Loss

Loss can be incorporated through BeamSplitter's sending photons with some probability to extra environment modes. If a physical Interferometer has m modes, we create extra m modes representing lost photons. In reality, these would not be accessible, but we may still keep this information if necessary. This allows to post-select events upon a certain loss pattern, such as finding l (lost) photons in the environment modes.

Conversions

In general, the function to_lossy converts physical m-mode objects into their 2m-modes counterpart fitting the above model. For instance

julia> n=3
m=4

first_modes(n,m)
state = [1, 1, 1, 0]

to_lossy(first_modes(n,m))
state = [1, 1, 1, 0, 0, 0, 0, 0]

# creating a Subset:
Subset(first_modes(n,m))
subset = [1, 2, 3]

# expanding it doesn't change the Subset
to_lossy(Subset(first_modes(n,m)))
subset = [1, 2, 3]

# but it is now of the correct size
to_lossy(Subset(first_modes(n,m))).m
8

Conventions

Each circuit element, such as BeamSplitter and PhaseShift can bear a certain amount of loss. We write it η_loss. It is the transmission amplitude of the beam splitter representing the loss process. Therefore the probability that a photon is not lost is η_loss^2.

Lossy interferometers

The inclusion of loss creates bigger Interferometer's, but half of their modes are not physical. For this reason, we use the subtype LossyInterferometer.

The fields are named in such a way that all computations can be done without changes, as if we now used a 2m*2m lossless interferometer. The physical quantities are labelled accordingly such as m_real and U_physical.

Models implemented

Let us now discuss the various lossy elements available.

• UniformLossInterferometer : This simplest model is one where photons have an identical chance of being lost.
• GeneralLossInterferometer This is a generic model as described in ...
• Lossy circuit elements : When constructing a Circuit from elements, each element has its own loss characteristics. We also introduce lines, representing for instance optical fibers that have no interaction but can still be lossy.

Circuits

When using circuit_elements to construct a lossy interferometer, the loss channel associated to mode i will always be mode m+i. Therefore, doing