Measurements

Note

In the Strawberry Fields we use the convention \(\hbar=2\) by default, but other conventions can also be chosen on engine initialization. In this document we keep \(\hbar\) explicit.

Homodyne measurement

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

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

Tip

Implemented in Strawberry Fields as a measurement operator by strawberryfields.ops.MeasureHomodyne

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.

Heterodyne measurement

Warning

The heterodyne measurement can only be performed in the Gaussian backend.

Definition

Heterodyne measurement is a Gaussian projective measurement given by projecting the state onto the coherent states,

\[\frac{1}{\pi} \ket{\alpha}\bra{\alpha}\]

Tip

Implemented in Strawberry Fields as a measurement operator by strawberryfields.ops.MeasureHeterodyne

Photon counting measurement

Warning

Photon counting is available in the Gaussian backend, but the state of the circuit is not updated after measurement (since it would be non-Gaussian).

Definition

Photon counting is a non-Gaussian projective measurement given by

\[\ket{n_i}\bra{n_i}\]

Tip

Implemented in Strawberry Fields as a measurement operator by strawberryfields.ops.MeasureFock