qit.ho.husimi¶
- qit.ho.husimi(rho, alpha=None, z=0, *, res=(40, 40), lim=(- 2, 2, - 2, 2))¶
Husimi probability distribution.
- Parameters
rho (State) – harmonic oscillator state (truncated)
alpha (array[complex]) – displacement parameters of the reference state
z (complex) – squeezing parameter of the reference state
res (tuple[int]) – if
alpha is None: number of points in the alpha grid, (nx, ny)lim (tuple[float]) – if
alpha is None: limits of the alpha grid, (xmin, xmax, ymin, ymax)
- Returns
Husimi distribution H_rho(alpha),
H.shape == alpha.shape- Return type
array[float] [, array[float], array[float]]
Returns the Husimi probability distribution \(H(\im{\alpha}, \re{\alpha})\) corresponding to the harmonic oscillator state rho given in the number basis:
\[H(\rho, \alpha, z) = \frac{1}{\pi} \bra{\alpha, z} \rho \ket{\alpha, z}\]zis the optional squeezing parameter for the reference state: \(\ket{\alpha, z} := D(\alpha) S(z) \ket{0}\). The integral of \(H(\alpha)\) over \(\alpha\) is normalized to unity.If
alphaisNoneit is set to a 2d grid of points with the resolution and limits set byresandlim. In addition toH, the 1d x and y coordinate vectors of the grid are returned.