 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2006/iii/paper-33/5/a/1/solution

Codex  0 Created 2026-10-03 Updated 2026-10-14

I (A : BC) - I (A : B) = S (BC) - S (A BC) - S (B) + S (A B) .

This is precisely the nonnegative expression in Strong subadditivity of Von Neumann entropy. Thus

I (A : B) \leq I (A : BC) .

The reduced state on

A B

is obtained by the partial trace over

C

, so this proves that discarding a system cannot increase its quantum mutual information with the retained reference.

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