Display the von Neumann entropy

Generally, the von Neumann entropy of a density matrix $\rho$ is defined by

$$S_{vN}(\rho)=-\mathrm{Tr}\rho\log_2\rho.$$ (14)

We use the binary logarithm (base 2) in this software. It is also written by using the eigenvalues $\{\lambda_i\}$ of $\rho$ as

$$S_{vN}(\rho)=-\sum_i\lambda_i\log_2\lambda_i.$$ (15)

This is because a density matrix $\rho$ can be diagonalized by a proper unitary transformation. Such a transformation preserves eigenvalues of $\rho$. A density matrix $\rho$ is an Hermitian matrix and its eigenvalues are non-negative real numbers.

  
The command

SvN;

shows the von Neumann entropy of the current density matrix.

  
The command

SvNRDO(bit labels);

shows the von Neumann entropy of the reduced density operator of the qubits specified by bit labels.