From dcda5040ee211dde45779c311b3fa8bca0cd19f5 Mon Sep 17 00:00:00 2001
From: "Kevin J. Sung" <kevjsung@umich.edu>
Date: Thu, 28 Sep 2023 05:21:17 -0400
Subject: [PATCH] fix PTM and Chi documentation (#10909)

* fix PTM documentation

* fix chi matrix documentation too

(cherry picked from commit e636991c51a9e7ef47cb62931f52e88e79c3fa17)
---
 qiskit/quantum_info/operators/channel/chi.py | 6 ++++--
 qiskit/quantum_info/operators/channel/ptm.py | 4 ++--
 2 files changed, 6 insertions(+), 4 deletions(-)

diff --git a/qiskit/quantum_info/operators/channel/chi.py b/qiskit/quantum_info/operators/channel/chi.py
index be8bd45c08a3..1b2b13fa7ea3 100644
--- a/qiskit/quantum_info/operators/channel/chi.py
+++ b/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.
 
diff --git a/qiskit/quantum_info/operators/channel/ptm.py b/qiskit/quantum_info/operators/channel/ptm.py
index 5cd8dda709de..5b248463cdd5 100644
--- a/qiskit/quantum_info/operators/channel/ptm.py
+++ b/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.