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In the context of Local Operations and Classical Communication (LOCC), given a bipartite mixed state represented as $\rho=\frac{1}{n}\sum_{i=1}^n|\psi_i\rangle\langle\psi_i|$, where $|\psi_i\rangle$ are non-orthogonal pure states (i.e. $\langle\psi_i|\psi_j\rangle\neq0$, for $i\neq j$), what is the maximum amount of information about each individual state $|\psi_i\rangle$ that can be unambiguously obtained?

Any related papers or suggestions are welcome.

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  • $\begingroup$ Please crosslink crossposts $\endgroup$ Commented Mar 6 at 6:36

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None.

What is meaningful is the state $\rho$, not the decomposition $\sum \lvert\psi_i\rangle\langle\psi_i$. There is many different such definitions, and there is no way to distinguish them by any kind of measurement (LOCC or not).

You can only learn information about $\rho$.

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