使用sympy实现复合系统AB纯态的施密特分解

import sympydef schimidt_decomposition(A):assert A.shape == (2, 2)U, D, V = A.singular_value_decomposition()U.simplify()D.simplify()V.simplify()"""print("begin debug")print(U)print(D)print(V)B=U@D@V.HB.simplify()print(B)print(A==B) # 可能Falseprint(A.equals(B)) # Trueprint("end debug")"""print(f"{A}的施密特分解：")for i in range(D.shape[0]):  # 不是range(2)，防止只有一个奇异值的情况if D[i, i]:if i:print("+", end="")print(f"({D[i, i]})*{U[:, i].T} tensor {V[:, i].T}", end="")print()A = sympy.Matrix([[1 / sympy.sqrt(3), 1 / sympy.sqrt(3)], [1 / sympy.sqrt(3), 0]])
B = sympy.Matrix([[sympy.Rational(1, 2), sympy.Rational(1, 2)], [sympy.Rational(1, 2), sympy.Rational(1, 2)]])
C = sympy.Matrix([[sympy.Rational(1, 2), sympy.Rational(-1, 2)], [sympy.Rational(1, 2), sympy.Rational(-1, 2)]])
D = sympy.Matrix([[1 / sympy.sqrt(2), 0], [0, -1 / sympy.sqrt(2)]])
schimidt_decomposition(A)
schimidt_decomposition(B)
schimidt_decomposition(C)
schimidt_decomposition(D)