Purity is a measure of how much a state is pure.

Suppose $\rho$ is a density matrix. Then purity $p$ is defined as $$ p = \mathrm{tr}(\rho^2). $$ I wonder if we can use purity for separable states? Or is it only used for entangled states?


1 Answer 1


Yes, purity $p=\mathrm{tr}(\rho^2)$ is well-defined for both separable and inseparable $\rho$.

Note that the purity of the state $\rho$ of a system $A$ does not tell us anything about internal entanglement across any particular partitioning $A=A_1A_2$. However, it tells us something about entanglement of $A$ with external systems. Namely, if $p=1$, then $A$ is not entangled with any other system.


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