matrix = densop.get_elm()
eigvals = eigh(matrix, eigvals_only=True)
eigvals_out = [eigvals[i] for i in range(len(eigvals)) if eigvals[i] > MIN_DOUBLE]
return eigvals_out
if __name__ == '__main__':
# whole quantum state
qubit_num = 5
qs = random_qstate(qubit_num)
de = DensOp(qstate=[qs], prob=[1.0]) # pure state
# partial density operators (system A and B)
id_A, id_B = random_qubit_id(qubit_num)
de_A = de.patrace(id_B)
de_B = de.patrace(id_A)
# eigen-values of density operators (system A and B)
eval_A = eigen_values(de_A)
eval_B = eigen_values(de_B)
print("== system A ==")
print("- qubit id =", id_A)
print("- square trace = ", de_A.sqtrace())
print("- eigen values =", eval_A)
print("- rank =", len(eval_A))
print("== system B ==")
print("- qubit id =", id_B)
print("- square trace = ", de_B.sqtrace())
from qlazy import QState, DensOp
qs = QState(4)
qs.h(0).h(1) # unitary operation for 0,1-system
qs.x(2).z(3) # unitary operation for 2,3-system
de1 = DensOp(qstate=[qs], prob=[1.0]) # product state
de1_reduced = de1.patrace([0,1]) # trace-out 0,1-system
print("== partial trace of product state ==")
print(" * trace = ", de1_reduced.trace())
print(" * square trace = ", de1_reduced.sqtrace())
qs.cx(1,3).cx(0,2) # entangle between 0,1-system and 2,3-system
de2 = DensOp(qstate=[qs], prob=[1.0]) # entangled state
de2_reduced = de2.patrace([0,1]) # trace-out 0,1-system
print("== partial trace of entangled state ==")
print(" * trace = ", de2_reduced.trace())
print(" * square trace = ", de2_reduced.sqtrace())
print("== partial state of entangled state ==")
qs.show([2,3])