Add Ket, rm quantum_utils, fix test, break examples

Author: sebastiendesignolle

Project.toml

@@ -1,7 +1,7 @@
 name = "BellPolytopes"
 uuid = "38bdb6f4-c11c-4b2a-9c62-3601ea4ec58a"
-authors = ["ZIB AISST"]
 version = "0.2.0"
+authors = ["ZIB AISST"]
 
 [deps]
 Combinatorics = "861a8166-3701-5b0c-9a16-15d98fcdc6aa"
@@ -16,6 +16,7 @@ Tullio = "bc48ee85-29a4-5162-ae0b-a64e1601d4bc"
 [compat]
 Combinatorics = "1"
 FrankWolfe = "0.6"
+Ket = "0.7.0"
 LinearAlgebra = "1"
 Polyhedra = "0.8"
 Printf = "1"
@@ -26,7 +27,8 @@ Tullio = "0.3"
 julia = "1.9"
 
 [extras]
+Ket = "412c778c-4733-41d8-b706-9e072557ba34"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Test"]
+test = ["Ket", "Test"]

examples/CHSH.jl

@@ -1,19 +1,31 @@
 # Bipartite example recovering the CHSH inequality together with a local model
 using BellPolytopes
 using FrankWolfe
+using Ket
 using LinearAlgebra
 
 N = 2 # bipartite scenario
+function mes(v::Matrix{T}) where {T <: Real}
+    σ = gellmann(T, 2)
+    res = Vector{Measurement{Complex{T}}}(undef, size(v, 1))
+    for i in axes(v, 1)
+        tmp = v[i, 1] * σ[2] + v[i, 2] * σ[3] + v[i, 3] * σ[4]
+        res[i] = [(σ[1] - tmp) / 2, (σ[1] + tmp) / 2]
+    end
+    return res
+end
 # Bloch vectors of the measurements to be performed on Alice's side
-measurements_vecA = [1 0 0; 0 0 1]
+vecA = [1 0 0; 0 0 1]
+mesA = mes(vecA)
 # Bloch vectors of the measurements to be performed on Bob's side
-measurements_vecB = [1 0 1; 1 0 -1] / sqrt(2)
-rho = rho_singlet() # shared state
+vecB = [1 0 1; 1 0 -1] / sqrt(2)
+mesB = mes(vecB)
+rho = state_psiminus() # shared state
 _, lower_bound, upper_bound, local_model, bell_inequality =
-    nonlocality_threshold([measurements_vecA, measurements_vecB], N; rho=rho)
+    nonlocality_threshold([measurements_vecA, measurements_vecB], N; rho)
 
 println("Correlation matrix")
-p = correlation_tensor([measurements_vecA, measurements_vecB], N; rho=rho, marg=false)
+p = tensor_correlation(rho, mesA, mesB; marg=false)
 display(p)
 
 println()

examples/Werner.jl

@@ -1,18 +1,22 @@
 # Bipartite example showing a better resistance to noise than the CHSH inequality
 using BellPolytopes
 using FrankWolfe
+using Ket
 using LinearAlgebra
 
 N = 2 # bipartite scenario
 # Bloch vectors of the measurements to be performed by all parties
 # obtained with https://github.com/sebastiendesignolle/polyhedronisme
-measurements_vec = polyhedronisme("../polyhedra/polyhedronisme-SASuSAuO.obj", 33)
-rho = rho_singlet() # shared state
-p = correlation_tensor(measurements_vec, N; rho=rho, marg=false)
+v = polyhedronisme("../polyhedra/polyhedronisme-SASuSAuO.obj", 33)
+σ = gellmann(2)
+mes = [[(σ[1] - v[i, 1] * σ[2] - v[i, 2] * σ[3] - v[i, 3] * σ[4]) / 2, (σ[1] + v[i, 1] * σ[2] + v[i, 2] * σ[3] + v[i, 3] * σ[4]) / 2] for i in axes(v, 1)]
+rho = state_psiminus() # shared state
+p = tensor_correlation(rho, mes, N; marg=false)
 @time x, ds, primal, dual_gap, as, M, β =
     bell_frank_wolfe(p; v0=1 / sqrt(2), verbose=3, epsilon=1e-4, mode_last=0, nb_last=10^6, callback_interval=10^5)
 # v_c ≤ 0.704914
 # As such, the function above gets this last bound heuristically
 # Change mode_last to 1 to check the exact bound (takes a few minutes)
+# Alternatively, use local_bound from Ket to compute it in parallel
 
 println()

src/BellPolytopes.jl

@@ -9,7 +9,6 @@ using Random
 using Serialization
 using Tullio
 
-include("quantum_utils.jl")
 include("types.jl")
 include("fw_methods.jl")
 include("utils.jl")

src/bell_frank_wolfe.jl

@@ -16,7 +16,7 @@ Returns:
 Optional arguments:
  - `o`: same type as `p`, corresponds to the noise to be added, by default the center of the polytope,
  - `prob`: a boolean, indicates if `p` is a corelation or probability array,
- - `marg`: a boolean, indicates if `p` contains marginals,
+ - `marg`: a boolean, indicates if `p` contains marginals (by convention in the last index of each dimension),
  - `v0`: the visibility used to make a nonlocal `p` closer to the local polytope,
  - `epsilon`: the tolerance, used as a stopping criterion (when the primal value or the dual gap go below its value), by default 1e-7,
  - `verbose`: an integer, indicates the level of verbosity from 0 to 3,