def pr_box(eta=1, name=False):
"""
The Popescu-Rohrlich box, or PR box, is the canonical non-signalling, non-local probability
distribution used in the study of superquantum correlations. It has two space-like seperated
inputs, X and Y, and two associated outputs, A and B.
`eta` is the noise level of this correlation. For 0 <= eta <= 1/2 the box can be realized
classically. For 1/2 < eta <= 1/sqrt(2) the box can be realized quantum-mechanically.
Parameters
----------
eta : float, 0 <= eta <= 1
The noise level of the box. Defaults to 1.
name : bool
Whether to set rv names or not. Defaults to False.
Returns
-------
pr : Distribution
The PR box distribution.
"""
outcomes = list(product([0, 1], repeat=4))
pmf = [ ((1+eta)/16 if (x*y == a^b) else (1-eta)/16) for x, y, a, b in outcomes ]
pr = Distribution(outcomes, pmf)
if name:
pr.set_rv_names("XYAB")
return pr
def test_parse_rvs2():
outcomes = ['00', '11']
pmf = [1 / 2] * 2
d = Distribution(outcomes, pmf)
d.set_rv_names('XY')
with pytest.raises(ditException):
parse_rvs(d, ['X', 'Y', 'Z'])
def test_parse_rvs2():
outcomes = ['00', '11']
pmf = [1/2]*2
d = Distribution(outcomes, pmf)
d.set_rv_names('XY')
with pytest.raises(ditException):
parse_rvs(d, ['X', 'Y', 'Z'])
def pr_box(eta=1, name=False):
"""
The Popescu-Rohrlich box, or PR box, is the canonical non-signalling,
non-local probability distribution used in the study of superquantum
correlations. It has two space-like seperated inputs, X and Y, and two
associated outputs, A and B.
`eta` is the noise level of this correlation. For 0 <= eta <= 1/2 the box
can be realized classically. For 1/2 < eta <= 1/sqrt(2) the box can be
realized quantum-mechanically.
Parameters
----------
eta : float, 0 <= eta <= 1
The noise level of the box. Defaults to 1.
name : bool
Whether to set rv names or not. Defaults to False.
Returns
-------
pr : Distribution
The PR box distribution.
"""
outcomes = list(product([0, 1], repeat=4))
pmf = [((1 + eta) / 16 if (x * y == a ^ b) else (1 - eta) / 16)
for x, y, a, b in outcomes]
pr = Distribution(outcomes, pmf)
if name:
pr.set_rv_names("XYAB")
return pr
def test_K4():
outcomes = ['00', '01', '10', '11', '22', '33']
pmf = [1/8, 1/8, 1/8, 1/8, 1/4, 1/4]
d = Distribution(outcomes, pmf)
assert_almost_equal(K(d), 1.5)
assert_almost_equal(K(d, [[0],[1]]), 1.5)
d.set_rv_names("XY")
assert_almost_equal(K(d, [['X'],['Y']]), 1.5)
def test_K1():
outcomes = ['00', '11']
pmf = [1/2, 1/2]
d = Distribution(outcomes, pmf)
assert_almost_equal(K(d), 1.0)
assert_almost_equal(K(d, [[0],[1]]), 1.0)
d.set_rv_names("XY")
assert_almost_equal(K(d, [['X'],['Y']]), 1.0)
def test_K3():
""" Test K for mixed events """
outcomes = ['00', '01', '11']
pmf = [1/3, 1/3, 1/3]
d = Distribution(outcomes, pmf)
assert_almost_equal(K(d), 0.0)
assert_almost_equal(K(d, [[0], [1]]), 0.0)
d.set_rv_names("XY")
assert_almost_equal(K(d, [['X'], ['Y']]), 0.0)
def test_fci2():
"""
Test known values w/ rv names.
"""
d = Distribution(['000', '011', '101', '110'], [1 / 4] * 4)
d.set_rv_names('XYZ')
assert F(d) == pytest.approx(2.0)
assert F(d, ['X', 'Y']) == pytest.approx(0.0)
assert F(d, ['X', 'Y'], 'Z') == pytest.approx(1.0)
def test_K3():
""" Test K for mixed events """
outcomes = ['00', '01', '11']
pmf = [1 / 3, 1 / 3, 1 / 3]
d = Distribution(outcomes, pmf)
assert_almost_equal(K(d), 0.0)
assert_almost_equal(K(d, [[0], [1]]), 0.0)
d.set_rv_names("XY")
assert_almost_equal(K(d, [['X'], ['Y']]), 0.0)
def test_K4():
""" Test K in a canonical example """
outcomes = ['00', '01', '10', '11', '22', '33']
pmf = [1/8, 1/8, 1/8, 1/8, 1/4, 1/4]
d = Distribution(outcomes, pmf)
assert K(d) == pytest.approx(1.5)
assert K(d, [[0], [1]]) == pytest.approx(1.5)
d.set_rv_names("XY")
assert K(d, [['X'], ['Y']]) == pytest.approx(1.5)
def test_K3():
""" Test K for mixed events """
outcomes = ['00', '01', '11']
pmf = [1/3, 1/3, 1/3]
d = Distribution(outcomes, pmf)
assert K(d) == pytest.approx(0.0)
assert K(d, [[0], [1]]) == pytest.approx(0.0)
d.set_rv_names("XY")
assert K(d, [['X'], ['Y']]) == pytest.approx(0.0)
def test_K1():
""" Test K for dependent events """
outcomes = ['00', '11']
pmf = [1 / 2] * 2
d = Distribution(outcomes, pmf)
assert K(d) == pytest.approx(1.0)
assert K(d, [[0], [1]]) == pytest.approx(1.0)
d.set_rv_names("XY")
assert K(d, [['X'], ['Y']]) == pytest.approx(1.0)
def test_K3():
""" Test K for mixed events """
outcomes = ['00', '01', '11']
pmf = [1 / 3] * 3
d = Distribution(outcomes, pmf)
assert K(d) == pytest.approx(0.0)
assert K(d, [[0], [1]]) == pytest.approx(0.0)
d.set_rv_names("XY")
assert K(d, [['X'], ['Y']]) == pytest.approx(0.0)
def test_K1():
""" Test K for dependent events """
outcomes = ['00', '11']
pmf = [1/2, 1/2]
d = Distribution(outcomes, pmf)
assert K(d) == pytest.approx(1.0)
assert K(d, [[0], [1]]) == pytest.approx(1.0)
d.set_rv_names("XY")
assert K(d, [['X'], ['Y']]) == pytest.approx(1.0)
def test_K4():
""" Test K in a canonical example """
outcomes = ['00', '01', '10', '11', '22', '33']
pmf = [1 / 8, 1 / 8, 1 / 8, 1 / 8, 1 / 4, 1 / 4]
d = Distribution(outcomes, pmf)
assert K(d) == pytest.approx(1.5)
assert K(d, [[0], [1]]) == pytest.approx(1.5)
d.set_rv_names("XY")
assert K(d, [['X'], ['Y']]) == pytest.approx(1.5)
def test_K1():
""" Test K for dependent events """
outcomes = ['00', '11']
pmf = [1 / 2, 1 / 2]
d = Distribution(outcomes, pmf)
assert_almost_equal(K(d), 1.0)
assert_almost_equal(K(d, [[0], [1]]), 1.0)
d.set_rv_names("XY")
assert_almost_equal(K(d, [['X'], ['Y']]), 1.0)
def test_K2():
""" Test conditional K for dependent events """
outcomes = ['00', '11']
pmf = [1 / 2, 1 / 2]
d = Distribution(outcomes, pmf)
assert K(d, [[0], [1]], [0]) == pytest.approx(0.0)
assert K(d, [[0], [1]], [1]) == pytest.approx(0.0)
d.set_rv_names("XY")
assert K(d, [['X'], ['Y']], ['X']) == pytest.approx(0.0)
assert K(d, [['X'], ['Y']], ['Y']) == pytest.approx(0.0)
def test_K2():
""" Test conditional K for dependent events """
outcomes = ['00', '11']
pmf = [1/2, 1/2]
d = Distribution(outcomes, pmf)
assert_almost_equal(K(d, [[0], [1]], [0]), 0.0)
assert_almost_equal(K(d, [[0], [1]], [1]), 0.0)
d.set_rv_names("XY")
assert_almost_equal(K(d, [['X'], ['Y']], ['X']), 0.0)
assert_almost_equal(K(d, [['X'], ['Y']], ['Y']), 0.0)
def test_K5():
outcomes = ['000', '010', '100', '110', '221', '331']
pmf = [1/8, 1/8, 1/8, 1/8, 1/4, 1/4]
d = Distribution(outcomes, pmf)
assert_almost_equal(K(d, [[0],[1]]), 1.5)
assert_almost_equal(K(d), 1.0)
assert_almost_equal(K(d, [[0],[1],[2]]), 1.0)
d.set_rv_names("XYZ")
assert_almost_equal(K(d, [['X'],['Y']]), 1.5)
assert_almost_equal(K(d, [['X'],['Y'],['Z']]), 1.0)
assert_almost_equal(K(d, ['X', 'Y'], ['Z']), 0.5)
assert_almost_equal(K(d, ['XY', 'YZ']), 2.0)
def test_K5():
""" Test K on subvariables and conditionals """
outcomes = ['000', '010', '100', '110', '221', '331']
pmf = [1 / 8, 1 / 8, 1 / 8, 1 / 8, 1 / 4, 1 / 4]
d = Distribution(outcomes, pmf)
assert K(d, [[0], [1]]) == pytest.approx(1.5)
assert K(d) == pytest.approx(1.0)
assert K(d, [[0], [1], [2]]) == pytest.approx(1.0)
d.set_rv_names("XYZ")
assert K(d, [['X'], ['Y']]) == pytest.approx(1.5)
assert K(d, [['X'], ['Y'], ['Z']]) == pytest.approx(1.0)
assert K(d, ['X', 'Y'], ['Z']) == pytest.approx(0.5)
assert K(d, ['XY', 'YZ']) == pytest.approx(2.0)
def test_K5():
""" Test K on subvariables and conditionals """
outcomes = ['000', '010', '100', '110', '221', '331']
pmf = [1/8, 1/8, 1/8, 1/8, 1/4, 1/4]
d = Distribution(outcomes, pmf)
assert K(d, [[0], [1]]) == pytest.approx(1.5)
assert K(d) == pytest.approx(1.0)
assert K(d, [[0], [1], [2]]) == pytest.approx(1.0)
d.set_rv_names("XYZ")
assert K(d, [['X'], ['Y']]) == pytest.approx(1.5)
assert K(d, [['X'], ['Y'], ['Z']]) == pytest.approx(1.0)
assert K(d, ['X', 'Y'], ['Z']) == pytest.approx(0.5)
assert K(d, ['XY', 'YZ']) == pytest.approx(2.0)
def test_M2():
""" Test M with rv names """
outcomes = ['000',
'a00',
'00c',
'a0c',
'011',
'a11',
'101',
'b01',
'01d',
'a1d',
'10d',
'b0d',
'110',
'b10',
'11c',
'b1c',]
pmf = [1/16]*16
d = Distribution(outcomes, pmf)
d.set_rv_names('XYZ')
assert_almost_equal(M(d), 2.0)
def test_M2():
""" Test M with rv names """
outcomes = [
'000',
'a00',
'00c',
'a0c',
'011',
'a11',
'101',
'b01',
'01d',
'a1d',
'10d',
'b0d',
'110',
'b10',
'11c',
'b1c',
]
pmf = [1 / 16] * 16
d = Distribution(outcomes, pmf)
d.set_rv_names('XYZ')
assert M(d) == pytest.approx(2.0)
from hypothesis import given, settings
import numpy as np
from dit import Distribution
from dit.example_dists.intrinsic import intrinsic_1, intrinsic_2, intrinsic_3
from dit.exceptions import ditException
from dit.multivariate import total_correlation
from dit.multivariate.secret_key_agreement import intrinsic_mutual_informations as IMI
from dit.utils.testing import distributions
dist1 = Distribution([(0,0,0), (0,1,1), (1,0,1), (1,1,0), (2,2,2), (3,3,3)], [1/8]*4+[1/4]*2)
dist2 = Distribution(['000', '011', '101', '110', '222', '333'], [1/8]*4+[1/4]*2)
dist2.set_rv_names('XYZ')
dist3 = Distribution(['00000', '00101', '11001', '11100', '22220', '33330'], [1/8]*4+[1/4]*2)
dist4 = Distribution(['00000', '00101', '11001', '11100', '22220', '33330'], [1/8]*4+[1/4]*2)
dist4.set_rv_names('VWXYZ')
dist5 = Distribution(['0000', '0011', '0101', '0110', '1001', '1010', '1100', '1111'], [1/8]*8)
dist6 = Distribution(['0000', '0011', '0101', '0110', '1001', '1010', '1100', '1111'], [1/8]*8)
dist6.set_rv_names('WXYZ')
@pytest.mark.flaky(reruns=5)
def test_itc1():
"""
Test against standard result.
"""
itc = IMI.intrinsic_total_correlation(dist1, [[0], [1]], [2])
assert itc == pytest.approx(0)
"""
from __future__ import division
import pytest
import numpy as np
from dit import Distribution
from dit.profiles import SchneidmanProfile
ex1 = Distribution(['000', '001', '010', '011', '100', '101', '110', '111'], [1/8]*8)
ex2 = Distribution(['000', '111'], [1/2]*2)
ex3 = Distribution(['000', '001', '110', '111'], [1/4]*4)
ex4 = Distribution(['000', '011', '101', '110'], [1/4]*4)
ex4.set_rv_names('XYZ')
@pytest.mark.parametrize(('ex', 'prof'), [
(ex1, (0.0, 0.0, 0.0)),
(ex2, (0.0, 2.0, 0.0)),
(ex3, (0.0, 1.0, 0.0)),
(ex4, (0.0, 0.0, 1.0)),
])
def test_schneidman_profile(ex, prof):
"""
Test against known examples.
"""
sp = SchneidmanProfile(ex)
assert np.allclose([sp.profile[i] for i in (1, 2, 3)], prof, atol=1e-5)
def test_parse_rvs2():
outcomes = ['00', '11']
pmf = [1/2]*2
d = Distribution(outcomes, pmf)
d.set_rv_names('XY')
assert_raises(ditException, parse_rvs, d, ['X', 'Y', 'Z'])
def test_parse_rvs2():
outcomes = ['00', '11']
pmf = [1 / 2] * 2
d = Distribution(outcomes, pmf)
d.set_rv_names('XY')
assert_raises(ditException, parse_rvs, d, ['X', 'Y', 'Z'])
"""
from __future__ import division
import pytest
import numpy as np
from dit import Distribution
from dit.profiles import ConnectedInformations, ConnectedDualInformations
ex1 = Distribution(['000', '001', '010', '011', '100', '101', '110', '111'], [1/8]*8)
ex2 = Distribution(['000', '111'], [1/2]*2)
ex3 = Distribution(['000', '001', '110', '111'], [1/4]*4)
ex4 = Distribution(['000', '011', '101', '110'], [1/4]*4)
ex4.set_rv_names('XYZ')
@pytest.mark.parametrize(('ex', 'prof'), [
(ex1, (0.0, 0.0, 0.0)),
(ex2, (0.0, 2.0, 0.0)),
(ex3, (0.0, 1.0, 0.0)),
(ex4, (0.0, 0.0, 1.0)),
])
def test_connected_information(ex, prof):
"""
Test against known examples.
"""
ci = ConnectedInformations(ex)
assert np.allclose([ci.profile[i] for i in (1, 2, 3)], prof, atol=1e-5)
from hypothesis import given
import numpy as np
from dit import Distribution
from dit.example_dists.intrinsic import intrinsic_1, intrinsic_2, intrinsic_3
from dit.exceptions import ditException
from dit.multivariate import total_correlation
from dit.multivariate.secret_key_agreement import intrinsic_mutual_informations as IMI
from dit.utils.testing import distributions
dist1 = Distribution([(0,0,0), (0,1,1), (1,0,1), (1,1,0), (2,2,2), (3,3,3)], [1/8]*4+[1/4]*2)
dist2 = Distribution(['000', '011', '101', '110', '222', '333'], [1/8]*4+[1/4]*2)
dist2.set_rv_names('XYZ')
dist3 = Distribution(['00000', '00101', '11001', '11100', '22220', '33330'], [1/8]*4+[1/4]*2)
dist4 = Distribution(['00000', '00101', '11001', '11100', '22220', '33330'], [1/8]*4+[1/4]*2)
dist4.set_rv_names('VWXYZ')
dist5 = Distribution(['0000', '0011', '0101', '0110', '1001', '1010', '1100', '1111'], [1/8]*8)
dist6 = Distribution(['0000', '0011', '0101', '0110', '1001', '1010', '1100', '1111'], [1/8]*8)
dist6.set_rv_names('WXYZ')
@pytest.mark.flaky(reruns=5)
def test_itc1():
"""
Test against standard result.
"""
itc = IMI.intrinsic_total_correlation(dist1, [[0], [1]], [2])
assert itc == pytest.approx(0)
