dq.purity
purity(x: QArrayLike) -> Array
Returns the purity of a ket or density matrix.
For a ket (a pure state), the purity is \(1\). For a density matrix \(\rho\), it is defined by \(\tr{\rho^2}\).
Parameters
-
x
(qarray-like of shape (..., n, 1) or (..., n, n))
–
Ket or density matrix.
Returns
(array of shape (...)) Real-valued purity.
Examples
>>> psi = dq.fock(2, 0)
>>> dq.purity(psi)
Array(1., dtype=float32)
>>> rho = (dq.fock_dm(2, 0) + dq.fock_dm(2, 1)).unit()
>>> dq.purity(rho)
Array(0.5, dtype=float32)