I'm trying to understand how measurement affects the non-measured qubits when I have more than two entangled qubits.
Question 1: Say I have three entangled qubits in the state 1/2 (|000> + |011> + |101> + |110>), i.e. an equal chance of any even parity bit pattern. I then measure the left bit, and say it's 0. Are the other two bits still entangled, or does the wave function collapse upon the measurement of any bit?
Question 2: Suppose I wrote the code:
qc = QuantumCircuit(3, 3)
# Let the transpiler figure out how to get the entangled state
matrix = np.array((1, 0, 0, 1, 0, 1, 1, 0), dtype=float) / 2
qc.initialize(matrix)
qc.measure(0, 0)
# See text below
qc.measure((1, 2), (1, 2))
result = Aer.get_backend('aer_simulator').run(qc).result()
In this code, I would get identical results whether or not the bits are entangled after the first measurement. Is there something I could add to the code above that would distinguish entangled qubits from qubits forced to be |0> or |1>.
Question 3. Suppose, instead, my state were A|000> + B|011> + C|101> + D|110>, and I measured the left bit to be 0. The new state is A'|001> + B'|110>. Are A' and B' just A and B multiplied by the appropriate scale factor so the norm is 1? Is there a phase shift of any sort?
