Null states from large superpositions of two-sided black holes

TL;DR

This paper investigates the linear dependencies among states with simple geometric duals in AdS/CFT, revealing that large superpositions of black hole states can approximate single black hole states, challenging classical geometric intuition.

Contribution

It introduces a framework to analyze linear dependencies between black hole states and derives bounds on fidelities, highlighting the non-linear nature of geometry in quantum gravity.

Findings

Fidelity between certain superpositions and individual states approaches 1 as the number of black holes increases.

States with different topologies can approximate thermofield double states through partial traces.

Linear dependencies exist among states with distinct geometries, impacting the understanding of quantum gravity.

Abstract

A standard insight of the AdS/CFT correspondence is that some aspects of the geometry of a bulk state are encoded in the entanglement structure of its dual boundary state. As entanglement is not a linear quantum observable, this means that geometry in a quantum theory of gravity should likewise not be a linear observable. This allows for linear dependencies between states with distinct geometries. We explore linear dependencies between certain states with simple geometric duals: states made up of $n$ copies of a thermofield double state and the states obtained from this one by permuting the $n$ right hand sides. There are $n!$ such states, all dual to distinct geometries. We derive expressions for the maximum fidelity between one such state and a linear combination of the others, and see that this fidelity approaches 1 as the number $n$ of black holes increases. We also consider the possibility of obtaining a single thermofield double state as the partial trace of a superposition of states whose topology does not connect the two untraced sides. We derive lower bounds for the fidelity between the thermofield double state and such partial traces and comment on the conceptual implications of the existence of such states.