dq.overlap

overlap(x: ArrayLike, y: ArrayLike) -> Array

Returns the overlap between two quantum states.

The overlap is computed

• as \(\lvert\braket{\psi|\varphi}\rvert^2\) if both arguments are kets \(\ket\psi\) and \(\ket\varphi\),
• as \(\lvert\bra\psi \rho \ket\psi\rvert\) if one argument is a ket \(\ket\psi\) and the other is a density matrix \(\rho\),
• as \(\tr{\rho^\dag\sigma}\) if both arguments are density matrices \(\rho\) and \(\sigma\).

Parameters

• x (array_like of shape (..., n, 1) or (..., n, n)) –

  Ket or density matrix.

• y (array_like of shape (..., n, 1) or (..., n, n)) –

  Ket or density matrix.

Returns

(array of shape (...)) Real-valued overlap.

Examples

>>> fock0 = dq.fock(3, 0)
>>> dq.overlap(fock0, fock0)
Array(1., dtype=float32)
>>> fock01_dm = 0.5 * (dq.fock_dm(3, 0) + dq.fock_dm(3, 1))
>>> dq.overlap(fock0, fock01_dm)
Array(0.5, dtype=float32)