Bell state
Noun
Meaning
Bell state (plural Bell states)
(quantum information science) One of a set of four entangled states, namely
|
Φ
+
⟩
=
1
2
(
|
00
⟩
+
|
11
⟩
)
{\displaystyle |\Phi ^{+}\rangle ={1 \over {\sqrt {2}}}(|00\rangle +|11\rangle )}
,
|
Φ
−
⟩
=
1
2
(
|
00
⟩
−
|
11
⟩
)
{\displaystyle |\Phi ^{-}\rangle ={1 \over {\sqrt {2}}}(|00\rangle -|11\rangle )}
,
|
Ψ
+
⟩
=
1
2
(
|
01
⟩
+
|
10
⟩
)
{\displaystyle |\Psi ^{+}\rangle ={1 \over {\sqrt {2}}}(|01\rangle +|10\rangle )}
, and
|
Ψ
−
⟩
=
1
2
(
|
01
⟩
−
|
10
⟩
)
{\displaystyle |\Psi ^{-}\rangle ={1 \over {\sqrt {2}}}(|01\rangle -|10\rangle )}
, where
|
x
y
⟩
:=
|
x
⟩
⊗
|
y
⟩
{\displaystyle |xy\rangle :=|x\rangle \otimes |y\rangle }
; these are the simplest examples of entangled states.
Examples
Assume parts of a maximally entangled Bell state are distributed to Alice and Bob.