title: Ruling out state |000> with a 3 qbits circuit executed on a real backend - statevector seems inconsistent
body: <p>I am trying to rule out the state <code>|000&gt;</code> for a simple 3 qbits quantum circuit executed on a real quantum backend.</p>
  <p>The code exctract below is unelegant but I guess it does the trick and for the time being the value <code>|000&gt;</code> hasn't come up. Still I don't clearly understand why the statevector based on the instructions set analysis (measurement excepted) shows that all the state are strictly equiprobable while the <code>CCNOT</code> gate is such that <code>q0</code> is forced to <code>|0&gt;</code> in all instances where both <code>q1</code> AND <code>q2</code> are in state <code>|0&gt;</code>. I tend to think that the explanation has to do with density matrixes applied to mixed states but I don't know where to get precisely from there...Could you point me in the right direction?</p>
  <pre class="lang-py prettyprint-override"><code>    qcM=QuantumCircuit (3)  
      qcM.h(0)
      qcM.h(1)
      qcM.h(2)
      qcM.x(1)
      qcM.x(2)
      qcM.ccx(1,2,0)
      qcM.x(1)
      qcM.x(2)
   
      #Statevector du circuit décrit
      st1 = Statevector.from_instruction(qcM)
      print('State vector : ', st1)
      qcM.measure_all()
  </code></pre>
  <p>The statevector I am getting upon execution is the following:</p>
  <pre><code>    The best backend is ibmq_manila
      State vector :  Statevector([0.35355339+0.j, 0.35355339+0.j, 0.35355339+0.j,
               0.35355339+0.j, 0.35355339+0.j, 0.35355339+0.j,
               0.35355339+0.j, 0.35355339+0.j],
              dims=(2, 2, 2))
  </code></pre>
  <p>Here is a picture of the circuit:</p>
  <p><img src="https://i.stack.imgur.com/sxXlj.png" alt="MyCircuit" /></p>
  <p>Thanks for your help,<br />
  Kind regards,<br />
  Bertrand</p>