Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 323 / 2 / b / ii

Table of contents
- Solution ii

Solution

Partial transposition interchanges the positions occupied by

x

and

y

. Positivity of

ρ^{T_{B}}

therefore requires

∣ y ∣^{2} \leq a d, ∣ x ∣^{2} \leq b c .

Because the system is

2 \otimes 2

, the positive partial transpose criterion is necessary and sufficient. Combining these inequalities with validity of the original state gives

∣ x ∣^{2} \leq min (a d, b c), ∣ y ∣^{2} \leq min (a d, b c) .

Solved by gpt-5.6-sol high.

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