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_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 = convert_to_picos(sdpRelaxation, 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"] - 0.139) < 10e-3)
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)
def _relax(self):
"""
Creates the sdp relaxation object from ncpol2sdpa.
"""
if self.solver == None:
self.solver = self.DEFAULT_SOLVER_PATH
self._eq_cons = [] # equality constraints
self._proj_cons = {} # projective constraints
self._A_ops = [] # Alice's operators
self._B_ops = [] # Bob's operators
self._obj = 0 # Objective function
self._obj_const = '' # Extra objective normalisation constant
self._sdp = None # SDP object
# Creating the operator constraints
nrm = ''
# Need as many decompositions as there are generating outcomes
for k in range(np.prod(self.generation_output_size)):
self._A_ops += [
ncp.generate_measurements(self.io_config[0],
'A' + str(k) + '_')
]
self._B_ops += [
ncp.generate_measurements(self.io_config[1],
'B' + str(k) + '_')
]
self._proj_cons.update(
ncp.projective_measurement_constraints(self._A_ops[k],
self._B_ops[k]))
#Also building a normalisation string for next step
nrm += '+' + str(k) + '[0,0]'
# Adding the constraints
# Normalisation constraint
self._eq_cons.append(nrm + '-1')
self._base_constraint_expressions = []
# Create the game expressions
for game in self.games:
tmp_expr = 0
for k in range(np.prod(self.generation_output_size)):
tmp_expr += -ncp.define_objective_with_I(
game._cgmatrix, self._A_ops[k], self._B_ops[k])
self._base_constraint_expressions.append(tmp_expr)
# Specify the scores for these expressions including any shifts
for i, game in enumerate(self.games):
#We must account for overshifting in the score coming from the decomposition
self._eq_cons.append(self._base_constraint_expressions[i] -
game.score - game._cgshift *
(np.prod(self.generation_output_size) - 1))
self._obj, self._obj_const = guessingProbabilityObjectiveFunction(
self.io_config, self.generation_inputs, self._A_ops, self._B_ops)
# Initialising SDP
ops = [
ncp.flatten([self._A_ops[0], self._B_ops[0]]),
ncp.flatten([self._A_ops[1], self._B_ops[1]]),
ncp.flatten([self._A_ops[2], self._B_ops[2]]),
ncp.flatten([self._A_ops[3], self._B_ops[3]])
]
self._sdp = ncp.SdpRelaxation(ops,
verbose=self.verbose,
normalized=False)
self._sdp.get_relaxation(level=self._relaxation_level,
momentequalities=self._eq_cons,
objective=self._obj,
substitutions=self._proj_cons,
extraobjexpr=self._obj_const)
