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 spins
• Ntraj: number of trajectories for the SSE
• Tfinal: final time of evolution
• measurement = :pd measurement (either :pd or :hd)
• dt: timestep of the evolution
• κ = 1: the noise coupling
• θ = 0: noise angle (0 parallel, π/2 transverse)
• ω = 0: local value of the frequency
• η = 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...)

• ZChop for 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).

MIT License