utils.py

# Code for
#
# Guarantees on the structure of experimental quantum networks
# npj Quantum Inf. 10, 117 (2024)
# arXiv:2403.02376
#
# Authors: Alejandro Pozas-Kerstjens
#
# Requires: numpy for array operations
#           pandas for dataset manipulation
#           sympy, symengine for symbolic operations
#           qutip for quantum states
#           csv, itertools, numbers
# 
# Last modified: Mar, 2024

import csv
import numpy as np
import pandas as pd
import qutip as qt

from itertools import product
from numbers import Real
from sympy import degree_list
from symengine import symbols

###############################################################################
# Functions for import and export of certificates
###############################################################################
def export_inequality(certificate, filename):
    if not len(certificate.as_coefficients_dict()) == 1:
        num_lines = max([sum(degree_list(mon))
                         for mon in certificate.as_coefficients_dict().keys()
                         if mon != 1])
    # Map from the symbols that represent inputs to a normalized notation
    input_map = {"-1": -1}
    input_idx = 0
    ineq_lines = []
    for mon, coeff in certificate.as_coefficients_dict().items():
        mon_lines = -np.ones((num_lines, 13), dtype=object)
        mon_lines[0, 0] = float(coeff)
        for idx in range(1, num_lines):
            mon_lines[idx, 0] = None
        if mon == 1:
            mon_lines[0, 0] = float(coeff)
        else:
            counter = 0
            for component in mon.as_ordered_factors():
                parties = np.array([ord(p) - 65
                           for p in str(component).split("(")[0][1:]])
                ins = []
                for ii in str(component).split("|")[1].split(")")[0]:
                    try:
                        ins.append(input_map[ii])
                    except KeyError:
                        input_map[ii] = input_idx
                        input_idx += 1
                        ins.append(input_map[ii])
                if len(str(component).split("**")) == 1:                   
                    line = -np.ones(12, dtype=object)
                    line[parties] = 0
                    line[6+parties] = ins
                    mon_lines[counter, 1:] = line
                    counter += 1
                else:
                    num_copies = int(str(component).split("**")[-1])
                    for _ in range(num_copies):
                        mon_lines[counter, 1+parties] = 0
                        mon_lines[counter, 1+6+parties] = ins
                        counter += 1
        ineq_lines += mon_lines.tolist()

    f = open(filename, "w")
    for line in ineq_lines:
        f.write(
            str(list(line))[1:-1].replace(" ", "").replace("None", ""))
        f.write("\n")
    f.close()

def import_ineq(ineq_path):
    with open(ineq_path) as csv_file:
        csv_reader = csv.reader(csv_file, delimiter=",")
        lines = []
        for row in csv_reader:
            lines.append(row)
    ineq_orig = np.array(lines)
    return ineq_orig

def eval_ineq(ineq, distribution):
    terms = []
    factors = []
    coeff = 0
    for line in ineq:
        if line[0] != "":
            terms.append([coeff, factors])
            coeff = float(line[0])
            factors = [process_line(line[1:], distribution)]
        else:
            factors.append(process_line(line[1:], distribution))
    # The very last line
    terms.append([coeff, factors])
    ineq_val = 0
    for term in terms:
        ineq_val += term[0] * np.prod(term[1])
    return ineq_val

def process_line(outs_ins, distribution):
    playing_parties = np.where(outs_ins[:6] == "0")[0]
    non_playing_parties = list(set(range(6)) - set(playing_parties.tolist()))
    ins = outs_ins[6:].astype(int)
    ins[non_playing_parties] = 0
    marginal = np.sum(
        distribution[...,ins[0],ins[1],ins[2],ins[3],ins[4],ins[5]],
        axis=tuple(non_playing_parties))
    if isinstance(marginal, float):
        return marginal
    else:
        return marginal.flatten()[0]    # Hack to get the p(0...0) element

###############################################################################
# Quantum states and distributions
###############################################################################
def rho_ghz_list():
    visqubed = [[1/16,-(1/16),0,0,0,0,-(1/16),1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),1/16,0,0,0,0,1/16,-(1/16),-(1/16),1/16,0,0,0,0,1/16,-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,-(1/16),0,0,0,0,-(1/16),1/16],
                [-(1/16),-(1/16),0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,1/16,1/16,1/16,1/16,0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,-(1/16),-(1/16)],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16,1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16)],
                [1/16,-(1/16),0,0,0,0,1/16,-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,-(1/16),0,0,0,0,1/16,-(1/16),-(1/16),1/16,0,0,0,0,-(1/16),1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),1/16,0,0,0,0,-(1/16),1/16],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [-(1/16),1/16,0,0,0,0,-(1/16),1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,-(1/16),0,0,0,0,1/16,-(1/16),-(1/16),1/16,0,0,0,0,-(1/16),1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,-(1/16),0,0,0,0,1/16,-(1/16)],
                [1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16,1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [1/16,1/16,0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,1/16,1/16,1/16,1/16,0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,1/16,1/16],
                [-(1/16),1/16,0,0,0,0,1/16,-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),1/16,0,0,0,0,1/16,-(1/16),-(1/16),1/16,0,0,0,0,1/16,-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),1/16,0,0,0,0,1/16,-(1/16)],
                [-(1/16),1/16,0,0,0,0,1/16,-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),1/16,0,0,0,0,1/16,-(1/16),-(1/16),1/16,0,0,0,0,1/16,-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),1/16,0,0,0,0,1/16,-(1/16)],
                [1/16,1/16,0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,1/16,1/16,1/16,1/16,0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,1/16,1/16],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
                [1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16,1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16],
                [-(1/16),1/16,0,0,0,0,-(1/16),1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,-(1/16),0,0,0,0,1/16,-(1/16),-(1/16),1/16,0,0,0,0,-(1/16),1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,-(1/16),0,0,0,0,1/16,-(1/16)],
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             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16),-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16)],
             [-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16),-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16)],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16,1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16],
             [1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16,1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16],
             [1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16,1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16],
             [1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16,1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16),-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16)],
             [-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16),-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16)],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16),-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16)],
             [-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16),-(1/16),-(1/16),0,0,0,0,1/16,1/16,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/16,1/16,0,0,0,0,-(1/16),-(1/16)],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16,1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16],
             [1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16,1/16,1/16,0,0,0,0,-(1/16),-(1/16),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/16),-(1/16),0,0,0,0,1/16,1/16]]
    return [qt.Qobj(state, dims=[[2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2]])
            for state in [visqubed, visquared, singlevis, novis]]

def rho_trident_list():
    visquart = [[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,-(1/64),0,1/64,0,-(1/64),0,1/64,0,-(1/64),0,-(1/64),0,1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,1/64,0,-(1/64),0,1/64,0,-(1/64),0,1/64,0,1/64,0,-(1/64)],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,1/64,0,-(1/64),0,-(1/64),0,1/64,0,1/64,0,1/64,0,1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,-(1/64),0,1/64,0,1/64,0,-(1/64),0,-(1/64),0,-(1/64),0,-(1/64),0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,-(1/64),0,1/64,0,-(1/64),0,1/64,0,-(1/64),0,-(1/64),0,1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,1/64,0,-(1/64),0,1/64,0,-(1/64),0,1/64,0,1/64,0,-(1/64)],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,-(1/64),0,1/64,0,1/64,0,-(1/64),0,-(1/64),0,-(1/64),0,-(1/64),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,1/64,0,-(1/64),0,-(1/64),0,1/64,0,1/64,0,1/64,0,1/64,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,-(1/64),0,1/64,0,-(1/64),0,1/64,0,-(1/64),0,-(1/64),0,1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,1/64,0,-(1/64),0,1/64,0,-(1/64),0,1/64,0,1/64,0,-(1/64)],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,-(1/64),0,1/64,0,1/64,0,-(1/64),0,-(1/64),0,-(1/64),0,-(1/64),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,1/64,0,-(1/64),0,-(1/64),0,1/64,0,1/64,0,1/64,0,1/64,0],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,-(1/64),0,1/64,0,-(1/64),0,1/64,0,-(1/64),0,-(1/64),0,1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,1/64,0,-(1/64),0,1/64,0,-(1/64),0,1/64,0,1/64,0,-(1/64)],
                [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,1/64,0,-(1/64),0,-(1/64),0,1/64,0,1/64,0,1/64,0,1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,-(1/64),0,1/64,0,1/64,0,-(1/64),0,-(1/64),0,-(1/64),0,-(1/64),0],
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             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,0,0,0,0,1/64,0,1/64,0,0,0,0,0,-(1/64),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
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             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,1/64,0,0,0,0,0,1/64,0,-(1/64),0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,-(1/64),0,0,0,0,0,-(1/64),0,1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,-(1/64),0,0,0,0,0,-(1/64),0,1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,0,0,0,0,-(1/64),0,-(1/64),0,0,0,0,0,1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,0,0,0,0,-(1/64),0,-(1/64),0,0,0,0,0,1/64,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,0,0,0,0,-(1/64),0,1/64,0,0,0,0,0,1/64,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,0,0,0,0,-(1/64),0,1/64,0,0,0,0,0,1/64],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,-(1/64),0,0,0,0,0,1/64,0,1/64,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,-(1/64),0,0,0,0,0,1/64,0,1/64,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,1/64,0,0,0,0,0,-(1/64),0,-(1/64),0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,1/64,0,0,0,0,0,-(1/64),0,-(1/64),0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,0,0,0,0,1/64,0,-(1/64),0,0,0,0,0,-(1/64),0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,-(1/64),0,0,0,0,0,1/64,0,-(1/64),0,0,0,0,0,-(1/64)],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,0,0,0,0,-(1/64),0,1/64,0,0,0,0,0,1/64,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,0,0,0,0,-(1/64),0,1/64,0,0,0,0,0,1/64],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,-(1/64),0,0,0,0,0,1/64,0,1/64,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,-(1/64),0,0,0,0,0,1/64,0,1/64,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,-(1/64),0,0,0,0,0,1/64,0,1/64,0,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,-(1/64),0,0,0,0,0,1/64,0,1/64,0,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,0,0,0,0,-(1/64),0,1/64,0,0,0,0,0,1/64,0],
             [0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1/64,0,0,0,0,0,-(1/64),0,1/64,0,0,0,0,0,1/64]]
    return [qt.Qobj(state, dims=[[2, 2, 2, 2, 2, 2], [2, 2, 2, 2, 2, 2]]) for state in [visquart, visqubed, visquared, singlevis, novis]]

def rho(name, vis=1):
    if name.lower() == "ghz":
        states = rho_ghz_list()
    elif name.lower() == "trident":
        states = rho_trident_list()
    else:
        raise ValueError(f"Unknown state name: {name}. "
                         + "It should be 'ghz' or 'trident'.")
    return sum(vis**(len(states)-k-1) * state for k, state in enumerate(states))

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_noin(vis, state, measurements):
    prob_array = np.zeros((2,2,2,2,2,2,1,1,1,1,1,1))
    meas_choices = [ord(inp) - 88 for inp in measurements]
    x, y, z, t, u, v = meas_choices
    if isinstance(vis, Real):
        st = rho(state, vis)
        for a,b,c,d,e,f in np.ndindex((2,2,2,2,2,2)):
            prob_array[a,b,c,d,e,f,0,0,0,0,0,0] \
                = qt.expect(st, qt.tensor(meas[x][a], meas[y][b],
                                          meas[z][c], meas[t][d],
                                          meas[u][e], meas[v][f]))
    else:
        states = rho_trident_list() if state == "trident" else rho_ghz_list()
        prob_array = np.asarray(prob_array, dtype=object)
        for a,b,c,d,e,f in np.ndindex((2,2,2,2,2,2)):
            operator = qt.tensor(meas[x][a], meas[y][b], meas[z][c],
                                 meas[t][d], meas[u][e], meas[v][f])
            prob_array[a,b,c,d,e,f,0,0,0,0,0,0] = \
                sum(vis**(len(states)-k-1) * qt.expect(st, operator)
                    for k, st in enumerate(states))
    return prob_array

def prob_2in(vis, state, bases):
    prob_array = np.zeros((2,2,2,2,2,2,2,2,2,2,2,2))
    bases = [ord(lett) - 88 for lett in bases]
    msmnts = [meas[bases[0]], meas[bases[1]]]
    st = rho(state, 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(st, qt.tensor(msmnts[x][a], msmnts[y][b], msmnts[z][c],
                                    msmnts[t][d], msmnts[u][e], msmnts[v][f]))
    return prob_array

###############################################################################
# Functions for certificate evaluation
###############################################################################
def read_ineq(path, num_inputs=1):
    inequality_data = np.loadtxt(path, delimiter=",", dtype=str)

    ineq = 0.
    parties = np.array(list("ABCDEF"))
    skip = np.where(inequality_data[:,0] != "")[0]
    skip = skip[1]- skip[0]
    for ii in range(0, len(inequality_data), skip):
        block = inequality_data[ii:ii+skip,:]
        term = 1.
        for line in block:
            if line[1:].tolist() == ["-1"] * 12:
                term *= 1.
            else:
                outputs = np.array(line[1:7])
                inputs = np.array(line[7:])
                relevant = np.where(outputs == "0")[0]
                prob_name = "p_{" + "".join(parties[relevant]) + "}"
                if num_inputs == 2:
                    prob_name += "(" + "".join(inputs[relevant]) + ")"
                prob = symbols(prob_name)
                term *= prob
        ineq += float(block[0, 0])*term
    return ineq

def expand_ineq(ineq):
    subs = {}
    for symb in ineq.free_symbols:
        parties = list(symb.name.split("{")[-1].split("}")[0])
        summationterms = np.array(list(product([0, 1],
                                               repeat=6-len(parties)))
                                  ).astype(str)
        parties_pos = [ord(party) - 65 for party in parties]
        # Hack so that np.insert works well.
        # It seems to do things sequentially, so for the second insertion we
        # have to take into account that the first one was done
        parties_ord = []
        for ii, party in enumerate(parties_pos):
            parties_ord.append(party-ii)
        summationterms = np.insert(summationterms, parties_ord, "0", 1)
        subs.update({symb: np.sum([symbols(
            ("p_{" + "".join(outs)).replace("0","T").replace("1","R") + "}"
                                           ) for outs in summationterms])})
    return ineq.subs(subs)

def error_expr(ineq):
    errorsquared = 0
    for symb in ineq.free_symbols:
        errorsquared += (ineq.diff(symb, 1)
                         * symbols(f"\Delta_{symb.name[2:]}"))**2
    return errorsquared

def get_distr_from_data(path, experiment_source, frac=1):
    """Obtain the empirical distributions"""
    if experiment_source.lower() == "ghz":
        names = ["".join(letters) for letters in product(["T","R"], repeat=6)]
        dataset = pd.read_csv(path, header=0).dropna(axis=1)[names]
        n_counts = dataset.values.sum()
        prob = dataset.sample(frac=frac).to_numpy().sum(axis=0)
    elif experiment_source.lower() == "trident":
        dataset = np.genfromtxt(path, delimiter=",")
        prob = dataset[17:]
        n_counts = np.sum(prob)
    return prob / np.sum(prob), n_counts

def expand_ineq_2in(ineq, available_bases, eval_bases="XZ"):
    subs = {}
    for symb in ineq.free_symbols:
        parties = list(symb.name.split("{")[-1].split("}")[0])
        inputs = list(symb.name.split("(")[-1].split(")")[0])
        try:
            inputs = [eval_bases[int(i)] for i in inputs]
        except ValueError:
            continue
        summationterms = np.array(list(product([0, 1],
                                               repeat=6-len(parties)))
                                  ).astype(str)
        parties_pos = [ord(party) - 65 for party in parties]

        summationbases = [bases for bases in available_bases
                          if all([bases[party] == inpt
                                  for party, inpt in zip(parties_pos, inputs)])]
        # Hack so that np.insert works well.
        # It seems to do things sequentially, so for the second insertion we
        # have to take into account that the first one was done
        parties_ord = []
        for ii, party in enumerate(parties_pos):
            parties_ord.append(party-ii)
        summationterms = np.insert(summationterms, parties_ord, "0", 1)
        subs.update({symb: 1/len(summationbases) * np.sum([symbols(
            ("p_{" + "".join(outs)).replace("0", "T").replace("1", "R")
             + "}(" + "".join(ins) + ")")
            for outs, ins in product(summationterms, summationbases)])})
    return ineq.subs(subs)

def get_means_stds(ineq, available_bases, eval_bases, exp_probs):
    """Obtain the average distribution and 1-sigma confidence intervals for
    the trident data"""
    means = {}
    stds  = {}

    for symb in ineq.free_symbols:
        parties = list(symb.name.split("{")[-1].split("}")[0])
        inputs = list(symb.name.split("(")[-1].split(")")[0])
        summationterms = np.array(list(product([0, 1],
                                               repeat=6-len(parties)))
                                  ).astype(str)
        parties_pos = [ord(party) - 65 for party in parties]
        inputs = [eval_bases[int(i)] for i in inputs]
        summationbases = [bases for bases in available_bases
                          if all([bases[party] == inpt
                                  for party, inpt in zip(parties_pos, inputs)])]
        # Hack so that np.insert works well.
        # It seems to do things sequentially, so for the second insertion we
        # have to take into account that the first one was done
        parties_ord = []
        for ii, party in enumerate(parties_pos):
            parties_ord.append(party-ii)
        summationterms = np.insert(summationterms, parties_ord, "0", 1)
        eval_per_base = []
        for base in summationbases:
            probs = exp_probs["".join(base)][1.0][0]
            eval_per_base.append(sum(probs[int("".join(outs), 2)]
                                     for outs in summationterms))
        means.update({symb: np.mean(eval_per_base)})
        stds.update({symbols(f"\Delta{symb.name[1:]}"): np.std(eval_per_base)})
    return means, stds