Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 323 / 2 / i

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- Solution i

Solution

A bipartite density operator is a separable quantum state when it has a convex combination decomposition

ρ_{A B} = \sum_{r} q_{r} ρ_{r}^{A} \otimes ρ_{r}^{B}, q_{r} \geq 0, \sum_{r} q_{r} = 1,

into product states. A state for which no such decomposition exists is an entangled state.

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