Add partial transpose function in quantum_info (#9566)

* partial_transpose included

* included partial_transpose

* included partial_transpose

* included partial_transpose

* included partial_transpose

* included partial_transpose

* included partial_transpose

* included partial_transpose

* included partial_transpose

* included partial_transpose

* included partial_transpose

* included partial_transpose

* included test for partial transpose

* included test for partial transpose

* included test for partial transpose

* added docstring

* included DensityMatrix(rho1)

* changed rho1

* addition of release note

* fix

* fix

* fir partial_transpose

* Update utils.py

* refactor and add tests

---------

Co-authored-by: Ikko Hamamura <ikkoham@users.noreply.github.com>

qiskit/quantum_info/states/densitymatrix.py

@@ -814,3 +814,22 @@ 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.
+        """
+        arr = self._data.reshape(self._op_shape.tensor_shape)
+        qargs = len(self._op_shape.dims_l()) - 1 - np.array(qargs)
+        n = len(self.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, self._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

@@ -12,21 +12,20 @@
 
 """Tests for DensityMatrix quantum state class."""
 
-import unittest
 import logging
-from ddt import ddt, data
+import unittest
+
 import numpy as np
+from ddt import data, ddt
 from numpy.testing import assert_allclose
 
-from qiskit.test import QiskitTestCase
-from qiskit import QiskitError
-from qiskit import QuantumRegister, QuantumCircuit
-from qiskit.circuit.library import HGate, QFT
-
-from qiskit.quantum_info.random import random_unitary, random_density_matrix, random_pauli
-from qiskit.quantum_info.states import DensityMatrix, Statevector
+from qiskit import QiskitError, QuantumCircuit, QuantumRegister
+from qiskit.circuit.library import QFT, HGate
 from qiskit.quantum_info.operators.operator import Operator
 from qiskit.quantum_info.operators.symplectic import Pauli, SparsePauliOp
+from qiskit.quantum_info.random import random_density_matrix, random_pauli, random_unitary
+from qiskit.quantum_info.states import DensityMatrix, Statevector
+from qiskit.test import QiskitTestCase
 
 logger = logging.getLogger(__name__)
 
@@ -1202,6 +1201,24 @@ 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"""
+        with self.subTest(msg="separable"):
+            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(rho.partial_transpose([0, 1]), DensityMatrix(rho1))
+            self.assertEqual(rho.partial_transpose([0, 2]), DensityMatrix(rho1))
+
+        with self.subTest(msg="entangled"):
+            rho = DensityMatrix([[0, 0, 0, 0], [0, 0.5, -0.5, 0], [0, -0.5, 0.5, 0], [0, 0, 0, 0]])
+            rho1 = DensityMatrix([[0, 0, 0, -0.5], [0, 0.5, 0, 0], [0, 0, 0.5, 0], [-0.5, 0, 0, 0]])
+            self.assertEqual(rho.partial_transpose([0]), DensityMatrix(rho1))
+            self.assertEqual(rho.partial_transpose([1]), DensityMatrix(rho1))
+
     def test_clip_probabilities(self):
         """Test probabilities are clipped to [0, 1]."""
         dm = DensityMatrix([[1.1, 0], [0, 0]])