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dq.wigner 

wigner(
    state: QArrayLike,
    xmax: float = 6.0,
    ymax: float = 6.0,
    npixels: int = 201,
    xvec: ArrayLike | None = None,
    yvec: ArrayLike | None = None,
    hbar: float = 0.5,
) -> tuple[Array, Array, Array]

Compute the Wigner distribution of a ket or density matrix.

The Wigner distribution is computed on a grid of coordinates \((x, y)\).

Parameters:

  • state (qarray-like of shape (..., n, 1) or (..., n, n)) –

    Ket or density matrix.

  • xmax –

    Maximum absolute value of the \(x\) coordinate.

  • ymax –

    Maximum absolute value of the \(y\) coordinate.

  • npixels –

    Number of pixels in each direction.

  • xvec (array-like of shape (nxvec,)) –

    \(x\) coordinates. If None, defaults to xvec = jnp.linspace(-xmax, xmax, npixels).

  • yvec (array-like of shape (nyvec,)) –

    \(y\) coordinates. If None, defaults to yvec = jnp.linspace(-ymax, ymax, npixels).

  • hbar –

    Value of \(\hbar\) in the commutation relation \([\hat{x}, \hat{p}] = i\hbar\). Common choices are 0.5 (default, coherent state \(\ket{\alpha}\) centered at \((\mathrm{Re}(\alpha), \mathrm{Im}(\alpha))\)), 1.0, and 2.0.

Returns:

  • xvec (array of shape (npixels,) or (nxvec,)) –

    \(x\) coordinates, or xvec if specified.

  • yvec (array of shape (npixels,) or (nyvec,)) –

    \(y\) coordinates, or yvec if specified.

  • w (array of shape (..., npixels, npixels) or (..., nyvec, nxvec)) –

    Wigner distribution.

See also