QuantumStateDistributions

Installation

The package can be installed with the Julia package manager. From the Julia REPL, type ] to enter the Pkg REPL mode and run:

pkg> add QuantumStateDistributions

Quick start

Construct a squeezed state via QuantumStateBase.jl and declare its quantum state distribution.

julia> using QuantumStateDistributions, QuantumStateBase

julia> r, θ, dim = 0.8, π/2, 100;

julia> ρ = SqueezedState(r, θ, Matrix, dim=dim)
100×100 Matrix{ComplexF64}:
       0.7477+0.0im          0.0+0.0im  …  -1.77607e-24-5.91946e-10im  0.0+0.0im
          0.0+0.0im          0.0+0.0im              0.0+0.0im          0.0+0.0im
 -2.14974e-17+0.351079im     0.0+0.0im      2.77945e-10-8.16923e-25im  0.0+0.0im
          0.0+0.0im          0.0+0.0im              0.0+0.0im          0.0+0.0im
             ⋮                          ⋱
          0.0+0.0im          0.0+0.0im              0.0+0.0im          0.0+0.0im
 -1.77607e-24+5.91946e-10im  0.0+0.0im      4.68637e-19+0.0im          0.0+0.0im
          0.0+0.0im          0.0+0.0im              0.0+0.0im          0.0+0.0im

julia> d = GaussianStateBHD(ρ);

Sample a point from the quantum state distribution in intensity-to-measurement-phase quadrature coordinate measured by balanced homodyne detection:

julia> rand(d)
2-element Vector{Float64}:
 0.8420476666965236
 1.6008878775912423

Sample n points from the quantum state distribution:

julia> n = 4096;

julia> rand(d, n)
2×4096 Matrix{Float64}:
  0.0018714   0.0034182   0.00403972  0.00780472  …   6.27393  6.27811    6.27884
 -0.706334   -1.16179    -0.195581    0.174201       -0.60763  0.853457  -0.217017

Estemate density matrix of a quantum state via MLE

Generate some data from a squeezed state:

julia> data = rand(d, 81920);

Construct a PositivePreservingIterator:

julia> t = 50;

julia> ppit = PositivePreservingIterator(data, t, dim=35);

Estermate density matrix:

julia> run!(ppit)

julia> ρ_mle = ppit.ρ