Here is A₀ again, followed by the six possibilities when one of its qubits is p-measured:

Qureg A0
State	Amplitude	Probability
│000 ⟩	+0.32272 − 0.12294i	0.11926
│001 ⟩	−0.16136 + 0.03074i	0.02698
│010 ⟩	−0.17673 − 0.19210i	0.06813
│011 ⟩	+0.25645 + 0.11105i	0.07810
│100 ⟩	+0.07684 + 0.39188i	0.15947
│101 ⟩	+0.22712 − 0.18991i	0.08765
│110 ⟩	+0.57598 − 0.25131i	0.39490
│111 ⟩	+0.23749 + 0.09535i	0.06549
naïve = 0.66390

p-measuring the first bit gives one of these:

Qureg A6 State Amplitude Probability │000 ⟩ +0.59673 − 0.22733i 0.40777 │001 ⟩ −0.29837 + 0.05683i 0.09225 │010 ⟩ −0.32678 − 0.35520i 0.23295 │011 ⟩ +0.47419 + 0.20534i 0.26702 │100 ⟩ 0 0 │101 ⟩ 0 0 │110 ⟩ 0 0 │111 ⟩ 0 0 naïve = 0.31688

Qureg A7 State Amplitude Probability │000 ⟩ 0 0 │001 ⟩ 0 0 │010 ⟩ 0 0 │011 ⟩ 0 0 │100 ⟩ +0.09135 + 0.46589i 0.22539 │101 ⟩ +0.27002 − 0.22578i 0.12389 │110 ⟩ +0.68476 − 0.29877i 0.55815 │111 ⟩ +0.28234 + 0.11336i 0.09257 naïve = 0.57119

p-measuring the second bit gives one of these:

Qureg A8 State Amplitude Probability │000 ⟩ +0.51455 − 0.19602i 0.30319 │001 ⟩ −0.25728 + 0.04900i 0.06859 │010 ⟩ 0 0 │011 ⟩ 0 0 │100 ⟩ +0.12251 + 0.62481i 0.40540 │101 ⟩ +0.36213 − 0.30280i 0.22282 │110 ⟩ 0 0 │111 ⟩ 0 0 naïve = 0.28620

Qureg A9 State Amplitude Probability │000 ⟩ 0 0 │001 ⟩ 0 0 │010 ⟩ −0.22691 − 0.24664i 0.11232 │011 ⟩ +0.32926 + 0.14258i 0.12874 │100 ⟩ 0 0 │101 ⟩ 0 0 │110 ⟩ +0.73951 − 0.32266i 0.65098 │111 ⟩ +0.30492 + 0.12242i 0.10796 naïve = 0.48651

p-measuring the third bit gives one of these:

Qureg A10 State Amplitude Probability │000 ⟩ +0.37471 − 0.14275i 0.16078 │001 ⟩ 0 0 │010 ⟩ −0.20520 − 0.22304i 0.09185 │011 ⟩ 0 0 │100 ⟩ +0.08922 + 0.45500i 0.21499 │101 ⟩ 0 0 │110 ⟩ +0.66876 − 0.29179i 0.53238 │111 ⟩ 0 0 naïve = 0.21997

Qureg A11 State Amplitude Probability │000 ⟩ 0 0 │001 ⟩ −0.31754 + 0.06048i 0.10449 │010 ⟩ 0 0 │011 ⟩ +0.50466 + 0.21853i 0.30244 │100 ⟩ 0 0 │101 ⟩ +0.44695 − 0.37373i 0.33944 │110 ⟩ 0 0 │111 ⟩ +0.46736 + 0.18764i 0.25363 naïve = 0.66578

Entanglement can increase when bits are p-measured, because nonvanishing amplitudes are scaled up to restore the total probability to unity.