Bloch vector (#103)

* bloch vector with tests

* version bump

Project.toml

@@ -1,7 +1,7 @@
 name = "QuantumInformation"
 uuid = "3c0b384b-479c-5684-b2ef-9d7a46dd931e"
 authors = ["Dariusz Kurzyk <[email protected]>", "Łukasz Pawela <[email protected]>", "Piotr Gawron <[email protected]>", "Marcin Przewięźlikowski <[email protected]>"]
-version = "0.4.9"
+version = "0.4.10"
 
 [deps]
 Convex = "f65535da-76fb-5f13-bab9-19810c17039a"

src/base.jl

@@ -1,4 +1,4 @@
-export ket, bra, ketbra, proj, res, unres, max_mixed, max_entangled,
+export ket, bra, ketbra, proj, bloch_vector, res, unres, max_mixed, max_entangled,
     werner_state, permutesystems
 
 function ket(::Type{T}, val::Int, dim::Int) where T<:AbstractVector{<:Number}
@@ -75,7 +75,19 @@ Return outer product \$|ket\\rangle\\langle ket|\$ of `ket`.
 """
 proj(ψ::AbstractVector{<:Number}) = ψ * ψ'
 
+"""
+$(SIGNATURES)
+- `ρ`: input qubit density matrix.
 
+Return the Bloch vector corresponding to the inpu quit state.
+"""
+function bloch_vector(ρ::AbstractMatrix{T}) where {T <: Number}
+    @assert size(ρ) == (2, 2)
+    x = 2real(ρ[1, 2])
+    y = 2imag(ρ[1, 2])
+    z = 2real(ρ[1, 1]) - 1
+    T[x, y, z]
+end
 
 """
 $(SIGNATURES)

test/base.jl

@@ -52,6 +52,33 @@ end
     @test norm(ϕϕ - ψψ) ≈ 0.
 end
 
+@testset "bloch_vector" begin
+    @testset "Test 1: Identity matrix" begin
+        ρ = Matrix{ComplexF64}(I, 2, 2)
+        @test bloch_vector(ρ) ≈ ComplexF64[0.0, 0.0, 1.0]
+    end
+
+    @testset "Test 2: X basis state" begin
+        ρ = [0.5 0.5; 0.5 0.5]
+        @test bloch_vector(ρ) ≈ Float64[1.0, 0.0, 0.0]
+    end
+
+    @testset "Test 3: Y basis state" begin
+        ρ = [0.5 0.5im; -0.5im 0.5]
+        @test bloch_vector(ρ) ≈ ComplexF64[0.0, 1.0, 0.0]
+    end
+
+    @testset "Test 4: Z basis state" begin
+        ρ = [1.0 0.0; 0.0 0.0]
+        @test bloch_vector(ρ) ≈ Float64[0.0, 0.0, 1.0]
+    end
+
+    @testset "Test 5: Arbitrary density matrix" begin
+        ρ = [0.6 0.3-0.2im; 0.3+0.2im 0.4]
+        @test bloch_vector(ρ) ≈ ComplexF64[0.6, -0.4, 0.2]
+    end
+end
+
 @testset "res" begin
     ρ = [0.25 0.25im; -0.25im 0.75]
     ϕ = res(ρ)