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dq.norm

norm(x: ArrayLike) -> Array

Returns the norm of a ket, bra or density matrix.

For a ket or a bra, the returned norm is \(\sqrt{\braket{\psi|\psi}}\). For a density matrix, it is \(\tr{\rho}\).

Parameters

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

    Ket, bra or density matrix.

Returns

(array of shape (...)) Real-valued norm of x.

Raises

  • ValueError

    If x is not a ket, bra or density matrix.

Examples

For a ket:

>>> psi = dq.fock(4, 0) + dq.fock(4, 1)
>>> dq.norm(psi)
Array(1.414, dtype=float32)

For a density matrix:

>>> rho = dq.fock_dm(4, 0) + dq.fock_dm(4, 1) + dq.fock_dm(4, 2)
>>> dq.norm(rho)
Array(3., dtype=float32)