def dbs_circuit_test_():
ns = 5 * 10**3
cxx = np.zeros(ns)
cyy = np.zeros(ns)
czz = np.zeros(ns)
p = np.zeros((2, 2))
a = np.zeros(4)
for j in range(0, ns):
rpv = rpvg.rpv_zhsl(4)
a = np.reshape(rpv, (2, 2))
alpha, beta, gamma = bds_circuit_angles(a)
psi = bds_circuit_(alpha, beta, gamma)
rhor = ptr.pTraceL(4, 4, mf.proj(16, psi))
cm = gm.corr_mat(2, 2, rhor)
cxx[j] = cm[0][0]
cyy[j] = cm[1][1]
czz[j] = cm[2][2]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(cxx, cyy, czz, c='b', marker='o', s=0.75)
ax.set_xlabel('c_xx')
ax.set_ylabel('c_yy')
ax.set_zlabel('c_zz')
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.set_zlim(-1, 1)
ax.plot([-1, 1], [-1, 1], [-1, -1], color='b')
ax.plot([-1, 1], [1, -1], [1, 1], color='b')
ax.plot([-1, 1], [-1, -1], [-1, 1], color='b')
ax.plot([-1, -1], [-1, 1], [-1, 1], color='b')
ax.plot([1, -1], [1, 1], [-1, 1], color='b')
ax.plot([1, 1], [1, -1], [-1, 1], color='b')
plt.show()
def dbs_rpv_test():
from states import bell
ns = 5 * 10**3
cxx = np.zeros(ns)
cyy = np.zeros(ns)
czz = np.zeros(ns)
for j in range(0, ns):
rpv = rpvg.rpv_zhsl(4)
rhor = rpv[0] * mf.proj(4, bell(0, 0)) + rpv[1] * mf.proj(
4, bell(0, 1))
rhor += (rpv[2] * mf.proj(4, bell(1, 0)) +
rpv[3] * mf.proj(4, bell(1, 1)))
cm = gm.corr_mat(2, 2, rhor)
cxx[j] = cm[0][0]
cyy[j] = cm[1][1]
czz[j] = cm[2][2]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(cxx, cyy, czz, c='b', marker='o', s=0.5)
ax.set_xlabel('c_xx')
ax.set_ylabel('c_yy')
ax.set_zlabel('c_zz')
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.set_zlim(-1, 1)
ax.plot([-1, 1], [-1, 1], [-1, -1], color='b')
ax.plot([-1, 1], [1, -1], [1, 1], color='b')
ax.plot([-1, 1], [-1, -1], [-1, 1], color='b')
ax.plot([-1, -1], [-1, 1], [-1, 1], color='b')
ax.plot([1, -1], [1, 1], [-1, 1], color='b')
ax.plot([1, 1], [1, -1], [-1, 1], color='b')
plt.show()
def dbs_circuit_test():
ns = 5 * 10**3
cxx = np.zeros(ns)
cyy = np.zeros(ns)
czz = np.zeros(ns)
for j in range(0, ns):
rpv = rpvg.rpv_zhsl(4)
theta = 2.0 * math.acos(math.sqrt(rpv[0] + rpv[1]))
alpha = 2.0 * math.acos(math.sqrt(rpv[0] + rpv[2]))
psi = bds_circuit(theta, alpha)
rhor = ptr.pTraceL(4, 4, mf.proj(16, psi))
cm = gm.corr_mat(2, 2, rhor)
cxx[j] = cm[0][0]
cyy[j] = cm[1][1]
czz[j] = cm[2][2]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(cxx, cyy, czz, c='b', marker='o', s=1)
ax.set_xlabel('c_xx')
ax.set_ylabel('c_yy')
ax.set_zlabel('c_zz')
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.set_zlim(-1, 1)
ax.plot([-1, 1], [-1, 1], [-1, -1], color='b')
ax.plot([-1, 1], [1, -1], [1, 1], color='b')
ax.plot([-1, 1], [-1, -1], [-1, 1], color='b')
ax.plot([-1, -1], [-1, 1], [-1, 1], color='b')
ax.plot([1, -1], [1, 1], [-1, 1], color='b')
ax.plot([1, 1], [1, -1], [-1, 1], color='b')
plt.show()
def steering(rho): # arXiv:1510.08030
import gell_mann as gm
# cm = np.zeros(3,3)
cm = gm.corr_mat(2, 2, rho)
W = np.zeros(3)
# W = LA.eigvalsh(cm)
u, W, vh = LA.svd(cm, full_matrices=True)
return max(0,
(sqrt((W[0]**2) + (W[1]**2) + (W[2]**2)) - 1) / (sqrt(3) - 1))
'''
def chsh(rho): # arXiv:1510.08030
import gell_mann as gm
# cm = np.zeros(3, 3)
cm = gm.corr_mat(2, 2, rho)
W = np.zeros(3)
# W = LA.eigvalsh(cm)
u, W, vh = LA.svd(cm, full_matrices=True)
no = np.sqrt(2) - 1
nl = (sqrt(W[0]**2 + W[1]**2 + W[2]**2 - min(W[0], W[1], W[2])**2) -
1) / no
return max(0, nl)
def hellinger(da, db, rho): # arXiv:1510.06995
daa = da**2 - 1
M = mat_sqrt(da * db, rho)
A = pTraceR(da, db, M)
bva = gm.bloch_vector(da, A) / sqrt(2 * db)
B = pTraceL(da, db, M)
bvb = gm.bloch_vector(db, B) / 2
cm = gm.corr_mat(da, db, M) / 2
ev = np.zeros(3)
ev = LA.eigvalsh(
outerr(daa, bva, bva) + np.matmul(cm, transpose(3, 3, cm)))
mev = max(ev[0], ev[1], ev[2])
bvbn = normr(2, bvb)
nor = 1 - 1 / sqrt(da)
return max(
0, (1 - sqrt((trace(da, A) / sqrt(2 * db))**2 + bvbn**2 + mev)) / nor)
def dbs_circuit_test_angles_():
ns = 20**3
cxx = np.zeros(ns)
cyy = np.zeros(ns)
czz = np.zeros(ns)
m = -1
da = math.pi / 20
alpha = -math.pi / 2 - da
for j in range(0, 20):
alpha += da
beta = -da
for k in range(0, 20):
beta += da
gamma = -da
for l in range(0, 20):
gamma += da
psi = bds_circuit_(alpha, beta, gamma)
rhor = ptr.pTraceL(4, 4, mf.proj(16, psi))
cm = gm.corr_mat(2, 2, rhor)
m += 1
cxx[m] = cm[0][0]
cyy[m] = cm[1][1]
czz[m] = cm[2][2]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(cxx, cyy, czz, c='b', marker='o', s=0.75)
ax.set_xlabel('c_xx')
ax.set_ylabel('c_yy')
ax.set_zlabel('c_zz')
ax.set_xlim(-1, 1)
ax.set_ylim(-1, 1)
ax.set_zlim(-1, 1)
ax.plot([-1, 1], [-1, 1], [-1, -1], color='b')
ax.plot([-1, 1], [1, -1], [1, 1], color='b')
ax.plot([-1, 1], [-1, -1], [-1, 1], color='b')
ax.plot([-1, -1], [-1, 1], [-1, 1], color='b')
ax.plot([1, -1], [1, 1], [-1, 1], color='b')
ax.plot([1, 1], [1, -1], [-1, 1], color='b')
plt.show()