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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.