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If I have a bipartite system of two qubits $A$ and $B$, and the density matrix $\rho$ is separable, how do I decompose it into its separable parts?

That is, give $\rho$, expand it as follows:

$$\rho = \sum_{i=0}^Np_i \ \rho_{i}^A \otimes \rho_{i}^B $$

Where $0 \le p_i \le 1$ and $\rho^{A,\ B}_i$ are density matrices on the two subsystems $A$ and $B $ for some $N$.


Cross-posted on physics.SE

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