nLab postselection

Idea

In probability theory and specifically in discussion of measurement one speaks of postselection if only processes with certain (measurement) outcomes are selected for (further) discussion.

Postselection plays a special role in quantum measurement due to the latter’s intrinsically non-deterministic nature, cf. repeat-until-success computing.

Related concepts

• PostBQP

• nondeterministic computation

References

General

See also:

• Wikipedia: Postselection

In quantum information

Early discussion of quantum (pre- and) post-selection in a context of a notion called “weak” quantum measurement:

• Yakir Aharonov, David Z. Albert, Lev Vaidman: How the result of a measurement of a component of the spin of a spin-$1/2$ particle can turn out to be $100$, Phys. Rev. Lett. 60 1351 [doi:10.1103/PhysRevLett.60.1351]

• Yakir Aharonov, Lev Vaidman: Complete description of a quantum system at a given time, J. Phys. A: Math. Gen. 24 (1991) 2315 [doi:10.1088/0305-4470/24/10/018]

• Yakir Aharonov, Lev Vaidman: The Two-State Vector Formalism of Qauntum Mechanics: an Updated Review [arXiv:quant-ph/0105101]

Review of the general notion of quantum postselection:

• A. Ch. N. Chowdhury: Quantum measurements with post-selection MasterThesis, Kolkata (2013) [handle:123456789/255, pdf, pdf]

See also:

• Masashi Ban: Conditional average in a quantum system with postselection, Quantum Stud.: Math. Found. 2 (2015) 263–273 [doi:10.1007/s40509-015-0043-9]

In the context of quantum complexity theory (cf. PostBQP):

• Scott Aaronson, Quantum computing, postselection, and probabilistic polynomial-time, Proceedings of the Royal Society A 461 2063 (2005) 3473–3482 [doi:10.1098/rspa.2005.1546, arXiv:quant-ph/0412187]

In the context of quantum advantage:

• Seth Lloyd et al.: Quantum advantage in postselected metrology, Nature Communications 11 3775 (2020) [doi:10.1038/s41467-020-17559-w]