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find_inequalities_trident.py
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find_inequalities_trident.py
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# Code for
#
# Guarantees on the structure of experimental quantum networks
#
# arXiv:2403.02376
#
# Authors: Alejandro Pozas-Kerstjens
#
# Requires: inflation for setting up and solving the problems
# numpy for array operations
# qutip for quantum operations
# sympy for symbolic operations
# tqdm for progress bars
# numbers, os
#
# Last modified: Mar, 2024
import os
import numpy as np
import qutip as qt
from inflation import InflationProblem, InflationSDP, max_within_feasible
from numbers import Real
from sympy import Symbol
from tqdm import tqdm
from utils import export_inequality, prob_noin, rho, rho_trident_list
dag = {"h1": ["A", "B", "C", "D"],
"h4": ["C", "D", "E", "F"]}
vis = Symbol("v")
data_path = "DATA_PATH"
ineq_path = "TridentInequalities"
measurements_list = [file[:6] for file in os.listdir(data_path)]
###############################################################################
# Single-input inequalities
###############################################################################
InfProb = InflationProblem(dag=dag,
outcomes_per_party=[2, 2, 2, 2, 2, 2],
inflation_level_per_source=2,
verbose=0
)
InfSDP = InflationSDP(InfProb)
Local1Len3 = InfSDP.build_columns('local1', max_monomial_length=3)
info = "Local1Len3"
InfSDP.generate_relaxation(Local1Len3)
try:
with open(f"tridentvisibilities_INF2{info}.txt", "r") as file:
visibilities = file.read()
except FileNotFoundError:
visibilities = ""
for measurements in tqdm(measurements_list, desc=f"Inequalities for {info}"):
if measurements in visibilities:
pass
else:
InfSDP.set_distribution(prob_noin(vis, "trident", measurements))
if any([not isinstance(val, Real)
for val in InfSDP.known_moments.values()]):
vcrit = max_within_feasible(InfSDP, InfSDP.known_moments, "dual")
if abs(vcrit - 1) > 1e-3:
InfSDP.reset("all")
v = np.ceil(vcrit * 1000) / 1000
InfSDP.set_distribution(prob_noin(v, "trident", measurements))
InfSDP.solve(feas_as_optim=True)
if InfSDP.solution_object["status"] == "feasible":
cert = InfSDP.certificate_as_probs()
export_inequality(cert,
f'{ineq_path}/{measurements}_INF2{info}.csv')
visibilities += \
f"Critical visibility for {measurements} is {vcrit}\n"
else:
print(f"Problem for {measurements} failed with status "
+ InfSDP.solution_object["status"])
else:
visibilities += f"Critical visibility for {measurements} is 1\n"
else:
visibilities += f"{measurements} produces a constant distribution\n"
with open(f"tridentvisibilities_INF2{info}.txt", "w") as fileexport:
fileexport.write(visibilities)
###############################################################################
# Binary-input inequalities
###############################################################################
meas = [[0.5*(qt.qeye(2)+qt.sigmax()), 0.5*(qt.qeye(2)-qt.sigmax())],
[0.5*(qt.qeye(2)+qt.sigmay()), 0.5*(qt.qeye(2)-qt.sigmay())],
[0.5*(qt.qeye(2)+qt.sigmaz()), 0.5*(qt.qeye(2)-qt.sigmaz())]]
def prob_2in(vis, bases):
prob_array = np.zeros((2,2,2,2,2,2,2,2,2,2,2,2))
msmnts = [meas[bases[0]], meas[bases[1]]]
if isinstance(vis, Real):
state = rho("trident", vis)
for a,b,c,d,e,f,x,y,z,t,u,v in np.ndindex((2,2,2,2,2,2,2,2,2,2,2,2)):
prob_array[a,b,c,d,e,f,x,y,z,t,u,v] \
= qt.expect(state, qt.tensor(msmnts[x][a],
msmnts[y][b],
msmnts[z][c],
msmnts[t][d],
msmnts[u][e],
msmnts[v][f]))
else:
states = rho_trident_list()
prob_array = np.asarray(prob_array, dtype=object)
for a,b,c,d,e,f,x,y,z,t,u,v in np.ndindex((2,2,2,2,2,2,2,2,2,2,2,2)):
operator = qt.tensor(msmnts[x][a], msmnts[y][b],
msmnts[z][c], msmnts[t][d],
msmnts[u][e], msmnts[v][f])
prob_array[a,b,c,d,e,f,x,y,z,t,u,v] = (
vis**4 * qt.expect(states[0], operator)
+ vis**3 * qt.expect(states[1], operator)
+ vis**2 * qt.expect(states[2], operator)
+ vis * qt.expect(states[3], operator)
+ qt.expect(states[4], operator))
return prob_array
InfProb = InflationProblem(dag=dag,
outcomes_per_party=[2, 2, 2, 2, 2, 2],
settings_per_party=[2, 2, 2, 2, 2, 2],
inflation_level_per_source=2,
verbose=0
)
InfSDP = InflationSDP(InfProb)
Local1Len2 = InfSDP.build_columns('local1', max_monomial_length=2)
info = "Local1Len2"
InfSDP.generate_relaxation(Local1Len2)
for measurements in tqdm([[0, 1], [0, 2], [1, 2]],
desc="Getting 2-input inequalities for INF2" + info):
if measurements == [0, 1]:
input_names = 'XY'
elif measurements == [0, 2]:
input_names = 'XZ'
elif measurements == [1, 2]:
input_names = 'YZ'
else:
print("An error with the parsing of measurements has occurred")
break
InfSDP.reset("all")
InfSDP.set_distribution(prob_2in(vis, measurements))
if any([not isinstance(val, Real)
for val in InfSDP.known_moments.values()]):
vcrit = max_within_feasible(InfSDP, InfSDP.known_moments, "dual")
if abs(vcrit - 1) > 1e-3:
InfSDP.reset("all")
v = np.ceil(vcrit * 1000) / 1000
InfSDP.set_distribution(prob_2in(v, measurements))
InfSDP.solve(feas_as_optim=True)
if InfSDP.solution_object["status"] == "feasible":
print(f"Critical visibility for {info} and {input_names} is ",
vcrit)
cert = InfSDP.certificate_as_probs()
export_inequality(cert,
f"{ineq_path}/twoin_{input_names}_INF2{info}.csv")
else:
print("Problem for " + input_names + " failed with status "
+ InfSDP.solution_object["status"])
else:
print(f"Critical visibility for {input_names} is 1")
else:
print("The measurements " + input_names +
" give a trivial distribution at this level")