• Source: Postselection

In probability theory, to postselect is to condition a probability space upon the occurrence of a given event. In symbols, once we postselect for an event



E


{\displaystyle E}

, the probability of some other event



F


{\displaystyle F}

changes from



Pr
⁡
[
F
]


{\textstyle \operatorname {Pr} [F]}

to the conditional probability



Pr
⁡
[
F


|


E
]


{\displaystyle \operatorname {Pr} [F\,|\,E]}

.
For a discrete probability space,



Pr
⁡
[
F


|


E
]
=



Pr
⁡
[
F

∩

E
]


Pr
⁡
[
E
]





{\textstyle \operatorname {Pr} [F\,|\,E]={\frac {\operatorname {Pr} [F\,\cap \,E]}{\operatorname {Pr} [E]}}}

, and thus we require that



Pr
⁡
[
E
]


{\textstyle \operatorname {Pr} [E]}

be strictly positive in order for the postselection to be well-defined.
See also PostBQP, a complexity class defined with postselection. Using postselection it seems quantum Turing machines are much more powerful: Scott Aaronson proved PostBQP is equal to PP.
Some quantum experiments use post-selection after the experiment as a replacement for communication during the experiment, by post-selecting the communicated value into a constant.




References

Kata Kunci Pencarian:

• Postselection
• PostBQP
• PP (complexity)
• Quantum Turing machine
• Weak value
• Scott Aaronson
• No-cloning theorem
• BQP
• Seth Lloyd
• BPP (complexity)