def get_estimate_for_k(k, ub = 8192, lb = 64):
m = C_EPSILON * MULTIPLICATIVE_CONSTANT * k
while True:
mb = (ub + lb) / 2
sl = log2(mb) * log2(log2(mb)) * m
if abs(sl - mb) < 1:
return ub
if sl > mb:
lb = mb
else:
ub = mb
def negativity(rho, subsys, method='tracenorm', logarithmic=False):
"""
Compute the negativity for a multipartite quantum system described
by the density matrix rho. The subsys argument is an index that
indicates which system to compute the negativity for.
.. note::
Experimental.
"""
mask = [idx == subsys for idx, n in enumerate(rho.dims[0])]
rho_pt = partial_transpose(rho, mask)
if method == 'tracenorm':
N = ((rho_pt.dag() * rho_pt).sqrtm().tr().real - 1) / 2.0
elif method == 'eigenvalues':
l = rho_pt.eigenenergies()
N = ((abs(l) - l) / 2).sum()
else:
raise ValueError("Unknown method %s" % method)
if logarithmic:
return log2(2 * N + 1)
else:
return N
def calculate_efficiency(length):
efficiency = 0.0
for i in original_p_dict:
efficiency += original_p_dict[i] * log2(original_p_dict[i])
efficiency = -1 * efficiency
return round(efficiency / length, 7)
def printTreeToConsole(tree):
levels = int(log2(len(tree)))
space_for_elements = math.pow(2, levels) * 3
heapKeyPos = 1; level = 0; levelBuffer = ''
for heapKey in tree:
if(int(log2(heapKeyPos)) > level):
print levelBuffer + '\n' ; level +=1 ; levelBuffer ='' ;
heapKeyStr = str(heapKey)
if heapKey is None:
heapKeyStr = "x"
space_for_element = int((space_for_elements/(math.pow(2, level))))
right_spacer = left_spacer = ' ' * ((space_for_element-len(heapKeyStr))/2)
if (space_for_element-len(heapKeyStr)) % 2 == 1:
right_spacer += ' '
levelBuffer += (left_spacer + heapKeyStr + right_spacer)
heapKeyPos +=1
if len(levelBuffer) > 0:
print levelBuffer + '\n'
def _entropy_relative(rho, sigma, base=e, sparse=False):
"""
****NEEDS TO BE WORKED ON****
Calculates the relative entropy S(rho||sigma) between two density
matrices.
Parameters
----------
rho : qobj
First density matrix.
sigma : qobj
Second density matrix.
base : {e,2}
Base of logarithm.
Returns
-------
rel_ent : float
Value of relative entropy.
"""
if rho.type != 'oper' or sigma.type != 'oper':
raise TypeError("Inputs must be density matrices..")
# sigma terms
svals = sp_eigs(sigma.data, sigma.isherm, vecs=False, sparse=sparse)
snzvals = svals[svals != 0]
if base == 2:
slogvals = log2(snzvals)
elif base == e:
slogvals = log(snzvals)
else:
raise ValueError("Base must be 2 or e.")
# rho terms
rvals = sp_eigs(rho.data, rho.isherm, vecs=False, sparse=sparse)
rnzvals = rvals[rvals != 0]
# calculate tr(rho*log sigma)
rel_trace = float(real(sum(rnzvals * slogvals)))
return -entropy_vn(rho, base, sparse) - rel_trace
def entropy_vn(rho, base=e, sparse=False):
"""
Von-Neumann entropy of density matrix
Parameters
----------
rho : qobj
Density matrix.
base : {e,2}
Base of logarithm.
sparse : {False,True}
Use sparse eigensolver.
Returns
-------
entropy : float
Von-Neumann entropy of `rho`.
Examples
--------
>>> rho=0.5*fock_dm(2,0)+0.5*fock_dm(2,1)
>>> entropy_vn(rho,2)
1.0
"""
if rho.type == 'ket' or rho.type == 'bra':
rho = ket2dm(rho)
vals = sp_eigs(rho.data, rho.isherm, vecs=False, sparse=sparse)
nzvals = vals[vals != 0]
if base == 2:
logvals = log2(nzvals)
elif base == e:
logvals = log(nzvals)
else:
raise ValueError("Base must be 2 or e.")
return float(real(-sum(nzvals * logvals)))
def is_estimate_valid(k):
n = get_estimate_for_k(k)
return (1.0 / (k * log2(n)))**(log2(log2(n))) <= (1 - EPSILON) / 2
def Entropy_value(frequency, length):
entropy = 0
for i in frequency:
entropy -= (frequency[i] / length * log2(frequency[i] / length))
return entropy
count[c] = 1
else:
count[c] += 1
#print(count)
for c in sorted(count):
print(c, "=>", count[c] / len(message))
#Alphabet
print("Count of different symblos(alphabet): ", len(count))
#Entropy
print("Entropy value: ", Entropy_value(count, len(message)))
#Equal Code
print("Equal code: ")
med = math.ceil(log2(len(count)))
print("Code length : ", med)
equable_dict = dict.fromkeys(count, "")
code = 0
for i in equable_dict:
equable_dict[i] = bin(code)
equable_dict[i] = equable_dict[i][2:len(equable_dict[i]):1]
while len(equable_dict[i]) != med:
equable_dict[i] = "0" + equable_dict[i]
code += 1
for i in sorted(equable_dict):
print(i, "=", equable_dict[i])
code_mes = ""
for i in message:
code_mes += equable_dict[i]
print("Message length in code: ", len(code_mes), "\nMessage code: ",