diff --git a/src/qasm-simulator-cpp/src/engines/vector_engine.hpp b/src/qasm-simulator-cpp/src/engines/vector_engine.hpp
index 6575610a845d..b8eea1e50859 100644
--- a/src/qasm-simulator-cpp/src/engines/vector_engine.hpp
+++ b/src/qasm-simulator-cpp/src/engines/vector_engine.hpp
@@ -172,10 +172,14 @@ void VectorEngine::execute(const Circuit &prog, BaseBackend<QubitVector> *be,
   // Check to see if circuit is ideal and allows for measurement optimization
   if (prog.opt_meas && prog.noise.ideal) {
 
+    // This optimization replaces the shots by a single shot + sampling
+    // We need to subtract the additional shots added by BaseEngine class
+    total_shots -= (nshots-1);
+
     // Find position of first measurement operation
     uint_t pos = 0;
-    while (prog.operations[pos].id != gate_t::Measure &&
-           pos < prog.operations.size()) {
+    while (pos < prog.operations.size() &&
+           prog.operations[pos].id != gate_t::Measure) {
       pos++;
     }
     // Execute operations before measurements
@@ -492,4 +496,4 @@ inline void from_json(const json_t &js, VectorEngine &eng) {
 //------------------------------------------------------------------------------
 } // end namespace QISKIT
 
-#endif
\ No newline at end of file
+#endif
diff --git a/test/python/qobj/cpp_measure_opt.json b/test/python/qobj/cpp_measure_opt.json
index d98dc31fe1e6..964d7cb7bfa6 100644
--- a/test/python/qobj/cpp_measure_opt.json
+++ b/test/python/qobj/cpp_measure_opt.json
@@ -3,7 +3,8 @@
     "config": {
         "shots": 2000,
         "seed": 1,
-        "backend_name": "local_qasm_simulator_cpp"
+        "backend_name": "local_qasm_simulator_cpp",
+        "data" : ["density_matrix", "probabilities"]
     },
     "circuits": [
         {
diff --git a/test/python/test_qasm_simulator_cpp.py b/test/python/test_qasm_simulator_cpp.py
index 2f8989aa83dc..e12391bb59ac 100644
--- a/test/python/test_qasm_simulator_cpp.py
+++ b/test/python/test_qasm_simulator_cpp.py
@@ -17,6 +17,8 @@
 
 # =============================================================================
 
+from test.python.common import QiskitTestCase
+
 import json
 import unittest
 import numpy as np
@@ -31,7 +33,6 @@
 from qiskit.backends.local.qasm_simulator_cpp import (QasmSimulatorCpp,
                                                       cx_error_matrix,
                                                       x90_error_matrix)
-from .common import QiskitTestCase
 
 
 class TestLocalQasmSimulatorCpp(QiskitTestCase):
@@ -205,13 +206,17 @@ def test_qobj_measure_opt(self):
             snapshots = result.get_snapshots(name)
             self.assertEqual(set(snapshots), {'0'},
                              msg=name + ' snapshot keys')
-            self.assertEqual(len(snapshots['0']), 1,
+            self.assertEqual(len(snapshots['0']), 3,
                              msg=name + ' snapshot length')
             state = snapshots['0']['statevector'][0]
             expected_state = expected_data[name]['statevector']
             fidelity = np.abs(expected_state.dot(state.conj())) ** 2
             self.assertAlmostEqual(fidelity, 1.0, places=10,
                                    msg=name + ' snapshot fidelity')
+            rho = snapshots['0']['density_matrix']
+            self.assertAlmostEqual(np.trace(rho), 1)
+            prob = snapshots['0']['probabilities']
+            self.assertAlmostEqual(np.sum(prob), 1)
 
     def test_qobj_measure_opt_flag(self):
         filename = self._get_resource_path('qobj/cpp_measure_opt_flag.json')