Print the total binary entropy

TBE (bit labels);
shows the sum of the binary entropies of individual qubits specified by bit labels. A binary entropy of the $ i$-th qubit is

$\displaystyle H_b(\varepsilon_i)=-\left(\frac{1+\varepsilon_i}{2}\log_2\frac{1+\varepsilon_i}{2}+\frac{1-\varepsilon_i}{2}\log_2\frac{1-\varepsilon_i}{2}\right),$ (16)

where $ \varepsilon_i$ is the intrinsic polarization of the $ i$-th qubit, which is calculated according to the eigenvalues, $ \lambda_i$ and $ 1-\lambda_i$, of the reduced density operator $ \tilde\rho_i$ of the qubit. In other words, the command shows the total binary entropy

$\displaystyle S_b=\sum_{specified~~i}S_{vN}(\tilde\rho_i),$ (17)

where $ S_{vN}$ denotes the von Neumann entropy.