Fisher information for magnetometry and frequency estimation with continuously monitored spin systems, with independent Markovian noise acting on each spin.
Companion code for F. Albarelli, M. A. C. Rossi, D. Tamascelli, and M, G. Genoni, Quantum 2, 110 (2018).
The algorithm is described in Sec. V of the paper.
This version is compatible with Julia v0.7 onwards
From the Julia pkg REPL (press ])
pkg> add https://github.com/matteoacrossi/ContinuousMeasurementFI using ContinuousMeasurementFI
(t, FI, QFI) = Eff_QFI(kwargs...)Evaluate the continuous-time FI and QFI of a final strong measurement for the estimation of the frequency ω with continuous monitoring of each half-spin particle affected by noise at an angle θ, with efficiency η using SME (stochastic master equation) or SSE (stochastic Schrödinger equation).
The function returns a tuple (t, FI, QFI) containing the time vector and the
vectors containing the FI and average QFI
Nj: number of spinsNtraj: number of trajectories for the SSETfinal: final time of evolutionmeasurement = :pdmeasurement (either:pdor:hd)dt: timestep of the evolutionκ = 1: the noise couplingθ = 0: noise angle (0 parallel, π/2 transverse)ω = 0: local value of the frequencyη = 1: measurement efficiency
using Plots
include("Eff_QFI.jl")
(t, fi, qfi) = Eff_QFI(Nj=5, Ntraj=10000, Tfinal=5., dt=.1; measurement=:pd, θ = pi/2, ω = 1)
plot(t, (fi + qfi)./t, xlabel="t", ylabel="Q/t")
ContinuousMeasurementFI can parallelize the Montecarlo evaluation
of trajectories using the builtin distributed computing system of Julia
using Distributed
addprocs(#_of_processes)
@everywhere using ContinuousMeasurementFI
(t, FI, QFI) = Eff_QFI(kwargs...)ZChopfor rounding off small imaginary parts in ρ
If you found the code useful for your research, please cite the paper:
F. Albarelli, M. A. C. Rossi, D. Tamascelli, and M, G. Genoni, Quantum 2, 110 (2018).