Density matrix simulator sometimes returns measurement results when ignore_measurement_results is True

Split off from #2567 . Input:

import cirq

q = cirq.LineQubit(0)
circuit1 = cirq.Circuit(cirq.measure(q))
circuit2 = circuit1 + cirq.I(q)

print('Circuit 1:')
print(circuit1)
print()
print('Circuit2:')
print(circuit2)
print()

simulator = cirq.DensityMatrixSimulator(noise=cirq.X, ignore_measurement_results=True)
result1 = simulator.run(circuit1, repetitions=10)
result2 = simulator.run(circuit2, repetitions=10)

print('Result 1:')
print(result1)
print()
print('Result 2:')
print(result2)
print()

Output:

Circuit 1:
0: ───M───

Circuit2:
0: ───M───I───

Result 1:
0=1111111111

Result 2:

[kevinsung]

Yes, that’s correct.

[balopat]

Thank you @akushnarov! It’s all yours!