def get_pqurec(state, post_state, p0, theta, niter, dim):
"""
to get pure quantum state
Eqs. (16,17) in the main text
>>> (P+ - P- + 2P1)
Re[psi]_n = --------------- (16)
psi_til(1+delta_n)
>>> PL - PR
Im[psi]_n = --------------- (17)
psi_til(1+deta_n)
"""
#p0 = abs(sum(state))**2/dim
niter = int(niter * p0 / 3.)
temp_rs = np.zeros((niter, 6, dim))
psi_til = abs(np.sum(dotx(post_state, state)))
prob = get_prob(state, post_state, theta, dim)
for i in range(niter):
temp_rs[i, :, :] = get_bisection(state, prob, dim)
ave_rs = np.zeros((6, dim))
for i in range(6):
for j in range(dim):
ave_rs[i, j] = cdf(temp_rs[:, i, j])
rtemp = np.zeros(dim)
itemp = np.zeros(dim)
rnorm = 0.0
for i in range(dim):
rtemp[i] = (ave_rs[2,i]-ave_rs[3,i]+2*ave_rs[1,i])/\
(psi_til*post_state[0,i])
itemp[i] = (ave_rs[4,i]-ave_rs[5,i])/\
(psi_til*post_state[0,i])
rnorm += rtemp[i]**2 + itemp[i]**2
rtemp /= sqrt(rnorm)
itemp /= sqrt(rnorm)
restate = np.zeros((dim, dim), dtype=complex)
for i in range(dim):
for j in range(dim):
restate[i,j] = (rtemp[i]+1j*itemp[i])*\
(rtemp[j]-1j*itemp[j])
return restate
def get_rho10(state, prob, niter, dim):
# to calculate rho10
# just for mixed state
N = np.int(niter / 2) #we just meas. 2 bases {+,-} and {L,R}
rho10 = np.zeros((dim, dim), dtype=complex)
temp_rs = np.zeros((N, 4, dim, dim))
for i in range(N):
temp_rs[i, :, :, :] = get_bisection(state, prob, dim)
ave_rs = np.zeros((4, dim, dim))
for i in range(4):
for j in range(dim):
for k in range(dim):
ave_rs[i, j, k] = cdf(temp_rs[:, i, j, k])
for x in range(dim):
for p in range(dim):
rho10[x,p] = 1/2.0*(ave_rs[0,x,p]-ave_rs[1,x,p]+\
1j*(ave_rs[2,x,p]-ave_rs[3,x,p]))
return rho10
def get_rho10_rho11(state, prob, niter, dim):
# to calculate rho10 and rho11
# just for mixed state
N = np.int(niter / 3)
rho10 = np.zeros((dim, dim), dtype=complex)
rho11 = np.zeros((dim, dim), dtype=complex)
temp_rs = np.zeros((N, 5, dim, dim))
for i in range(N):
temp_rs[i, :, :, :] = get_bisection(state, prob, dim)
ave_rs = np.zeros((5, dim, dim))
for i in range(5):
for j in range(dim):
for k in range(dim):
ave_rs[i, j, k] = cdf(temp_rs[:, i, j, k])
for x in range(dim):
for p in range(dim):
rho10[x,p] = 1/2.0*(ave_rs[0,x,p]-ave_rs[1,x,p]+\
1j*(ave_rs[2,x,p]-ave_rs[3,x,p]))
rho11[x, p] = ave_rs[4, x, p]
return rho10, rho11
def get_pqurec(state, theta, niter, prob, dim):
# to get pure quantum state
sin_tt = sin(pi * theta)
rpsi = np.real(state)
ipsi = np.imag(state)
psit = sqrt(sum(rpsi)**2 + sum(ipsi)**2)
p0 = (sum(rpsi)**2 + sum(ipsi)**2) / dim
N = np.int(niter * p0 / 3)
temp_rs = np.zeros((N, 5, dim))
for i in range(N):
temp_rs[i, :, :] = get_bisection(state, prob, dim)
ave_rs = np.zeros((5, dim))
for i in range(5):
for j in range(dim):
ave_rs[i, j] = cdf(temp_rs[:, i, j])
rtemp = np.zeros(dim)
itemp = np.zeros(dim)
rnorm = 0.0
for i in range(dim):
rtemp[i] = (ave_rs[0,i]-ave_rs[1,i]+2.0*tan(pi*theta/2.0)*\
ave_rs[4,i])*dim/(2*psit*sin_tt)
itemp[i] = (ave_rs[2, i] - ave_rs[3, i]) * dim / (2 * psit * sin_tt)
rnorm += rtemp[i]**2 + itemp[i]**2
rtemp /= sqrt(rnorm)
itemp /= sqrt(rnorm)
restate = np.zeros((dim, dim), dtype=complex)
for i in range(dim):
for j in range(dim):
restate[i,j] = (rtemp[i]+1j*itemp[i])*\
(rtemp[j]-1j*itemp[j])
return restate
def get_rho(state, prob, niter, dim):
# to calculate rho10
# just for mixed state
N = np.int(niter / 3) #we measure 3 bases {+,-}, {L,R}, {0,1}
rho = np.zeros((2, dim, dim), dtype=complex)
temp_rs = np.zeros((N, 6, dim, dim))
for i in range(N):
temp_rs[i, :, :, :] = get_bisection(state, prob, dim)
ave_rs = np.zeros((6, dim, dim))
for i in range(6):
for j in range(dim):
for k in range(dim):
ave_rs[i, j, k] = cdf(temp_rs[:, i, j, k])
for x in range(dim):
for p in range(dim):
#rho10
rho[0,x,p] = 1/2.0*(ave_rs[0,x,p]-ave_rs[1,x,p]+\
1j*(ave_rs[2,x,p]-ave_rs[3,x,p]))
#rho11
rho[1, x, p] = ave_rs[5, x, p]
return rho