def bipartitepurestate_partialtranspose_densitymatrix(bipartite_tensor,
pt_subsys):
""" Calculate the partial transpose of a density matrix.
:param bipartite_tensor: matrix for the bipartite system
:param pt_subsys: subsystem to transpose (either 0 or 1)
:return: density matrix after partial transpose
:type bipartite_tensor: numpy.ndarray
:type pt_subsys: int
:rtype: numpy.ndarray
"""
if not (pt_subsys in [0, 1]):
raise ValueError('pt_subsys can only be 0 or 1!')
ketnode = tn.Node(bipartite_tensor)
branode = tn.Node(np.conj(bipartite_tensor))
final_node = tn.outer_product(ketnode, branode)
e0, e1, e2, e3 = final_node[0], final_node[1], final_node[2], final_node[3]
if pt_subsys == 0:
final_node.reorder_edges([e2, e1, e0, e3])
else:
final_node.reorder_edges([e0, e3, e2, e1])
return final_node.tensor
def test_outer_product_without_legs(a, b, expected_val, expected_shape,
expected_name, backend):
node1 = tn.Node(a, name="A", backend=backend)
node2 = tn.Node(b, name="B", backend=backend)
node3 = tn.outer_product(node1, node2, name=expected_name)
np.testing.assert_allclose(node3.tensor, expected_val)
assert node3.shape == expected_shape
assert node3.name == expected_name
def test_outer_product(backend):
a = tn.Node(np.ones((2, 4, 5)), name="A", backend=backend)
b = tn.Node(np.ones((4, 3, 6)), name="B", backend=backend)
c = tn.Node(np.ones((3, 2)), name="C", backend=backend)
tn.connect(a[1], b[0])
tn.connect(a[0], c[1])
tn.connect(b[1], c[0])
# Purposely leave b's 3rd axis undefined.
d = tn.outer_product(a, b, name="D")
tn.check_correct({c, d})
assert d.shape == (2, 4, 5, 4, 3, 6)
np.testing.assert_allclose(d.tensor, np.ones((2, 4, 5, 4, 3, 6)))
assert d.name == "D"
def bipartitepurestate_densitymatrix(bipartitepurestate_tensor):
"""Calculate the whole density matrix of the bipartitite system
Given a discrete normalized quantum system, given in terms of 2-D numpy array ``bipartitepurestate_tensor``,
each element of ``bipartitepurestate_tensor[i, j]`` is the coefficient of the ket :math:`|ij\\rangle`,
calculate the whole density matrix.
:param bipartitepurestate_tensor: tensor describing the bi-partitite states, with each elements the coefficients for :math:`|ij\\rangle`
:return: density matrix
:type bipartitepurestate_tensor: numpy.ndarray
:rtype: numpy.ndarray
"""
ketnode = tn.Node(bipartitepurestate_tensor)
branode = tn.Node(np.conj(bipartitepurestate_tensor))
denmat_node = tn.outer_product(ketnode, branode)
return denmat_node.tensor
