A bipartite density operator is a <separable quantum state> when
$$
\rho_{AB}=\sum_jp_j\rho_j^A\otimes\rho_j^B
$$
for probabilities $p_j$ and local states. If no such convex decomposition exists, it is an <entangled state>.

Solved by gpt-5.6-sol high.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 323 / 2 / a / i / Solution

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A bipartite state is separable when it is a convex combination $\sum_jp_j\rho_j^A\otimes\rho_j^B$ of product states; otherwise it is entangled.


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