Geometric quantum states beyond the AdS/CFT correspondence

We characterize the quantum states dual to entanglement wedges in arbitrary spacetimes, in settings where the matter entropy can be neglected compared to the geometric entropy. In AdS/CFT, such states obey special entropy inequalities known as the holographic entropy cone. In particular, the mutual information of CFT subregions is monogamous (MMI). We extend this result to arbitrary spacetimes, using a recent proposal for the generalized entanglement wedge <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>e</a:mi><a:mo stretchy="false">(</a:mo><a:mi>a</a:mi><a:mo stretchy="false">)</a:mo></a:math> of a gravitating region <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>a</e:mi></e:math>. Given independent input regions <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>a</g:mi></g:math>, <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>b</i:mi></i:math>, and <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>c</k:mi></k:math>, we prove MMI: <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>Area</m:mi><m:mo stretchy="false">[</m:mo><m:mi>e</m:mi><m:mo stretchy="false">(</m:mo><m:mi>a</m:mi><m:mo stretchy="false">)</m:mo><m:mo stretchy="false">]</m:mo><m:mo>+</m:mo><m:mi>Area</m:mi><m:mo stretchy="false">[</m:mo><m:mi>e</m:mi><m:mo stretchy="false">(</m:mo><m:mi>b</m:mi><m:mo stretchy="false">)</m:mo><m:mo stretchy="false">]</m:mo><m:mo>+</m:mo><m:mi>Area</m:mi><m:mo stretchy="false">[</m:mo><m:mi>e</m:mi><m:mo stretchy="false">(</m:mo><m:mi>c</m:mi><m:mo stretchy="false">)</m:mo><m:mo stretchy="false">]</m:mo><m:mo>−</m:mo><m:mi>Area</m:mi><m:mo stretchy="false">[</m:mo><m:mi>e</m:mi><m:mo stretchy="false">(</m:mo><m:mi>a</m:mi><m:mi>b</m:mi><m:mo stretchy="false">)</m:mo><m:mo stretchy="false">]</m:mo><m:mo>−</m:mo><m:mspace linebreak="goodbreak"/><m:mi>Area</m:mi><m:mo stretchy="false">[</m:mo><m:mi>e</m:mi><m:mo stretchy="false">(</m:mo><m:mi>b</m:mi><m:mi>c</m:mi><m:mo stretchy="false">)</m:mo><m:mo stretchy="false">]</m:mo><m:mo>−</m:mo><m:mi>Area</m:mi><m:mo stretchy="false">[</m:mo><m:mi>e</m:mi><m:mo stretchy="false">(</m:mo><m:mi>c</m:mi><m:mi>a</m:mi><m:mo stretchy="false">)</m:mo><m:mo stretchy="false">]</m:mo><m:mo>+</m:mo><m:mi>Area</m:mi><m:mo stretchy="false">[</m:mo><m:mi>e</m:mi><m:mo stretchy="false">(</m:mo><m:mi>a</m:mi><m:mi>b</m:mi><m:mi>c</m:mi><m:mo stretchy="false">)</m:mo><m:mo stretchy="false">]</m:mo><m:mo>≤</m:mo><m:mn>0</m:mn></m:math>. We expect that the full holographic entropy cone can be extended to arbitrary spacetimes using similar methods. Published by the American Physical Society 2024