Generalized entanglement entropy, charges, and intertwiners

Furuya, Keiichiro; Lashkari, Nima; Ouseph, Shoy

doi:10.1007/jhep08(2020)046

Cited by 4 publications

(5 citation statements)

References 33 publications

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“…A similar observation was discussed in a recent paper [6]. Given a ρ-preserving conditional expectation we can define a measure of the information lost under the conditional expectation [29]. This leads to entropic uncertainty relations that play an important role in the derivation of the Ryu-Takayanagi formula in holography [5,6].…”

Section: Jhep01(2022)170mentioning

confidence: 68%

“…The correctable subalgebra is the subalgebra of operators that commute with V † r V s . 29 We would like to generalize this to arbitrary von Neumann algebras. If there exists no correctable states the correctable subalgebra is empty.…”

Section: Error Correction In Arbitrary Von Neumann Algebramentioning

confidence: 99%

“…(A.56) It is the simplest example of a σ-preserving conditional expectation [29]. The conditional expectations in (A.55) are labelled by density matrices σ on A 2 .…”

Section: Jhep01(2022)170mentioning

confidence: 99%

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Real-space RG, error correction and Petz map

Furuya

Lashkari

Ouseph

2022

J. High Energ. Phys.

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There are two parts to this work: first, we study the error correction properties of the real-space renormalization group (RG). The long-distance operators are the (approximately) correctable operators encoded in the physical algebra of short-distance operators. This is closely related to modeling the holographic map as a quantum error correction code. As opposed to holography, the real-space RG of a many-body quantum system does not have the complementary recovery property. We discuss the role of large N and a large gap in the spectrum of operators in the emergence of complementary recovery.Second, we study the operator algebra exact quantum error correction for any von Neumann algebra. We show that similar to the finite dimensional case, for any error map in between von Neumann algebras the Petz dual of the error map is a recovery map if the inclusion of the correctable subalgebra of operators has finite index.

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Section: Jhep01(2022)170mentioning

confidence: 68%

Section: Error Correction In Arbitrary Von Neumann Algebramentioning

confidence: 99%

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Real-space RG, error correction and Petz map

Furuya

Lashkari

Ouseph

2022

J. High Energ. Phys.

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“…von Neumann entanglement entropy in the LSV background. -In few words, the von Neumann entanglement entropy quantifies the degree of entanglement within a system [33][34][35][36]. Mathematically it is expressed as…”

Section: Boson Pair Production In the Lorentz-violatingmentioning

confidence: 99%

Effect of a critical magnetic field on the control of scalar neutral boson pair production in the context of Lorentz-symmetry violation

Jirón,

Obispo,

Espinoza Loayza

et al. 2024

EPL

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This study investigates the production of neutral scalar boson pairs in static electromagnetic fields resulting from Lorentz-symmetry violation (LSV), with a focus on the parity-even sector of the CPT-even photon sector in the Standard Model Extension (SME). Utilizing a cross-configuration involving inhomogeneous static electric fields and homogeneous static magnetic fields, the analysis of the probability of bosons pair production identifies three different regimes determined by a critical magnetic field. Below the critical value, creation is exponentially suppressed; at the critical value, the number density of created bosons remains constant, and above the critical field, there is exponential amplification. This behavior prompts an additional investigation using von Neumann entanglement entropy to analyze fluctuations in the bosonic vacuum.

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“…In a QFT with a global symmetry the algebra of charge-neutral operators can be enlarged by the generator of the symmetry group on A [24]. The modular operator for the charge-neutral subalgebra has non-trivial centralizers that correspond to ⊕λ r 1 r where 1 r is the identity operator in the irreducible representation r of the symmetry group.…”

Section: Jhep04(2021)189mentioning

confidence: 99%

Modular zero modes and sewing the states of QFT

Lashkari

2021

J. High Energ. Phys.

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We point out an important difference between continuum relativistic quantum field theory (QFT) and lattice models with dramatic consequences for the theory of multi-partite entanglement. On a lattice given a collection of density matrices ρ(1), ρ(2), ⋯, ρ(n) there is no guarantee that there exists an n-partite pure state |Ω〉12⋯n that reduces to these marginals. The state |Ω〉12⋯n exists only if the eigenvalues of the density matrices ρ(i) satisfy certain polygon inequalities. We show that in QFT, as opposed to lattice systems, splitting the space into n non-overlapping regions any collection of local states ω(1), ω(2), ⋯ ω(n) come from the restriction of a global pure state. The reason is that rotating any local state ω(i) by unitary Ui localized in the ith region we come arbitrarily close to any other local state ψ(i). We construct explicit examples of such local unitaries using the cocycle.

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Generalized entanglement entropy, charges, and intertwiners

Cited by 4 publications

References 33 publications

Real-space RG, error correction and Petz map

Real-space RG, error correction and Petz map

Effect of a critical magnetic field on the control of scalar neutral boson pair production in the context of Lorentz-symmetry violation

Modular zero modes and sewing the states of QFT

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