I know for a pure state $\rho$, if its subsystems are mixed then $\rho$ is entangled.
Is the result true if $\rho$ is mixed state?
Is the above law generalized for a $n$-qubit state?
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What is true is p is a mixed state? and what do you mean by entanglement of purity? – FDGod Jan 29 '24 at 17:04
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The first sentence is about a pure state, im asking what if p is a mixed state? – reza Jan 29 '24 at 17:34
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No, entanglement entropy is only reliable as an entanglement quantifier for pure states. You can see it easily considering what it gives for $\frac{1}{\sqrt2}(|00\rangle+|11\rangle)$ and $\frac12(|00\rangle\!\langle00|+|11\rangle\!\langle 11|)$. Both give the same reduced states, but clearly have entirely different entanglement properties. See also this related answer on physics.SE.
glS
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