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:
Fropuff/Tables/Qubit states
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<
User:Fropuff
|
Tables
cos
θ
2
|
0
⟩
+
e
i
ϕ
sin
θ
2
|
1
⟩
{\displaystyle \cos {\frac {\theta }{2}}|0\rangle +e^{i\phi }\sin {\frac {\theta }{2}}|1\rangle }
tan
θ
2
e
i
ϕ
{\displaystyle \tan {\frac {\theta }{2}}e^{i\phi }}
(
sin
θ
cos
ϕ
,
sin
θ
sin
ϕ
,
cos
θ
)
{\displaystyle (\sin \theta \cos \phi ,\sin \theta \sin \phi ,\cos \theta )}
|
0
⟩
{\displaystyle |0\rangle }
0
{\displaystyle 0}
(
0
,
0
,
1
)
{\displaystyle (0,0,1)}
|
1
⟩
{\displaystyle |1\rangle }
∞
{\displaystyle \infty }
(
0
,
0
,
−
1
)
{\displaystyle (0,0,-1)}
cos
θ
2
|
0
⟩
+
sin
θ
2
|
1
⟩
{\displaystyle \cos {\frac {\theta }{2}}|0\rangle +\sin {\frac {\theta }{2}}|1\rangle }
tan
θ
2
{\displaystyle \tan {\frac {\theta }{2}}}
(
sin
θ
,
0
,
cos
θ
)
{\displaystyle (\sin \theta ,0,\cos \theta )}
1
2
(
|
0
⟩
+
|
1
⟩
)
{\displaystyle {\frac {1}{\sqrt {2}}}\left(|0\rangle +|1\rangle \right)}
1
{\displaystyle 1}
(
1
,
0
,
0
)
{\displaystyle (1,0,0)}
|
+
⟩
{\displaystyle |+\rangle }
1
2
(
|
0
⟩
−
|
1
⟩
)
{\displaystyle {\frac {1}{\sqrt {2}}}\left(|0\rangle -|1\rangle \right)}
−
1
{\displaystyle -1}
(
−
1
,
0
,
0
)
{\displaystyle (-1,0,0)}
|
−
⟩
{\displaystyle |-\rangle }
1
2
(
|
0
⟩
+
e
i
ϕ
|
1
⟩
)
{\displaystyle {\frac {1}{\sqrt {2}}}\left(|0\rangle +e^{i\phi }|1\rangle \right)}
e
i
ϕ
{\displaystyle e^{i\phi }}
(
cos
ϕ
,
sin
ϕ
,
0
)
{\displaystyle (\cos \phi ,\sin \phi ,0)}
1
2
(
|
0
⟩
+
i
|
1
⟩
)
{\displaystyle {\frac {1}{\sqrt {2}}}\left(|0\rangle +i|1\rangle \right)}
i
{\displaystyle i}
(
0
,
1
,
0
)
{\displaystyle (0,1,0)}
1
2
(
|
0
⟩
−
i
|
1
⟩
)
{\displaystyle {\frac {1}{\sqrt {2}}}\left(|0\rangle -i|1\rangle \right)}
−
i
{\displaystyle -i}
(
0
,
−
1
,
0
)
{\displaystyle (0,-1,0)}
cos
θ
2
|
0
⟩
+
i
sin
θ
2
|
1
⟩
{\displaystyle \cos {\frac {\theta }{2}}|0\rangle +i\sin {\frac {\theta }{2}}|1\rangle }
i
tan
θ
2
{\displaystyle i\tan {\frac {\theta }{2}}}
(
0
,
sin
θ
,
cos
θ
)
{\displaystyle (0,\sin \theta ,\cos \theta )}