def test_wigner_bell1_su2parity():
"""wigner: testing the SU2 parity of the first Bell state.
"""
psi = bell_state('00')
steps = 25
theta = np.tile(np.linspace(0, np.pi, steps), 2).reshape(2, steps)
phi = np.tile(np.linspace(0, 2 * np.pi, steps), 2).reshape(2, steps)
slicearray = ['l', 'l']
wigner_analyt = np.zeros((steps, steps))
for t in range(steps):
for p in range(steps):
wigner_analyt[t, p] = np.real(((1 + np.sqrt(3)
* np.cos(theta[0, t]))
* (1 + np.sqrt(3)
* np.cos(theta[1, t]))
+ 3 * (np.sin(theta[0, t])
* np.exp(-1j * phi[0, p])
* np.sin(theta[1, t])
* np.exp(-1j * phi[1, p])
+ np.sin(theta[0, t])
* np.exp(1j * phi[0, p])
* np.sin(theta[1, t])
* np.exp(1j * phi[1, p]))
+ (1 - np.sqrt(3)
* np.cos(theta[0, t]))
* (1 - np.sqrt(3)
* np.cos(theta[1, t]))) / 8.)
wigner_theo = wigner_transform(psi, 0.5, False, steps, slicearray)
assert_(np.sum(np.abs(wigner_analyt - wigner_theo)) < 1e-11)
def test_wigner_ghz_su2parity():
"""wigner: testing the SU2 wigner transformation of the GHZ state.
"""
psi = (ket([0, 0, 0]) + ket([1, 1, 1])) / np.sqrt(2)
steps = 100
N = 3
theta = np.tile(np.linspace(0, np.pi, steps), N).reshape(N, steps)
phi = np.tile(np.linspace(0, 2 * np.pi, steps), N).reshape(N, steps)
slicearray = ['l', 'l', 'l']
wigner_analyt = np.zeros((steps, steps))
for t in range(steps):
for p in range(steps):
wigner_analyt[t, p] = np.real(
((1 + np.sqrt(3) * np.cos(theta[0, t])) *
(1 + np.sqrt(3) * np.cos(theta[1, t])) *
(1 + np.sqrt(3) * np.cos(theta[2, t])) + 3**(3 / 2) *
(np.sin(theta[0, t]) * np.exp(-1j * phi[0, p]) *
np.sin(theta[1, t]) * np.exp(-1j * phi[1, p]) *
np.sin(theta[2, t]) * np.exp(-1j * phi[2, p]) +
np.sin(theta[0, t]) * np.exp(1j * phi[0, p]) *
np.sin(theta[1, t]) * np.exp(1j * phi[1, p]) *
np.sin(theta[2, t]) * np.exp(1j * phi[2, p])) +
(1 - np.sqrt(3) * np.cos(theta[0, t])) *
(1 - np.sqrt(3) * np.cos(theta[1, t])) *
(1 - np.sqrt(3) * np.cos(theta[2, t]))) / 16.)
wigner_theo = wigner_transform(psi, 0.5, False, steps, slicearray)
assert_(np.sum(np.abs(wigner_analyt - wigner_theo)) < 1e-11)
def test_wigner_bell1_su2parity():
"""wigner: testing the SU2 parity of the first Bell state.
"""
psi = bell_state('00')
steps = 25
theta = np.tile(np.linspace(0, np.pi, steps), 2).reshape(2, steps)
phi = np.tile(np.linspace(0, 2 * np.pi, steps), 2).reshape(2, steps)
slicearray = ['l', 'l']
wigner_analyt = np.zeros((steps, steps))
for t in range(steps):
for p in range(steps):
wigner_analyt[t, p] = np.real(
((1 + np.sqrt(3) * np.cos(theta[0, t])) *
(1 + np.sqrt(3) * np.cos(theta[1, t])) + 3 *
(np.sin(theta[0, t]) * np.exp(-1j * phi[0, p]) *
np.sin(theta[1, t]) * np.exp(-1j * phi[1, p]) +
np.sin(theta[0, t]) * np.exp(1j * phi[0, p]) *
np.sin(theta[1, t]) * np.exp(1j * phi[1, p])) +
(1 - np.sqrt(3) * np.cos(theta[0, t])) *
(1 - np.sqrt(3) * np.cos(theta[1, t]))) / 8.)
wigner_theo = wigner_transform(psi, 0.5, False, steps, slicearray)
assert_(np.sum(np.abs(wigner_analyt - wigner_theo)) < 1e-11)
def test_angle_slicing():
"""wigner: tests angle slicing.
"""
psi1 = bell_state('00')
psi2 = bell_state('01')
psi3 = bell_state('10')
psi4 = bell_state('11')
steps = 100
j = 0.5
wigner1 = wigner_transform(psi1, j, False, steps, ['l', 'l'])
wigner2 = wigner_transform(psi2, j, False, steps, ['l', 'z'])
wigner3 = wigner_transform(psi3, j, False, steps, ['l', 'x'])
wigner4 = wigner_transform(psi4, j, False, steps, ['l', 'y'])
assert_(np.sum(np.abs(wigner2 - wigner1)) < 1e-11)
assert_(np.sum(np.abs(wigner3 - wigner2)) < 1e-11)
assert_(np.sum(np.abs(wigner4 - wigner3)) < 1e-11)
assert_(np.sum(np.abs(wigner4 - wigner1)) < 1e-11)
def test_angle_slicing():
"""wigner: tests angle slicing.
"""
psi1 = bell_state('00')
psi2 = bell_state('01')
psi3 = bell_state('10')
psi4 = bell_state('11')
steps = 100
j = 0.5
wigner1 = wigner_transform(psi1, j, False, steps, ['l', 'l'])
wigner2 = wigner_transform(psi2, j, False, steps, ['l', 'z'])
wigner3 = wigner_transform(psi3, j, False, steps, ['l', 'x'])
wigner4 = wigner_transform(psi4, j, False, steps, ['l', 'y'])
assert_(np.sum(np.abs(wigner2 - wigner1)) < 1e-11)
assert_(np.sum(np.abs(wigner3 - wigner2)) < 1e-11)
assert_(np.sum(np.abs(wigner4 - wigner3)) < 1e-11)
assert_(np.sum(np.abs(wigner4 - wigner1)) < 1e-11)
def test_wigner_bell4_su2parity():
"""wigner: testing the SU2 parity of the fourth Bell state.
"""
psi = bell_state('11')
steps = 100
slicearray = ['l', 'l']
wigner_analyt = np.zeros((steps, steps))
for t in range(steps):
for p in range(steps):
wigner_analyt[t, p] = -0.5
wigner_theo = wigner_transform(psi, 0.5, False, steps, slicearray)
assert_(np.sum(np.abs(wigner_analyt - wigner_theo)) < 1e-11)
def test_wigner_bell4_su2parity():
"""wigner: testing the SU2 parity of the fourth Bell state.
"""
psi = bell_state('11')
steps = 100
slicearray = ['l', 'l']
wigner_analyt = np.zeros((steps, steps))
for t in range(steps):
for p in range(steps):
wigner_analyt[t, p] = -0.5
wigner_theo = wigner_transform(psi, 0.5, False, steps, slicearray)
assert_(np.sum(np.abs(wigner_analyt - wigner_theo)) < 1e-11)
def test_wigner_bell4_fullparity():
"""wigner: testing the parity of the fourth Bell state using the parity of
the full space.
"""
psi = bell_state('11')
steps = 100
slicearray = ['l', 'l']
wigner_analyt = np.zeros((steps, steps))
for t in range(steps):
for p in range(steps):
wigner_analyt[t, p] = -0.30901699
print("wigner anal: ", wigner_analyt)
wigner_theo = wigner_transform(psi, 0.5, True, steps, slicearray)
print("wigner theo: ", wigner_theo)
assert_(np.sum(np.abs(wigner_analyt - wigner_theo)) < 1e-4)
def test_wigner_pure_su2():
"""wigner: testing the SU2 wigner transformation of a pure state.
"""
psi = (ket([1]))
steps = 100
theta = np.linspace(0, np.pi, steps)
phi = np.linspace(0, 2 * np.pi, steps)
theta = theta[None, :]
phi = phi[None, :]
slicearray = ['l']
wigner_analyt = np.zeros((steps, steps))
for t in range(steps):
for p in range(steps):
wigner_analyt[t, p] = (1 + np.sqrt(3) * np.cos(theta[0, t])) / 2.
wigner_theo = wigner_transform(psi, 0.5, False, steps, slicearray)
assert_(np.sum(np.abs(wigner_analyt - wigner_theo)) < 1e-11)
def test_wigner_pure_su2():
"""wigner: testing the SU2 wigner transformation of a pure state.
"""
psi = (ket([1]))
steps = 100
theta = np.linspace(0, np.pi, steps)
phi = np.linspace(0, 2 * np.pi, steps)
theta = theta[None, :]
phi = phi[None, :]
slicearray = ['l']
wigner_analyt = np.zeros((steps, steps))
for t in range(steps):
for p in range(steps):
wigner_analyt[t, p] = (1 + np.sqrt(3) * np.cos(theta[0, t])) / 2.
wigner_theo = wigner_transform(psi, 0.5, False, steps, slicearray)
assert_(np.sum(np.abs(wigner_analyt - wigner_theo)) < 1e-11)
def test_wigner_bell4_fullparity():
"""wigner: testing the parity of the fourth Bell state using the parity of
the full space.
"""
psi = bell_state('11')
steps = 100
slicearray = ['l', 'l']
wigner_analyt = np.zeros((steps, steps))
for t in range(steps):
for p in range(steps):
wigner_analyt[t, p] = -0.30901699
print("wigner anal: ", wigner_analyt)
wigner_theo = wigner_transform(psi, 0.5, True, steps, slicearray)
print("wigner theo: ", wigner_theo)
assert_(np.sum(np.abs(wigner_analyt - wigner_theo)) < 1e-4)
def test_wigner_ghz_su2parity():
"""wigner: testing the SU2 wigner transformation of the GHZ state.
"""
psi = (ket([0, 0, 0]) + ket([1, 1, 1])) / np.sqrt(2)
steps = 100
N = 3
theta = np.tile(np.linspace(0, np.pi, steps), N).reshape(N, steps)
phi = np.tile(np.linspace(0, 2 * np.pi, steps), N).reshape(N, steps)
slicearray = ['l', 'l', 'l']
wigner_analyt = np.zeros((steps, steps))
for t in range(steps):
for p in range(steps):
wigner_analyt[t, p] = np.real(((1 + np.sqrt(3)*np.cos(theta[0, t]))
* (1 + np.sqrt(3)
* np.cos(theta[1, t]))
* (1 + np.sqrt(3)
* np.cos(theta[2, t]))
+ 3**(3 / 2) * (np.sin(theta[0, t])
* np.exp(-1j * phi[0, p])
* np.sin(theta[1, t])
* np.exp(-1j * phi[1, p])
* np.sin(theta[2, t])
* np.exp(-1j * phi[2, p])
+ np.sin(theta[0, t])
* np.exp(1j * phi[0, p])
* np.sin(theta[1, t])
* np.exp(1j * phi[1, p])
* np.sin(theta[2, t])
* np.exp(1j * phi[2, p]))
+ (1 - np.sqrt(3)
* np.cos(theta[0, t]))
* (1 - np.sqrt(3)
* np.cos(theta[1, t]))
* (1 - np.sqrt(3)
* np.cos(theta[2, t]))) / 16.)
wigner_theo = wigner_transform(psi, 0.5, False, steps, slicearray)
assert_(np.sum(np.abs(wigner_analyt - wigner_theo)) < 1e-11)
