W state Entanglement Breaks During $X$-Basis Measurement

Question

I'm encountering a problem in my Qiskit simulation involving W-state entanglement. The issue arises when attempting to measure all three qubits in the $X$ measurement basis. Surprisingly, the entanglement breaks, and this behavior is consistent even when running the code on a real quantum device.

import numpy as np
Define a F_gate
def F_gate(circ, q, i, j, n, k):
    theta = np.arccos(np.sqrt(1/(n-k+1)))
    circ.ry(-theta, q[j])
    circ.cz(q[i], q[j])
    circ.ry(theta, q[j])
    circ.barrier(q[i])
Define the cxrv gate which uses reverse CNOT instead of CNOT
def cxrv(circ, q, i, j):
    circ.h(q[i])
    circ.h(q[j])
    circ.cx(q[j], q[i])
    circ.h(q[i])
    circ.h(q[j])
    circ.barrier(q[i], q[j])
Define the flag_qx2 variable
flag_qx2 = True  # Set it to True or False based on your requirements
singlet = QuantumCircuit(qr, cr)
singlet.x(qr[2])  # start is |100>
F_gate(singlet, qr, 2, 1, 3, 1)  # Applying F12
F_gate(singlet, qr, 1, 0, 3, 2)  # Applying F23
if flag_qx2:  # option ibmqx2
    singlet.cx(qr[1], qr[2])  # cNOT 21
    singlet.cx(qr[0], qr[1])  # cNOT 32
else:  # option ibmqx4
    cxrv(singlet, qr, 1, 2)
    cxrv(singlet, qr, 0, 1)
for i in range(3):
    singlet.h(qr[i])  # Apply Hadamard gate for X basis
    singlet.measure(qr[i], cr[i])

The problem seems to be related to measuring in the $X$ basis. When measuring in the Z basis, the W state is correctly obtained which is $|001\rangle, |010\rangle, |001\rangle$. However, measuring in the $X$ basis results in the breakdown of entanglement and giving significant state of $|000\rangle , |011\rangle$ etc.

I appreciate any insights or suggestions on how to address this issue and preserve entanglement during $X$-basis measurements.

I attempted to simulate a quantum circuit using Qiskit, specifically focusing on a W-state entanglement scenario. The goal was to measure all three qubits in the $X$ measurement basis. I expected that the entanglement would be preserved, as observed when measuring in the $Z$ basis. However, the actual result was a breakdown of entanglement during $X$-basis measurements. This behavior persisted when running the code on both the simulator and a real quantum device. I am seeking insights or suggestions on how to address this issue and maintain entanglement in the $X$-basis measurements.

NOTE: I know W state is not a singlet state rather it can be say as Triplet state.

W state Entanglement Breaks During $X$-Basis Measurement

Define a F_gate

Define the cxrv gate which uses reverse CNOT instead of CNOT

Define the flag_qx2 variable

0 Answers0