bibkey: abbott2019anomalous authors: Alastair A. Abbott; Ralph Silva; Julian Wechs; Nicolas Brunner; Cyril Branciard year: 2019 title: “Anomalous Weak Values Without Post-Selection” doi: 10.22331/q-2019-10-14-194 url: https://arxiv.org/abs/1805.09364v3 claim: “Without post-selection the mean product of the pointer positions of n sequential weak measurements of A_1, …, A_n on rho is 2^(-(n-1)) Tr[{A_1, {A_2, …, {A_(n-1), A_n}…}} rho]; for two projection observables (eigenvalues 0 and 1) it is at least -1/8, and the authors conjecture the bound -1/8 for every number n of projection observables.” strata_touched:

• D5/S3/Quantum/Measurement/SequentialWeakPointerRefutation license: citation-only triage: anchor

Anomalous Weak Values Without Post-Selection

A. A. Abbott, R. Silva, J. Wechs, N. Brunner and C. Branciard, arXiv:1805.09364 (v1 2018-05-23, v3 2019-09-12); Quantum 3, 194 (2019). Subject: quant-ph.

The paper shows that sequential weak measurements without post-selection can produce anomalous weak values. For two sequential weak measurements of A then B on ψ, the mean product of the pointer positions is the real part of the sequential weak value (BA)_ψ = ⟨ψ|BA|ψ⟩. For two projection observables (eigenvalues 0 and 1) the Appendix proves Re[(BA)_ψ] ≥ −1/8 for every pure or mixed state. For n measurements the Appendix expresses the mean product of the pointer positions as the nested anticommutator 2^{−(n−1)} Tr[{A_1, {A_2, …, {A_{n−1}, A_n}…}} ρ], and the section on more measurements states:

Interestingly, by numerically minimising the mean product of the pointer positions for sequences of up to 5 projection observables, we were unable to obtain a value smaller than −1/8, and we conjecture that this is in fact the case for all n.

Verified locator

• DOI: https://doi.org/10.22331/q-2019-10-14-194 (the journal page was not read).
• URL: https://arxiv.org/abs/1805.09364v3 (source retrieved 2026-09-30): anomalous_wv_no_postselection_final.tex, section “More measurements” (the conjecture), Appendix “Proof that Re[(BA)_ψ] ≥ −1/8 for two projection observables” and subsection “Generalisation to n sequential weak measurements” (the nested anticommutator).