Modular Hamiltonians on the null plane and the Markov property of the vacuum state

Casini, Horacio; Testé, Eduardo; Torroba, Gonzalo

doi:10.1088/1751-8121/aa7eaa

Cited by 142 publications

(272 citation statements)

References 51 publications

(116 reference statements)

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“…In general it is not possible to saturate SSA in the vacuum of a QFT – this is a consequence of the Reeh‐Schlieder theorem. However, one can achieve this when the spatial regions defining the subsystems lie on a null plane . If SSA is saturated for a certain choice of configuration, the density matrix is a quantum Markov state, implying again the structure for

ρ_{scriptA scriptC}

.…”

Section: Discussionmentioning

confidence: 99%

The Holographic Entropy Arrangement

Hubeny

Rangamani

Rota

2019

Fortschritte der Physik

116

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We develop a convenient framework for characterizing multipartite entanglement in composite systems, based on relations between entropies of various subsystems. This continues the program initiated in [1], of using holography to effectively recast the geometric problem into an algebraic one. We prove that, for an arbitrary number of parties, our procedure identifies a finite set of entropic information quantities that we conveniently represent geometrically in the form of an arrangement of hyperplanes. This leads us to define the holographic entropy arrangement, whose algebraic and combinatorial aspects we explore in detail. Using the framework, we derive three new information quantities for four parties, as well as a new infinite family for any number of parties. A natural construct from the arrangement is the holographic entropy polyhedron which captures holographic entropy inequalities describing the physically allowed region of entropy space. We illustrate how to obtain the polyhedron by winnowing down the arrangement through a sieve to pick out candidate sign‐definite information quantities. Comparing the polyhedron with the holographic entropy cone, we find perfect agreement for 4 parties and corroborating evidence for the conjectured 5‐party entropy cone. We work with explicit configurations in arbitrary (time‐dependent) states leading to both simple derivations and an intuitive picture of the entanglement pattern.

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ρ_{scriptA scriptC}

.…”

Section: Discussionmentioning

confidence: 99%

The Holographic Entropy Arrangement

Hubeny

Rangamani

Rota

2019

Fortschritte der Physik

116

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“…Similarly, the stronger statement of non‐negativity of the conditional mutual information, known as strong subadditivity (SSA), is satisfied by all classical probability distributions and quantum density matrices. Since one can think of this property as the monotonicity of correlations under inclusion, its saturation implies a Markov property of the subsystems …”

Section: Introductionmentioning

confidence: 99%

“…Since one can think of this property as the monotonicity of correlations under inclusion, its saturation implies a Markov property of the subsystems. [5,6] However, not all interesting information quantities obey universal bounds: some may satisfy certain inequalities only in one can alternately work directly with the local algebra of observables, thereby circumventing the notion of partitioning of the Hilbert space (which strictly-speaking does not apply). 2 Relative entropy is another quantity which is both finite and meaningful in QFTs.…”

Section: Introductionmentioning

confidence: 99%

Holographic Entropy Relations

Hubeny

Rangamani

Rota

2018

Fortschritte der Physik

127

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We develop a framework for the derivation of new information theoretic quantities which are natural from a holographic perspective. We demonstrate the utility of our techniques by deriving the tripartite information (the quantity associated to monogamy of mutual information) using a set of abstract arguments involving bulk extremal surfaces. Our arguments rely on formal manipulations of surfaces and not on local surgery or explicit computation of entropies through the holographic entanglement entropy prescriptions. As an application, we show how to derive a family of similar information quantities for an arbitrary number of parties. The present work establishes the foundation of a broader program that aims at the understanding of the entanglement structures of geometric states for an arbitrary number of parties. We stress that our method is completely democratic with respect to bulk geometries and is equally valid in static and dynamical situations. While rooted in holography, we expect that our construction will provide a useful characterization of multipartite correlations in quantum field theories.

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“…In shock-wave collisions, QNEC is never saturated in the hydrodynamic regime, but it is saturated in the far-fromequilibrium region, regardless of whether NEC is valid. Reference [40] (see also [41]) conjectures that saturation of QNEC can lead to a simplified expression for (part of) the modular Hamiltonian of a half-space in vacuum. …”

Section: Discussionmentioning

confidence: 99%

Saturation of the quantum null energy condition in far-from-equilibrium systems

et al. 2018

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The quantum null energy condition (QNEC) is a new local energy condition that a general quantum field theory (QFT) is believed to satisfy, relating the classical null energy condition (NEC) to the second functional derivative of the entanglement entropy in the corresponding null direction. We present the first series of explicit computations of QNEC in a strongly coupled QFT, using holography. We consider the vacuum, thermal equilibrium, a homogeneous far-from-equilibrium quench as well as a colliding system that violates NEC. For the vacuum and thermal phase, QNEC is always weaker than NEC. While for the homogeneous quench QNEC is satisfied with a finite gap, we find the interesting result that the colliding system can saturate QNEC, depending on the null direction.

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Modular Hamiltonians on the null plane and the Markov property of the vacuum state

Cited by 142 publications

References 51 publications

The Holographic Entropy Arrangement

The Holographic Entropy Arrangement

Holographic Entropy Relations

Saturation of the quantum null energy condition in far-from-equilibrium systems

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