|q⟩
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The Bell state
∣
Φ
+
⟩
=
(
∣
00
⟩
+
∣
11
⟩
)
/
2
|\Phi^+\rangle = (|00\rangle + |11\rangle)/\sqrt{2}
∣
Φ
+
⟩
=
(
∣00
⟩
+
∣11
⟩)
/
2
has reduced density matrix
ρ
A
\rho_A
ρ
A
obtained by tracing out qubit B. What is the (0,0) entry
ρ
A
[
0
]
[
0
]
\rho_A[0][0]
ρ
A
[
0
]
[
0
]
, i.e. the probability of measuring qubit A in
∣
0
⟩
|0\rangle
∣0
⟩
?
🔬 try it before you answer
1.0 (treated it as a pure
∣
0
⟩
|0\rangle
∣0
⟩
)
0.25
0.5
1
/
2
≈
0.707
1/\sqrt{2} \approx 0.707
1/
2
≈
0.707
(used the amplitude, not its square)
Check answer