# Other¶

Note

In Strawberry Fields we use the convention \(\hbar=2\) by default, but other
conventions can also be chosen by setting the global variable `sf.hbar`

at the beginning of a session.
In this document we keep \(\hbar\) explicit.

## Loss channel¶

Loss is implemented by a CPTP map whose Kraus representation is

Definition

Loss is implemented by coupling mode \(\a\) to another bosonic mode \(\hat{b}\) prepared in the vacuum state, by using the following transformation

and then tracing it out. Here, \(T\) is the *energy* transmissivity. For \(T = 0\) the
state is mapped to the vacuum state, and for \(T=1\) one has the identity map.

Tip

*Implemented in Strawberry Fields as a quantum channel by* `strawberryfields.ops.LossChannel`

One useful identity is

In particular \(\mathcal{N}(T)\left\{\ket{0}\bra{0} \right\} = \pr{0}\).

## Thermal loss channel¶

Definition

Thermal loss is implemented by coupling mode \(\a\) to another bosonic mode \(\hat{b}\) prepared in the thermal state \(\ket{\bar{n}}\), by using the following transformation

and then tracing it out. Here, \(T\) is the *energy* transmissivity. For \(T = 0\) the
state is mapped to the thermal state \(\ket{\bar{n}}\) with mean photon number
\(\bar{n}\), and for \(T=1\) one has the identity map.

Tip

*Implemented in Strawberry Fields as a quantum channel by*
`strawberryfields.ops.ThermalLossChannel`

Note that if \(\bar{n}=0\), the thermal loss channel is equivalent to the loss channel.

## Commutation relations¶

A collection of commutation relations between the gates.

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