def test_guessing_probability(self):
p = [
0.5, 0.5, 0.5, 0.5, 0.4267766952966368, 0.4267766952966368,
0.4267766952966368, 0.07322330470336313
]
P = Probability([2, 2], [2, 2])
behaviour_constraint = [
P([0], [0], 'A') - p[0],
P([0], [1], 'A') - p[1],
P([0], [0], 'B') - p[2],
P([0], [1], 'B') - p[3],
P([0, 0], [0, 0]) - p[4],
P([0, 0], [0, 1]) - p[5],
P([0, 0], [1, 0]) - p[6],
P([0, 0], [1, 1]) - p[7]
]
behaviour_constraint.append("-0[0,0]+1.0")
sdpRelaxation = SdpRelaxation(P.get_all_operators(),
normalized=False,
verbose=0)
sdpRelaxation.get_relaxation(1,
objective=-P([0], [0], 'A'),
momentequalities=behaviour_constraint,
substitutions=P.substitutions)
sdpRelaxation.solve()
self.assertTrue(abs(sdpRelaxation.primal + 0.5) < 10e-5)
def __main__():
# chsh quantum bound : 4
# mermin quantum bound : 4
# svetlichny quantum bound 4sqrt(2) ~ 5.65
P = Probability([2, 2], [2, 2], [2, 2])
Chsh = chsh(P)
Mermin = mermin(P)
Svetlichny = svetlichny(P)
dx = 0
div = 1.0
step = 0.4
lim = 5.6
x = []
y = []
while dx <= lim:
print(dx)
ineq = []
ineq.append(Svetlichny - dx)
ineq.append(-1 * Svetlichny + dx)
sdpRelaxation = SdpRelaxation(P.get_all_operators(), verbose=0)
sdpRelaxation.get_relaxation(2,
substitutions=P.substitutions,
inequalities=ineq)
sdpRelaxation.set_objective(-Chsh)
solve_sdp(sdpRelaxation, solver="cvxopt")
x.append(dx)
y.append(abs(sdpRelaxation.primal) / div)
dx = dx + step
plt.plot(x, y, 'k')
plt.show()
def __main__():
# chsh quantum bound : 4
# mermin quantum bound : 4
# svetlichny quantum bound 4sqrt(2) ~ 5.65
P = Probability([2, 2], [2, 2], [2, 2])
Chsh = chsh(P)
Mermin = mermin(P)
Svetlichny = svetlichny(P)
dx = 0
div = 1.0
step = 0.4
lim = 5.6
x = []
y = []
while dx <= lim :
print (dx)
ineq = []
ineq.append(Svetlichny - dx)
ineq.append(-1*Svetlichny + dx)
sdpRelaxation = SdpRelaxation(P.get_all_operators(), verbose=0)
sdpRelaxation.get_relaxation(2, substitutions = P.substitutions,inequalities = ineq)
sdpRelaxation.set_objective(-Chsh)
solve_sdp(sdpRelaxation, solver="cvxopt")
x.append(dx)
y.append(abs(sdpRelaxation.primal)/div)
dx = dx + step
plt.plot(x,y,'k')
plt.show()
def test_maximum_violation(self):
I = [[0, -1, 0], [-1, 1, 1], [0, 1, -1]]
P = Probability([2, 2], [2, 2])
relaxation = SdpRelaxation(P.get_all_operators())
relaxation.get_relaxation(1,
objective=define_objective_with_I(I, P),
substitutions=P.substitutions,
extramonomials=P.get_extra_monomials('AB'))
relaxation.solve()
self.assertTrue(abs(relaxation.primal + (np.sqrt(2)-1)/2) < 10e-5)
def test_maximum_violation(self):
I = [[0, -1, 0], [-1, 1, 1], [0, 1, -1]]
P = Probability([2, 2], [2, 2])
relaxation = SdpRelaxation(P.get_all_operators())
relaxation.get_relaxation(1,
objective=define_objective_with_I(I, P),
substitutions=P.substitutions,
extramonomials=P.get_extra_monomials('AB'))
relaxation.solve()
self.assertTrue(abs(relaxation.primal + (np.sqrt(2) - 1) / 2) < 10e-5)
def test_guessing_probability(self):
p = [0.5, 0.5, 0.5, 0.5, 0.4267766952966368, 0.4267766952966368, 0.4267766952966368, 0.07322330470336313]
P = Probability([2, 2], [2, 2])
behaviour_constraint = [
P([0], [0], "A") - p[0],
P([0], [1], "A") - p[1],
P([0], [0], "B") - p[2],
P([0], [1], "B") - p[3],
P([0, 0], [0, 0]) - p[4],
P([0, 0], [0, 1]) - p[5],
P([0, 0], [1, 0]) - p[6],
P([0, 0], [1, 1]) - p[7],
]
behaviour_constraint.append("-0[0,0]+1.0")
sdpRelaxation = SdpRelaxation(P.get_all_operators(), normalized=False, verbose=0)
sdpRelaxation.get_relaxation(
1, objective=-P([0], [0], "A"), momentequalities=behaviour_constraint, substitutions=P.substitutions
)
sdpRelaxation.solve()
self.assertTrue(abs(sdpRelaxation.primal + 0.5) < 10e-5)
def test_violation(self):
I = [[0, -1, 0],
[-1, 1, 1],
[0, 1, -1]]
P = Probability([2, 2], [2, 2])
objective = define_objective_with_I(I, P)
sdpRelaxation = MoroderHierarchy([flatten(P.parties[0]),
flatten(P.parties[1])],
verbose=0, normalized=False)
sdpRelaxation.get_relaxation(1, objective=objective,
substitutions=P.substitutions)
Problem = sdpRelaxation.convert_to_picos(duplicate_moment_matrix=True)
X = Problem.get_variable('X')
Y = Problem.get_variable('Y')
Z = Problem.add_variable('Z', (sdpRelaxation.block_struct[0],
sdpRelaxation.block_struct[0]))
Problem.add_constraint(Y.partial_transpose() >> 0)
Problem.add_constraint(Z.partial_transpose() >> 0)
Problem.add_constraint(X - Y + Z == 0)
Problem.add_constraint(Z[0, 0] == 1)
solution = Problem.solve(verbose=0)
self.assertTrue(abs(solution["obj"] - 0.1236) < 10e-3)
# -*- coding: utf-8 -*-
"""
This example calculates the maximum quantum violation of the CHSH inequality in
the probability picture with a mixed-level relaxation of 1+AB.
Created on Mon Dec 1 14:19:08 2014
@author: Peter Wittek
"""
from ncpol2sdpa import Probability, SdpRelaxation, define_objective_with_I
level = 1
I = [[ 0, -1, 0 ],
[-1, 1, 1 ],
[ 0, 1, -1 ]]
P = Probability([2, 2], [2, 2])
objective = define_objective_with_I(I, P)
sdpRelaxation = SdpRelaxation(P.get_all_operators())
sdpRelaxation.get_relaxation(level, objective=objective,
substitutions=P.substitutions,
extramonomials=P.get_extra_monomials('AB'))
sdpRelaxation.solve()
print(sdpRelaxation.primal, sdpRelaxation.status)
