Correlation functions and quantum measures of descendant states

Enrico M. Brehm; Matteo Broccoli

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Correlation functions and quantum measures of descendant states

Enrico M. Brehm, Matteo Broccoli

High Energy Physics - Theory · Submitted 21 Dec 2020

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our results provide a test of the conjectured R\'enyi QNEC and new tools to analyse the holographic description of descendant states at large $c$.

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We discuss a computer implementation of a recursive formula to calculate correlation functions of descendant states in two-dimensional CFT. This allows us to obtain any $N$-point function of vacuum descendants, or to express the correlator as a differential operator acting on the respective primary correlator in case of non-vacuum descendants. With this tool at hand, we then study some entanglement and distinguishability measures between descendant states, namely the R\'enyi entropy, trace square distance and sandwiched R\'enyi divergence. Our results provide a test of the conjectured R\'enyi QNEC and new tools to analyse the holographic description of descendant states at large $c$.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We discuss a computer implementation of a recursive formula to calculate correlation functions of descendant states in two-dimensional CFT.	method 0.51	0.89	0.05	asserted 0.96
s1	This allows us to obtain any $N$-point function of vacuum descendants, or to express the correlator as a differential operator acting on the respective primary correlator in case of non-vacuum descendants.	method 0.79	0.82	0.10	asserted 0.93
s2	With this tool at hand, we then study some entanglement and distinguishability measures between descendant states, namely the R\'enyi entropy, trace square distance and sandwiched R\'enyi divergence.	contribution 0.99	0.91	0.09	asserted 0.99
s3	Our results provide a test of the conjectured R\'enyi QNEC and new tools to analyse the holographic description of descendant states at large $c$.	interpretation 0.72	0.86	0.69	asserted 0.98

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The paper

Original abstract

We discuss a computer implementation of a recursive formula to calculate correlation functions of descendant states in two-dimensional CFT. This allows us to obtain any $N$-point function of vacuum descendants, or to express the correlator as a differential operator acting on the respective primary correlator in case of non-vacuum descendants. With this tool at hand, we then study some entanglement and distinguishability measures between descendant states, namely the R\'enyi entropy, trace square distance and sandwiched R\'enyi divergence. Our results provide a test of the conjectured R\'enyi QNEC and new tools to analyse the holographic description of descendant states at large $c$.

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4 arXiv papers cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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In 2d CFT a detailed study of the entanglement properties of descendants was initiated in [ref] [See [ref] for earlier work on the 2nd Rényi entropy of descendants. ].

Precision tests of bulk entanglement entropy · Introduction · 0.95
Previous studies of SRD in the context of QFT and holography include [ref] .

Proof of Renyi QNEC for free fermions · Discussion · 1.00

What it cites · 41 sentences without a confident label

Uses the method or tool of 5 papers

However, if $ρ_1$ is the reduced density matrix of the theory's vacuum then there is a technique introduced in [ref] to express it in terms of correlation functions.

Constraining Quantum Fields using Modular Theory · Sandwiched Rényi divergence · 0.96
It is possible to define the limiting process [ref]

Relative Entropies in Conformal Field Theory · Relative entropy · 0.89
It is possible to define the limiting process [ref]

Modular Hamiltonian of Excited States in Conformal Field Theory · Relative entropy · 0.89

Compares with 3 papers

The results here agree with those in [ref] when present.

Renyi entanglement entropies of descendant states in critical systems with boundaries: conformal field theory and spin chains · Rényi entanglement entropy · 0.99
Some results of the REE in the Ising and three-states Potts models were already considered in [ref] ; we checked that our code produces the same analytic results studied in these references.

Excited state entanglement in one dimensional quantum critical systems: Extensivity and the role of microscopic details · Rényi entanglement entropy · 1.00
Some results of the REE in the Ising and three-states Potts models were already considered in [ref] ; we checked that our code produces the same analytic results studied in these references.

Entanglement Entropies in Conformal Systems with Boundaries · Rényi entanglement entropy · 1.00

Cites as support 1 paper

In all the examples that we considered, the SRD proved to be a convex function of $x$, providing further evidence to the validity of the Rényi QNEC in two dimensions [ref] for large enough central charge.

A Renyi Quantum Null Energy Condition: Proof for Free Field Theories · Sandwiched Rényi divergence · 0.96

Cites as background 20 papers

The latter is the Quantum Null Energy Condition (QNEC) which follows from the so-called Quantum Focusing Conjecture [ref] .

A Quantum Focussing Conjecture · Sandwiched Rényi divergence · 0.94
It also appears in the context of holography where it can be used to formulate important bulk energy conditions (see e.g. [ref] ).

Tomography from Entanglement · Relative entropy · 0.92
It also appears in the context of holography where it can be used to formulate important bulk energy conditions (see e.g. [ref] ).

Canonical Energy is Quantum Fisher Information · Relative entropy · 0.92

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