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 $H(\mathrm{Im}\alpha ,\mathrm{Re}\alpha )$ corresponding to the harmonic oscillator state rho given in the number basis:

$$H(\rho ,\alpha ,z)=\frac{1}{\pi }⟨\alpha ,z|\rho |\alpha ,z⟩$$

z is the optional squeezing parameter for the reference state: $|\alpha ,z⟩:=D(\alpha )S(z)|0⟩$. The integral of $H(\alpha )$ over $\alpha$ is normalized to unity.

If alpha is None it is set to a 2d grid of points with the resolution and limits set by res and lim. In addition to H, the 1d x and y coordinate vectors of the grid are returned.