Using Qiskit State Tomography on Subsystems

Question

I have a version of the following circuit set up.

from qiskit import QuantumCircuit

circuit=QuantumCircuit(2)
initial_state0=[1/np.sqrt(2),1/np.sqrt(2)]     
circuit.initialize(initial_state0, 0)
initial_state1=[1, 0]
circuit.initialize(initial_state1,1)
circuit.cx(0,1)

I have seen that I can use StateTomography by coding the following

from qiskit_experiments.library import StateTomography   
from qiskit.providers.aer import Aer
backend = Aer.get_backend('qasm_simulator')

# QST Experiment
qstexp1 = StateTomography(circuit)
qstdata1 = qstexp1.run(backend, seed_simulation=1000).block_for_results()

# Print results
for result in qstdata1.analysis_results():
    print(result)

By using the coding above I am able to see how this tomography can be used to approximate the state of the entire system with fidelity being a comparison to the state of the circuit, but my goal is to use Quantum State Tomography (QST) on only $q_1$ and use the fidelity to compare this to $q_0$.

I have seen in the tutorial on Qiskit that I can run the tomography on parallel subsystems, but I'm not sure how to extend this to my goal described above. Any help would be greatly appreciated!

(Previous edit removed as I resolved that issue independently)

Answer 1

In the tutorial, tomography on parallel subsystems assumes that subsystems are independent. From your post, I deduce you are interested in something different, i.e., performing tomography of one state after a single circuit has been executed on several qubits. To this purpose, just modify your code using qstexp1 = StateTomography(circuit, measurement_qubits=[1]). In this way, you will obtain the density matrix of $q_1$. Analytically, such a matrix can be obtained as the partial trace with respect to the density matrix of whole output state -- $I/2$, in your example. Indeed, your result will be (about) $I/2$, as expected.