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For the pure state
∣
ψ
⟩
=
cos
(
θ
)
∣
00
⟩
+
sin
(
θ
)
∣
11
⟩
|\psi\rangle = \cos(\theta)|00\rangle + \sin(\theta)|11\rangle
∣
ψ
⟩
=
cos
(
θ
)
∣00
⟩
+
sin
(
θ
)
∣11
⟩
with
θ
=
π
/
8
\theta = \pi/8
θ
=
π
/8
, the concurrence is
C
=
∣
sin
(
2
θ
)
∣
C = |\sin(2\theta)|
C
=
∣
sin
(
2
θ
)
∣
. The entanglement of formation is
E
F
=
h
(
x
)
E_F = h(x)
E
F
=
h
(
x
)
, where
x
=
(
1
+
1
−
C
2
)
/
2
x = (1 + \sqrt{1 - C^2})/2
x
=
(
1
+
1
−
C
2
)
/2
and
h
(
x
)
=
−
x
log
2
(
x
)
−
(
1
−
x
)
log
2
(
1
−
x
)
h(x) = -x\log_2(x) - (1-x)\log_2(1-x)
h
(
x
)
=
−
x
lo
g
2
(
x
)
−
(
1
−
x
)
lo
g
2
(
1
−
x
)
is the binary entropy. What is
E
F
E_F
E
F
, in ebits?
🔬 try it before you answer
1.000
0.601
0.354
0.707
Check answer