Add partial transpose function in quantum_info

qiskit/quantum_info/states/densitymatrix.py

@@ -809,3 +809,29 @@ def to_statevector(self, atol=None, rtol=None):
 
         psi = evecs[:, np.argmax(evals)]  # eigenvectors returned in columns.
         return Statevector(psi)
+
+    def partial_transpose(self, qargs):
+        """Return partially transposed density matrix.
+
+        Args:
+            qargs (list): The subsystems to be transposed.
+
+        Returns:
+            DensityMatrix: The partially transposed density matrix.
+
+        Raises:
+            QiskitError: if input state is invalid.
+
+        """
+        from qiskit.quantum_info.states import utils
+
+        state = utils._format_state(self, validate=False)
+        arr = state._data.reshape(state._op_shape.tensor_shape)
+        qargs = len(state._op_shape.dims_l()) - 1 - np.array(qargs)
+        n = len(state.dims())
+        lst = list(range(2 * n))
+        for i in qargs:
+            lst[i], lst[i + n] = lst[i + n], lst[i]
+        rho = np.transpose(arr, lst)
+        rho = np.reshape(rho, state._op_shape.shape)
+        return DensityMatrix(rho)

releasenotes/notes/adding-partial-transpose-040a6ff00228841b.yaml

@@ -0,0 +1,5 @@
+
+features:
+  - |
+    The partial transpose operation has been integrated into the quantum_info module, allowing for partial transposition of matrices.
+    This operation is key in detecting entanglement between bipartite quantum system.

test/python/quantum_info/states/test_densitymatrix.py

@@ -1202,6 +1202,17 @@ def test_drawings(self):
             with self.subTest(msg=f"draw('{drawtype}')"):
                 dm.draw(drawtype)
 
+    def test_density_matrix_partial_transpose(self):
+        """Test partial_transpose function on density matrices"""
+        rho = DensityMatrix.from_label("10+")
+        rho1 = np.zeros((8, 8), complex)
+        rho1[4, 4] = 0.5
+        rho1[4, 5] = 0.5
+        rho1[5, 4] = 0.5
+        rho1[5, 5] = 0.5
+        self.assertEqual(DensityMatrix.partial_transpose(rho, [0, 1]), DensityMatrix(rho1))
+        self.assertEqual(DensityMatrix.partial_transpose(rho, [0, 2]), DensityMatrix(rho1))
+
 
 if __name__ == "__main__":
     unittest.main()