fix PTM and Chi documentation (#10909)

* fix PTM documentation

* fix chi matrix documentation too

(cherry picked from commit e636991)

qiskit/quantum_info/operators/channel/chi.py

@@ -39,11 +39,13 @@ class Chi(QuantumChannel):
 
     .. math::
 
-        \mathcal{E}(ρ) = \sum_{i, j} \chi_{i,j} P_i ρ P_j
+        \mathcal{E}(ρ) = \frac{1}{2^n} \sum_{i, j} \chi_{i,j} P_i ρ P_j
 
     where :math:`[P_0, P_1, ..., P_{4^{n}-1}]` is the :math:`n`-qubit Pauli basis in
     lexicographic order. It is related to the :class:`Choi` representation by a change
-    of basis of the Choi-matrix into the Pauli basis.
+    of basis of the Choi-matrix into the Pauli basis. The :math:`\frac{1}{2^n}`
+    in the definition above is a normalization factor that arises from scaling the
+    Pauli basis to make it orthonormal.
 
     See reference [1] for further details.
 

qiskit/quantum_info/operators/channel/ptm.py

@@ -40,7 +40,7 @@ class PTM(QuantumChannel):
 
     .. math::
 
-        R_{i,j} = \mbox{Tr}\left[P_i \mathcal{E}(P_j) \right]
+        R_{i,j} = \frac{1}{2^n} \mbox{Tr}\left[P_i \mathcal{E}(P_j) \right]
 
     where :math:`[P_0, P_1, ..., P_{4^{n}-1}]` is the :math:`n`-qubit Pauli basis in
     lexicographic order.
@@ -53,7 +53,7 @@ class PTM(QuantumChannel):
         |\mathcal{E}(\rho)\rangle\!\rangle_P = S_P |\rho\rangle\!\rangle_P
 
     where :math:`|A\rangle\!\rangle_P` denotes vectorization in the Pauli basis
-    :math:`\langle i | A\rangle\!\rangle_P = \mbox{Tr}[P_i A]`.
+    :math:`\langle i | A\rangle\!\rangle_P = \sqrt{\frac{1}{2^n}} \mbox{Tr}[P_i A]`.
 
     See reference [1] for further details.