def test_eval_trace():
# This test includes tests with dependencies between TensorProducts
#and density operators. Since, the test is more to test the behavior of
#TensorProducts it remains here
A, B, C, D, E, F = symbols('A B C D E F', commutative=False)
# Density with simple tensor products as args
t = TensorProduct(A, B)
d = Density([t, 1.0])
tr = Tr(d)
assert tr.doit() == 1.0 * Tr(A * Dagger(A)) * Tr(B * Dagger(B))
## partial trace with simple tensor products as args
t = TensorProduct(A, B, C)
d = Density([t, 1.0])
tr = Tr(d, [1])
assert tr.doit() == 1.0 * A * Dagger(A) * Tr(B * Dagger(B)) * C * Dagger(C)
tr = Tr(d, [0, 2])
assert tr.doit() == 1.0 * Tr(A * Dagger(A)) * B * Dagger(B) * Tr(
C * Dagger(C))
# Density with multiple Tensorproducts as states
t2 = TensorProduct(A, B)
t3 = TensorProduct(C, D)
d = Density([t2, 0.5], [t3, 0.5])
t = Tr(d)
assert t.doit() == (0.5 * Tr(A * Dagger(A)) * Tr(B * Dagger(B)) +
0.5 * Tr(C * Dagger(C)) * Tr(D * Dagger(D)))
t = Tr(d, [0])
assert t.doit() == (0.5 * Tr(A * Dagger(A)) * B * Dagger(B) +
0.5 * Tr(C * Dagger(C)) * D * Dagger(D))
#Density with mixed states
d = Density([t2 + t3, 1.0])
t = Tr(d)
assert t.doit() == (1.0 * Tr(A * Dagger(A)) * Tr(B * Dagger(B)) +
1.0 * Tr(A * Dagger(C)) * Tr(B * Dagger(D)) +
1.0 * Tr(C * Dagger(A)) * Tr(D * Dagger(B)) +
1.0 * Tr(C * Dagger(C)) * Tr(D * Dagger(D)))
t = Tr(d, [1])
assert t.doit() == (1.0 * A * Dagger(A) * Tr(B * Dagger(B)) +
1.0 * A * Dagger(C) * Tr(B * Dagger(D)) +
1.0 * C * Dagger(A) * Tr(D * Dagger(B)) +
1.0 * C * Dagger(C) * Tr(D * Dagger(D)))
def test_eval_trace():
up = JzKet(S.Half, S.Half)
down = JzKet(S.Half, Rational(-1, 2))
d = Density((up, 0.5), (down, 0.5))
t = Tr(d)
assert t.doit() == 1
#test dummy time dependent states
class TestTimeDepKet(TimeDepKet):
def _eval_trace(self, bra, **options):
return 1
x, t = symbols('x t')
k1 = TestTimeDepKet(0, 0.5)
k2 = TestTimeDepKet(0, 1)
d = Density([k1, 0.5], [k2, 0.5])
assert d.doit() == (0.5 * OuterProduct(k1, k1.dual) +
0.5 * OuterProduct(k2, k2.dual))
t = Tr(d)
assert t.doit() == 1