Closed BoltzmannEntropy closed 1 year ago
To my best knowledge, concurrence is not defined. For von-Neumann entropy, please check
julia> Yao.von_neumann_entropy
For Schmidt decomposition, it is just
julia> reg = rand_state(5)
ArrayReg{2, ComplexF64, Array...}
active qubits: 5/5
nlevel: 2
julia> focus!(reg, (1,2,4)) # separate the qubits into system and environment
ArrayReg{2, ComplexF64, Array...}
active qubits: 3/5
nlevel: 2
julia> using LinearAlgebra
julia> LinearAlgebra.svd(reg.state)
SVD{ComplexF64, Float64, Matrix{ComplexF64}, Vector{Float64}}
U factor:
8×4 Matrix{ComplexF64}:
-0.261431-0.0960797im 0.260523+0.376523im -0.237475+0.232969im -0.389497-0.321233im
-0.22806+0.25927im 0.0843631+0.161655im 0.45936-0.301496im -0.0629732-0.0823107im
0.32522+0.169679im 0.271214+0.362034im 0.535053+0.121561im 0.146547-0.000847907im
0.223615+0.37805im -0.128325+0.366616im -0.254146-0.157601im -0.201075-0.119976im
-0.032563+0.0675164im -0.234217+0.187352im 0.205174-0.305651im -0.24895+0.110838im
-0.315045+0.0352616im 0.51662-0.0836399im -0.077368-0.0583198im 0.143729-0.38788im
0.0166898+0.34663im -0.0139973-0.0142509im -0.0350241+0.105815im 0.315063-0.453482im
0.326669-0.377421im -0.175984-0.0799332im 0.185893+0.0710434im -0.0332874-0.326603im
singular values:
4-element Vector{Float64}:
0.6835581617109449
0.531229886056492
0.41629565712466526
0.27792260357499565
Vt factor:
4×4 Matrix{ComplexF64}:
0.459486+0.0im 0.558193-0.382603im 0.298438+0.160865im 0.322012-0.335073im
-0.551793+0.0im -0.165489-0.222685im 0.566234+0.44381im 0.25724+0.186518im
0.252128+0.0im 0.158808-0.230465im 0.265749-0.336733im -0.146302+0.807887im
0.648713+0.0im -0.597857+0.171156im 0.166966+0.394436im 0.0475861+0.0819934im
For entanglement testing. Thanks.