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CHSH-DifferentShadowInnerInvariance.py
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CHSH-DifferentShadowInnerInvariance.py
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from ncpol2sdpa import generate_operators, SdpRelaxation
import numpy as np
import matplotlib.pyplot as plt
import igraph as ig
def plot(n, initial_weight, final_weight):
n_vertices = 8
edges_A_CHSH = {(0,1),(2,3),(4,5),(6,7),(1,5),(0,4),(2,6),(3,7)};
edges_B_CHSH = {(1,2),(3,4),(5,6),(0,7),(1,5),(0,4),(2,6),(3,7)};
edges_A1 = {(0,1),(2,3),(4,5),(6,7),(0,4),(2,6),(3,7)};
edges_B1 = {(1,2),(3,4),(5,6),(0,7),(0,4),(2,6),(3,7)};
edges_A2 = {(0,1),(2,3),(4,5),(6,7),(2,6),(3,7)};
edges_B2 = {(1,2),(3,4),(5,6),(0,7),(2,6),(3,7)};
edges_A3 = {(0,1),(2,3),(4,5),(6,7),(1,5),(3,7)};
edges_B3 = {(1,2),(3,4),(5,6),(0,7),(1,5),(3,7)};
edges_A4 = {(0,1),(2,3),(4,5),(6,7),(3,7)};
edges_B4 = {(1,2),(3,4),(5,6),(0,7),(3,7)};
edges_A5 = {(0,1),(2,3),(4,5),(6,7)};
edges_B5 = {(1,2),(3,4),(5,6),(0,7)};
arr1 = np.array(initial_weight);
arr2 = np.array(final_weight);
file = open('InnerInvarianceDifferentShadow.txt','w');
epsilon = np.linspace(0,1,n);
i = 0;
t = 0;
while (i < n):
s = np.add((1-epsilon[i])*arr1, (epsilon[i])*arr2);
theta_CHSH = lovasz(n_vertices, edges_A_CHSH, edges_B_CHSH, s);
t = t + 1
print('otimização ' + str(t) + '\n')
theta1 = lovasz(n_vertices, edges_A1, edges_B1, s);
t = t + 1
print('otimização ' + str(t) + '\n')
theta2 = lovasz(n_vertices, edges_A2, edges_B2, s);
t = t + 1
print('otimização ' + str(t) + '\n')
theta3 = lovasz(n_vertices, edges_A3, edges_B3, s);
t = t + 1
print('otimização ' + str(t) + '\n')
theta4 = lovasz(n_vertices, edges_A4, edges_B4, s);
t = t + 1
print('otimização ' + str(t) + '\n')
theta5 = lovasz(n_vertices, edges_A5, edges_B5, s);
t = t + 1
print('otimização ' + str(t) + '\n')
print('\n' + '\n' + 'epsilon = ' + str(epsilon[i]) + '\n' + 'CHSH = ' + str(theta_CHSH) + '\n' + '34,34 = ' + str(theta1) + '\n' + '114,33 = ' + str(theta2) + '\n' + '33,33 = ' + str(theta3) + '\n' + '113,113 = ' + str(theta4) + '\n' + '1111,1111 = ' + str(theta5) + '\n' + '\n');
file.write(str(epsilon[i]) + " " + str(theta_CHSH) + " " + str(theta1) + " " + str(theta2) + " " + str(theta3) + " " + str(theta4) + " " + str(theta5) + '\n');
i = i + 1
file.close();
data = np.loadtxt('InnerInvarianceDifferentShadow.txt');
analytical_epsilon = np.linspace(0,1,100)
alphaCHSH = (1-analytical_epsilon)*pondered_independence_number(n_vertices, edges_A_CHSH, edges_B_CHSH, initial_weight) + analytical_epsilon*pondered_independence_number(n_vertices, edges_A_CHSH, edges_B_CHSH, final_weight)
alpha1 = (1-analytical_epsilon)*pondered_independence_number(n_vertices, edges_A1, edges_B1, initial_weight) + analytical_epsilon*pondered_independence_number(n_vertices, edges_A1, edges_B1, final_weight)
alpha2 = (1-analytical_epsilon)*pondered_independence_number(n_vertices, edges_A2, edges_B2, initial_weight) + analytical_epsilon*pondered_independence_number(n_vertices, edges_A2, edges_B2, final_weight)
alpha3 = (1-analytical_epsilon)*pondered_independence_number(n_vertices, edges_A3, edges_B3, initial_weight) + analytical_epsilon*pondered_independence_number(n_vertices, edges_A3, edges_B3, final_weight)
alpha4 = (1-analytical_epsilon)*pondered_independence_number(n_vertices, edges_A4, edges_B4, initial_weight) + analytical_epsilon*pondered_independence_number(n_vertices, edges_A4, edges_B4, final_weight)
alpha5 = (1-analytical_epsilon)*pondered_independence_number(n_vertices, edges_A5, edges_B5, initial_weight) + analytical_epsilon*pondered_independence_number(n_vertices, edges_A5, edges_B5, final_weight)
x = data[:, 0];
y = data[:, 1];
#y1 = data[:, 2];
#y2 = data[:, 3];
#y3 = data[:, 4];
#y4 = data[:, 5];
#y5 = data[:, 6];
plt.plot(analytical_epsilon,alphaCHSH);
#plt.plot(analytical_epsilon,alpha1);
#plt.plot(analytical_epsilon,alpha2);
#plt.plot(analytical_epsilon,alpha3);
#plt.plot(analytical_epsilon,alpha4);
#plt.plot(analytical_epsilon,alpha5);
#plt.plot(x, y,'.', label=r'$\mathcal{G}_{CHSH}$');
#plt.plot(x, y1,'x', label=r'$\mathcal{G}_{34,34}$');
#plt.plot(x, y2,'+', label=r'$\mathcal{G}_{114,33}$');
#plt.plot(x, y3,'x', label=r'$\mathcal{G}_{33,33}$');
#plt.plot(x, y4,'+', label=r'$\mathcal{G}_{113,113}$');
#plt.plot(x, y5,'.', label=r'$\mathcal{G}_{1111,1111}$');
plt.gca().set_xlabel(r'$\epsilon$')
plt.gca().set_ylabel(r'$\theta(\mathcal{G} ,\omega^\epsilon)$')
plt.subplots_adjust(top=1.5)
plt.legend()
plt.figure()
def lovasz(n_vertices, edges_A, edges_B, b):
level = 1
"Adjacency matrices"
adj_matrix_A = np.zeros((n_vertices,n_vertices))
adj_matrix_B = np.zeros((n_vertices,n_vertices))
for i in range(n_vertices):
for j in range(n_vertices):
if (i,j) in edges_A:
adj_matrix_A[i,j] = 1
if (i,j) in edges_B:
adj_matrix_B[i,j] = 1
"Set operators"
A = generate_operators('A', n_vertices, hermitian=True)
B = generate_operators('B', n_vertices, hermitian=True)
"Set objective"
obj = -sum([b[i]*A[i]*B[i] for i in range(n_vertices)]) #sum of weighted components of the behaviour
"Substitutions"
subs = {A[i]**2:A[i] for i in range(n_vertices)} #conditions of projectors
subs.update({B[i]**2:B[i] for i in range(n_vertices)}) #conditions of projectors
(subs.update({B[j]*A[i]:A[i]*B[j] for i in range(n_vertices) for j in
range(n_vertices)})) #symmetry
(subs.update({A[i]*A[j]:0 for i in range(n_vertices) for j in
range(n_vertices) if adj_matrix_A[i,j] == 1})) #orthogonality relation
(subs.update({B[i]*B[j]:0 for i in range(n_vertices) for j in
range(n_vertices) if adj_matrix_B[i,j] == 1})) #orthogonality relation
"Extra monomials"
extra = ([A[i]*B[j] for i in range(n_vertices) for j in range(n_vertices)])
"Set problem"
sdpRelaxation = SdpRelaxation(A+B, verbose=1);
sdpRelaxation.get_relaxation(level, objective=obj,
substitutions=subs, extramonomials=extra);
"Solve"
sdpRelaxation.solve(solver = 'mosek')
"Final"
return(-sdpRelaxation.primal)
def pondered_independence_number(n_vertices, edges_A, edges_B, weight):
g = ig.Graph()
g.add_vertices(n_vertices)
edges = list(edges_A) + list(edges_B)
g.add_edges(edges)
arrays_maximais = np.array(g.maximal_independent_vertex_sets(), dtype = object)
i = 0
j = 0
alpha = np.zeros(shape=(len(arrays_maximais),1))
while(i < len(arrays_maximais)):
j = 0
while(j < len(arrays_maximais[i])):
alpha[i] = alpha[i] + weight[arrays_maximais[i][j]]
j = j + 1
i = i + 1
return(np.max(alpha))
#Example
#initial_weight = [1/8,1/8,1/8,1/8,1/8,1/8,1/8,1/8]
#final_weight = [0,0,0,1/5,1/5,1/5,1/5,1/5]
#n = 15
#plot(n, initial_weight, final_weight)