Von Neumann entropy

Summary

The von Neumann entropy of a density matrix $\rho$ is $S(\rho) = -\tr(\rho \log \rho)$, the Shannon entropy of the eigenvalues of $\rho$. It measures how mixed a quantum state is: it vanishes exactly on pure states and is largest for the maximally mixed state. It is the quantum analogue of Shannon entropy and the basic quantity of quantum information theory. For a pure bipartite state, the entropy of either reduced state measures its entanglement.