# entanglement in that state and BOUND/BOUND_PPT is the lower bound on the GNM
# that can be achieved using NMIN/NMIN_PPT measurements.
# The difference between (NMIN, BOUND) and (NMIN, BOUNT_PPT) is that in the first
# fully decomposable witnesses are constructed, wheras in the second one fully
# PPT witnesses are used.
import gmntools, numpy
from gmntools import gmn, randomstates, randomlocalmeas
# number of runs
n = 100
subsystems = [2, 2]
# initialize necesarry classes
locmeas = randomlocalmeas(subsystems)
rho = randomstates(subsystems)
GMN = gmn(subsystems)
dim = numpy.prod(numpy.array(subsystems))
for i in range(n):
GMN.setdensitymatrix(rho.random())
genneg = rho.negativity([0])
if genneg > 0:
meas = []
for j in range(dim ** 2):
expvalue = numpy.trace(numpy.dot(rho.matrix, locmeas.random())).real
meas += [(locmeas.matrix, expvalue)]
xlow = 0
xhigh = dim ** 2
while True:
x = (xhigh + xlow) / 2
# where GNM is the genuine multipartice negativity of the random state, NMIN is # the minimal number of measurements necessary to detect genuine multiparticle # entanglement in that state and BOUND is the lower bound on the GNM that # can be achieved using NMIN measurements. import gmntools, numpy from gmntools import gmn, randomstates, randomlocalmeas #number of runs n = 100 subsystems = [2,2,2] weight = 0.5 #the maximal weight the mixed state can have in the mixture with the pure one # initialize necesarry classes locmeas = randomlocalmeas(subsystems) rhomixed = randomstates(subsystems) GMN = gmn(subsystems) dim = numpy.prod(numpy.array(subsystems)) def randstate(minweight): psi = numpy.random.randn(dim) + 1.j*numpy.random.randn(dim) p = minweight*numpy.random.rand(1) rhopure = numpy.outer(psi.conjugate(),psi) rhopure /= numpy.trace(rhopure) return (1-p)*rhopure + p*rhomixed.random() for i in range(n): rho = randstate(weight) GMN.setdensitymatrix(rho) genneg = GMN.gmn(altsolver='dsdp') if genneg > 0:
