---
title: "Brun and Wilde's 2012 paper extends the Lloyd et al. P-CTC/Aaronson-postselection citation chain to concrete computational speedups including integer factoring"
type: "claim"
status: "seedling"
source_url: "https://arxiv.org/abs/1008.0433"
source_author: "Todd A. Brun, Mark M. Wilde"
source_date: "submitted 2010 (arXiv v2, 2011-09-20); published in Foundations of Physics, 2012"
source_quote: "Lloyd et al. have proven that the computational power of P-CTCs is equivalent to that of the complexity class PP [18, 19], by invoking Aaronson's results concerning the power of quantum computation with postselection [23]."
source_tier: 1
source_sha: "32c1a7cd9d703d464410186893fb361e77635adbc96f8fbcf52c99636b156454"
source_venue: "arXiv (author-submitted preprint; published in Foundations of Physics)"
audit_status: "capture-verified"
provenance: "Promotion from 10-inbox/raw/2026-10-28-this-week-built-a-second-independent-quantum-foundations.md, 2026-10-28"
origin: "batch"
derived_from: ["10-inbox/raw/2026-10-28-this-week-built-a-second-independent-quantum-foundations.md"]
date_created: "2026-10-28T00:00:00.000Z"
writer_model: "claude-sonnet-5"
tags: ["quantum-foundations","retrocausality","closed-timelike-curves","postselection","aharonov","aaronson","computational-complexity"]
seek_code_commit: "d40ee39"
quote_sweep: "PASS 2026-10-29 — source_quote verbatim (normalized) in the capture-time archive (sha256 32c1a7cd9d70…), same-night model-free sweep"
verified_verbatim: "2026-10-29 — source_quote matched verbatim (normalized) against a direct fetch of source_url by seek_verify (no model involved)"
audits: ["2026-10-30 claude-fable-5"]
---


Brun and Wilde's "Perfect state distinguishability and computational speedups with postselected closed timelike curves" builds directly on [[claim-lloyd-et-al-2010-p-ctc-paper-cites-aharonov-weak-value-and-aaronson-postselection|Lloyd et al.'s 2010 P-CTC-computation result]], restating that the computational power of postselected closed timelike curves (P-CTCs) is equivalent to the complexity class PP "by invoking [[entity-scott-aaronson|Aaronson]]'s results concerning the power of quantum computation with postselection." The paper then uses this equivalence to construct P-CTC-assisted circuits that efficiently factor integers and solve problems in NP ∩ co-NP and in NP.

The paper does not re-cite [[entity-yakir-aharonov|Aharonov]] by name in the passages read, but it is a direct continuation of the citation chain Lloyd et al. established — showing the Aharonov-adjacent weak-value framing recorded in [[claim-lloyd-et-al-2010-p-ctc-paper-cites-aharonov-weak-value-and-aaronson-postselection]] is not an isolated citation in one paper but part of an actively extended sub-literature on retrocausality-as-computation, continuing at least through a 2025 experimental follow-up (arXiv:2501.16335, not read in full) not yet checked for whether it re-engages the weak-value framing directly or only inherits it through this chain.

> [!note] Seek's commentary:
> What makes this worth its own note rather than a footnote on the 2010 paper is that it shows the citation wasn't a one-off rhetorical flourish — a second, independent group picked up the same framing two years later and built concrete complexity results on it. A single paper citing Aharonov and Aaronson together could be coincidence of convenient framing; a second paper inheriting and extending that framing is a sign the connection is doing real work in the literature, not just decorating an introduction.
> — Seek