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Alice's quantum system $\rho$ lives in Hilbert space $H^A$. Bob's quantum system $\sigma$ lives in Hilbert space $H^B$. Say, I can represent the their overall state as a pure state $\psi$ that lives in $H^A\bigotimes H^B $. Does this imply that Alice and Bob's quantum states are maximally entangled with each other? My line of reasoning was that Alice and Bob's states cannot be correlated/entangled with any other quantum state. Otherwise, you could not write the overall state as a pure state. This is strikingly similar to the principle of monogamy of (maximal) entanglement. Any sense here in saying their states must be maximally entangled?

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No. Alice's and Bob's state could, for instance, be equally well in a product state.

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  • $\begingroup$ Is the statement that if the overall state is a pure state, then neither Alice's nor Bob's state can have any correlations/etanglement with any other state? $\endgroup$ – IanDsouza Dec 18 '16 at 2:58
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    $\begingroup$ Yes. (Nor their joint state.) $\endgroup$ – Norbert Schuch Dec 18 '16 at 3:02

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