---
title: "weak value"
type: "entity"
entity_kind: "concept"
status: "hub"
canonical_name: "weak value"
aliases: ["weak measurement"]
first_seen: "2026-10-23T00:00:00.000Z"
writer_model: "claude-sonnet-5"
connects_to: ["two-state vector formalism","pre- and post-selection","Yakir Aharonov","Lev Vaidman","quantum pigeonhole principle"]
seek_code_commit: "d40ee39"
---


A weak value is the quantity Aw = ⟨ϕ|A|ψ⟩/⟨ϕ|ψ⟩ obtained from a weak — minimally disturbing — measurement of an observable A on a quantum system pre-selected into state |ψ⟩ and later post-selected into state |ϕ⟩; because the denominator can be small, a weak value can lie outside A's normal eigenvalue range. Introduced by Aharonov, Albert & [[entity-lev-vaidman|Vaidman]] in 1988, it is the formal device behind both the original "spin can turn out to be 100" result and the 2016 quantum pigeonhole principle, and underlies the [[entity-two-state-vector-formalism|two-state vector formalism]] that [[entity-yakir-aharonov|Yakir Aharonov]] and Vaidman built around it.

## References
- [[claim-aharonov-1988-weak-value-origin-disturbance-scales-epsilon-squared]]
- [[claim-aharonov-2016-quantum-pigeonhole-three-particles-two-boxes-weak-value]]
- [[claim-lloyd-et-al-2010-p-ctc-paper-cites-aharonov-weak-value-and-aaronson-postselection]]

- 2026-10-28: a 2010 physics paper on postselected closed timelike curves (P-CTCs) cites the 1988 weak-value paper directly to describe why P-CTCs lack a unique definite state at a given time — the weak-value concept's one documented reach into the physics-of-computation literature outside its originating foundations-of-QM context ([[claim-lloyd-et-al-2010-p-ctc-paper-cites-aharonov-weak-value-and-aaronson-postselection]]).