study of Bell's inequalities in the more physical case of gauge theories such as: the Higgs models, for which local BRST invariant operators describing both the massive gauge boson as well as the Higgs particle have been devised. These operators can be naturally exponentiated, leading to BRST invariant type of Weyl operators useful to analyze Bell's inequalities within an invariant BRST environment.

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“…Entanglement has become an increasingly valuable probe of fundamental physics. It can reveal the structure of quantum field theories and states of matter in flat space [71]. In curved space times, it is central to our understanding of black holes [86][87][88] and particle production [89].…”

Section: Detector Entanglementmentioning

confidence: 99%

“…Famously, the entanglement entropy of the fields on a finite region is expected to be proportional to the area for the quantum vacuum [69,70] and the volume for a generic excited state (see e.g. [71] for review). While the entanglement entropy is not a quantity we can easily measure (or calculate), naturally one would like to understand if the non-Gaussian signature of the quantum vacuum state is related.…”

Section: Introductionmentioning

confidence: 99%

A Flat Space Analogue for the Quantum Origin of Structure

Green,

Huang

2022

Preprint

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The analytic structure of non-Gaussian correlators in inflationary cosmologies has recently been proposed as a test of the quantum origin of structure in the universe. To further understand this proposal, we explore the analogous equal-time in-in correlators in flat space and show they exhibit the same features as their cosmological counterparts. The quantum vacuum is uniquely identified by in-in correlators with a total energy pole and no additional poles at physical momenta. We tie this behavior directly to the S-matrix and show that poles at physical momenta always arise from scattering of particles present in the initial state. We relate these flat-space in-in correlators to the probability amplitude for exciting multiple Unruh-de Witt detectors. Localizing the detectors in spacetime, through the uncertainty principle, provides the energy and momentum needed to excite the vacuum and explains the connection to cosmological particle production. In addition, the entanglement of these detectors provides a probe of the entangled state of the underlying field and connects the properties of the correlators to the range of entanglement of the detectors.

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Lectures on entanglement in quantum field theory

Cited by 10 publications

References 99 publications

Entanglement entropy of gravitational edge modes

Entanglement entropy of gravitational edge modes

Remarks on the Clauser-Horne-Shimony-Holt inequality in relativistic quantum field theory

A Flat Space Analogue for the Quantum Origin of Structure

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