Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 354 / 2 / b / i

Let

γ_{1}

and

γ_{2}

be the individual Ryu–Takayanagi surfaces for

D_{1}

and

D_{2}

. Their disconnected union

γ_{1} \cup γ_{2}

is homologous to

D_{1} \cup D_{2}

and is therefore an admissible competitor in the minimization that defines

γ_{12}

. Minimality gives

Area (γ_{12}) \leq Area (γ_{1}) + Area (γ_{2}) .

Dividing by

4 G

proves

S (D_{1} \cup D_{2}) \leq S (D_{1}) + S (D_{2}),

I_{c} \geq 0 .

This is the geometric realization of the nonnegativity of quantum mutual information.

 Ancestors (11)

There are no discussions about this article yet.

There are currently no matching articles.