# sf.ops.MeasureX¶

MeasureX = <strawberryfields.ops.MeasureHomodyne object>

Performs a homodyne measurement, measures one quadrature of a mode.

• Position basis measurement: $$\phi = 0$$ (also accessible via the shortcut variable MeasureX).

• Momentum basis measurement: $$\phi = \pi/2$$. (also accessible via the shortcut variable MeasureP)

The measured mode is reset to the vacuum state.

Parameters
• phi (float) – measurement angle $$\phi$$

• select (None, float) – (Optional) desired values of measurement result. Allows the post-selection of specific measurement results instead of randomly sampling.

Definition

Homodyne measurement is a Gaussian projective measurement given by projecting the state onto the states

$\ket{x_\phi}\bra{x_\phi},$

defined as eigenstates of the Hermitian operator

$\hat{x}_\phi = \cos(\phi) \hat{x} + \sin(\phi)\hat{p}.$

In the Gaussian backend, this is done by projecting onto finitely squeezed states approximating the $$x$$ and $$p$$ eigenstates. Due to the finite squeezing approximation, this results in a measurement variance of $$\sigma_H^2$$, where $$\sigma_H=2\times 10^{-4}$$.

In the Fock backends, this is done by using Hermite polynomials to calculate the $$\x_\phi$$ probability distribution over a specific range and number of bins, before taking a random sample.

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