qics.quantum.entropy

qics.quantum.entropy(x)

Computes either the classical (Shannon) entropy

\[H(x) = -\sum_{i=1}^n x_i \log(x_i),\]

for nonnegative vector \(x\), or the quantum (von Neumann) entropy

\[S(X) = -\text{tr}[X \log(X)],\]

for positive semidefinite matrix \(X\).

Parameters:

xndarray

If this is a nonnegative array of size (n,) or (n, 1), we compute the classical entropy of \(x\). If this is a symmetric or Hermitian positive semidefinite array of size (n, n), then we compute the quantum entropy of \(X\)

Returns:

float

Classical entropy of \(x\) or quantum entropy of \(X\).