Add Horodecki state

dev-ket · Jan 16, 2025 · 447c99a · 447c99a
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diff --git a/docs/src/api.md b/docs/src/api.md
@@ -119,6 +119,8 @@ state_w_ket
 state_w
 state_dicke_ket
 state_dicke
+state_horodecki33
+state_horodecki24
 white_noise
 white_noise!
 ```

diff --git a/src/states.jl b/src/states.jl
@@ -254,3 +254,58 @@ function state_dicke(::Type{T}, k::Integer, N::Integer; v::Real = 1) where {T<:N
 end
 state_dicke(k::Integer, N::Integer; kwargs...) = state_dicke(ComplexF64, k, N; kwargs...)
 export state_dicke
+
+"""
+    state_horodecki33([T=ComplexF64,] a::Real)
+
+Produces the 3 × 3 bipartite PPT-entangled Horodecki state with parameter `a`.
+
+Reference: Paweł Horodecki, [arXiv:quant-ph/9703004](https://arxiv.org/abs/quant-ph/9703004)
+"""
+function state_horodecki33(::Type{T}, a::Real; v::Real = 1) where {T<:Number}
+    @assert 0 ≤ a ≤ 1 "Parameter `a` must be in [0, 1]"
+    x = (1 + a) / 2
+    y = sqrt(1 - a^2) / 2
+    rho = T[
+        a 0 0 0 a 0 0 0 a
+        0 a 0 0 0 0 0 0 0
+        0 0 a 0 0 0 0 0 0
+        0 0 0 a 0 0 0 0 0
+        a 0 0 0 a 0 0 0 a
+        0 0 0 0 0 a 0 0 0
+        0 0 0 0 0 0 x 0 y
+        0 0 0 0 0 0 0 a 0
+        a 0 0 0 a 0 y 0 x
+    ]
+    rho ./= 8a + 1
+    return white_noise!(Hermitian(rho), v)
+end
+state_horodecki33(a::Real) = state_horodecki33(ComplexF64, a)
+export state_horodecki33
+
+"""
+    state_horodecki24([T=ComplexF64,] b::Real)
+
+Produces the 2 × 4 bipartite PPT-entangled Horodecki state with parameter `b`.
+
+Reference: Paweł Horodecki, [arXiv:quant-ph/9703004](https://arxiv.org/abs/quant-ph/9703004)
+"""
+function state_horodecki24(::Type{T}, b::Real; v::Real = 1) where {T<:Number}
+    @assert 0 ≤ b ≤ 1 "Parameter `b` must be in [0, 1]"
+    x = (1 + b) / 2
+    y = sqrt(1 - b^2) / 2
+    rho = T[
+        b 0 0 0 0 b 0 0
+        0 b 0 0 0 0 b 0
+        0 0 b 0 0 0 0 b
+        0 0 0 b 0 0 0 0
+        0 0 0 0 x 0 0 y
+        b 0 0 0 0 b 0 0
+        0 b 0 0 0 0 b 0
+        0 0 b 0 y 0 0 x
+    ]
+    rho ./= 7b + 1
+    return white_noise!(Hermitian(rho), v)
+end
+state_horodecki24(b::Real) = state_horodecki24(ComplexF64, b)
+export state_horodecki24
diff --git a/test/states.jl b/test/states.jl
@@ -25,5 +25,19 @@
         rho = state_supersinglet(T, 3)
         @test U * rho * U' ≈ rho
         @test kron(I(5),shift(5,3)*clock(5,2))*state_phiplus_ket(5) ≈ state_bell_ket(3,2,5)
+        rho = state_horodecki33(T, 1)
+        ref = Matrix{T}(I, 9, 9)
+        ref[1:4:9, 1:4:9] .= 1
+        ref ./= 9
+        @test rho ≈ ref
+        @test minimum(eigvals(partial_transpose(rho, 1))) ≥ 0
+        rho = state_horodecki24(T, 1)
+        ref = Matrix{T}(I, 8, 8)
+        ref[1:5:8, 1:5:8] .= 1
+        ref[2:5:8, 2:5:8] .= 1
+        ref[3:5:8, 3:5:8] .= 1
+        ref ./= 8
+        @test rho ≈ ref
+        @test minimum(eigvals(partial_transpose(rho, 1, [2, 4]))) ≥ 0
     end
 end