code: def _su2su2_to_tensor_products(U):
      r"""Given a matrix :math:`U = A \otimes B` in SU(2) x SU(2), extract the two SU(2)
      operations A and B.
  
      This process has been described in detail in the Appendix of Coffey & Deiotte
      https://link.springer.com/article/10.1007/s11128-009-0156-3
      """
  
      # First, write A = [[a1, a2], [-a2*, a1*]], which we can do for any SU(2) element.
      # Then, A \otimes B = [[a1 B, a2 B], [-a2*B, a1*B]] = [[C1, C2], [C3, C4]]
      # where the Ci are 2x2 matrices.
      C1 = U[0:2, 0:2]
      C2 = U[0:2, 2:4]
      C3 = U[2:4, 0:2]
      C4 = U[2:4, 2:4]
  
      # From the definition of A \otimes B, C1 C4^\dag = a1^2 I, so we can extract a1
      C14 = math.dot(C1, math.conj(math.T(C4)))
      a1 = math.sqrt(math.cast_like(C14[0, 0], 1j))
  
      # Similarly, -C2 C3^\dag = a2^2 I, so we can extract a2
      C23 = math.dot(C2, math.conj(math.T(C3)))
      a2 = math.sqrt(-math.cast_like(C23[0, 0], 1j))
  
      # This gets us a1, a2 up to a sign. To resolve the sign, ensure that
      # C1 C2^dag = a1 a2* I
      C12 = math.dot(C1, math.conj(math.T(C2)))
  
      if not math.is_abstract(C12):
          if not math.allclose(a1 * math.conj(a2), C12[0, 0]):
              a2 *= -1
      else:
          sign_is_correct = math.allclose(a1 * math.conj(a2), C12[0, 0])
          sign = (-1) ** (
              sign_is_correct + 1
          )  # True + 1 = 2, False + 1 = 1
          a2 *= sign
  
      # Construct A
      A = math.stack(
          [
              math.stack([a1, a2]),
              math.stack([-math.conj(a2), math.conj(a1)]),
          ]
      )
  
      # Next, extract B. Can do from any of the C, just need to be careful in
      # case one of the elements of A is 0.
      # We use B1 unless division by 0 would cause all elements to be inf.
      use_B2 = math.allclose(A[0, 0], 0.0, atol=1e-6)
      if not math.is_abstract(A):
          B = (
              C2 / math.cast_like(A[0, 1], 1j)
              if use_B2
              else C1 / math.cast_like(A[0, 0], 1j)
          )
      elif qml.math.get_interface(A) == "jax":
          B = qml.math.cond(
              use_B2,
              lambda x: C2 / math.cast_like(A[0, 1], 1j),
              lambda x: C1 / math.cast_like(A[0, 0], 1j),
              [0],  # arbitrary value for x
          )
  
      return math.convert_like(A, U), math.convert_like(B, U)
  
file_path: pennylane/pennylane/ops/op_math/decompositions/two_qubit_unitary.py
imports: import numpy
  import pennylane
  from pennylane import math
  from .single_qubit_unitary import one_qubit_decomposition
label_desc: Use image node_id 3 for calling a global function with example usage: _su2su2_to_tensor_products(U) and returns: math,  math