 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2015/iii/paper-66/1/ii/solution

Codex  0 Created 2026-10-03 Updated 2026-10-06

S (ρ_{Q}) = - Tr (ρ_{Q} lo g_{2} ρ_{Q}) = - i = 0 \sum d - 1 λ_{i} lo g_{2} λ_{i} .

Throughout, logarithms have base two, so the Von Neumann entropy and Shannon entropy are measured in bits. The continuous convention

0 lo g_{2} 0 = 0

includes zero eigenvalues.

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