Coincidence Measurements

Coincidence measurements are implemented by BellMeasure. There are three possible types of measurements, one for each basis X, Y, and Z.

BellMeasure is supported by QuantumClifford's apply!, but more importantly, it is supported by mctrajectories, which provides for an easy way to run multiple Monte Carlo simulation trajectories. A successful coincidence measurement lets the simulations continue. A failed coincidence ends the simulations with a reported error.

Measurement results depending on basis

As seen in the code example below, the meaning of the measurements is as follows

Call	Basis & Check	States passed
`BellMeasure(1,_)`	X coincidence	`00`&`01`
`BellMeasure(2,_)`	Y anticoincidence	`00`&`11`
`BellMeasure(3,_)`	Z coincidence	`00`&`10`

For reference, here are the states in different representations

`BPGates` notation	Stabilizer tableaux	Kets	in X basis	in Y basis
`00`	`+XX +ZZ`	`∣00⟩+∣11⟩`	`∣++⟩+∣--⟩`	`∣i₊i₋⟩+∣i₋i₊⟩`
`01`	`+XX -ZZ`	`∣01⟩+∣10⟩`	`∣++⟩-∣--⟩`	`∣i₊i₊⟩-∣i₋i₋⟩`
`10`	`-XX +ZZ`	`∣00⟩-∣11⟩`	`∣+-⟩+∣-+⟩`	`∣i₊i₊⟩+∣i₋i₋⟩`
`11`	`-XX -ZZ`	`∣01⟩-∣10⟩`	`∣+-⟩-∣-+⟩`	`∣i₊i₋⟩-∣i₋i₊⟩`

julia> all_states = [BellState([0,0]), BellState([1,0]), BellState([0,1]), BellState([1,1])];
julia> filter_true(meas) = [state
           for state in all_states
           if bellmeasure!(copy(state), meas)[2]];
julia> filter_true(BellMeasure(1,1))2-element Vector{BellState}:
 BellState(Bool[0, 0])
 BellState(Bool[0, 1])
julia> filter_true(BellMeasure(2,1))2-element Vector{BellState}:
 BellState(Bool[0, 0])
 BellState(Bool[1, 1])
julia> filter_true(BellMeasure(3,1))2-element Vector{BellState}:
 BellState(Bool[0, 0])
 BellState(Bool[1, 0])