The complexity class QMA(2), featuring two unentangled quantum provers, occupies a central yet poorly understood position in quantum complexity theory. While superficially a modest extension of QMA, unentanglement fundamentally changes both the algorithmic and complexitytheoretic landscape, connecting QMA(2) to deep questions in separability testing, polynomial optimization, and hardness of approximation. Over the past two decades, QMA(2) has inspired a rich body of work spanning restricted verification models, semidefinite and Sum-of-Squares hierarchies, and surprising links to classical problems such as the Unique Games Conjecture. This survey provides an overview of these developments, emphasizing structural insights, algorithmic techniques, and known barriers, while highlighting how progress on QMA(2) continues to illuminate the interplay between quantum information, convex optimization, and classical complexity theory.
The PCP theorem [AS98, ALM + 98, Din07] is a breakthrough in theoretical CS with a wide range of applications. In this article, we discuss the work of [BMVY25] that constructs improved probabilistically checkable proofs (PCPs) from high-dimensional expanders (HDX). Our goal is to explain the main components of their construction, while also giving historical context for how the key ideas emerged across the PCP, HDX and routing literature. We aim for a largely self-contained overview, with additional pointers for technical details. We focus on the following ingredients: PCPs from expanders [Din07]; the abstraction of direct product testing [GS00]; recent constructions of linear size direct product testers with small soundness [BM24, BLM24, DD24a, DD24c, DDL24], and the role of high-dimensional expansion in enabling these results. We then explain how [BMVY25] turned such direct product testers into PCPs via a new connection to fault-tolerant routing, and a construction of such algorithms for HDX. Finally, we conclude with some other applications that these techniques have found and future directions.
This Issue's Column! This issue's Open Problem Column is by William Gasarch and is Relationships Between the Busy Beaver Function and Mathematics I: What is the Smallest n such that BB(n) > ... Request for Columns! I invite any reader who has knowledge of some area to contact me and arrange to write a column about open problems in that area. That area can be (1) broad or narrow or anywhere in between, and (2) really important or really unimportant or anywhere in between.
''Laplacian'' is one of those buzzwords that can stop a conversation. Algebraic techniques in a distributed setting can be frightening: they feel complicated, definition-heavy, and out of reach for the ordinary distributed computing researcher. I am here to tell you that it is not so bad. In this survey, I will outline the main ideas and techniques in the field, while simplifying to the level that you do not even need to remember much from your linear algebra classes.
Dear Readers, For this issue, Geoffroy Couteau contributed a wonderful guest column on the cryptographic problem of ''compressing'' correlated randomness and its surprising applications to cooking Chicken Tikka Masala (please do read the column for more details!). In the upcoming issues of SIGACT News, we expect to feature columns by Jesse Goodman (on seedless extractors); Davi Castro-Silva, Arkopal Dutt, and Tom Gur (on connections between additive combinatorics and quantum complexity theory); Debarati Das; and Jeroen Zuiddam (on matrix multiplication, moment polytopes and asymptotic spectra).
