---
res:
  bibo_abstract:
  - We prove quantitative lower bounds on the semidefinite extension complexity of
    the set of separable quantum states on $\mathbb{C}^d\otimes\mathbb{C}^d$. We consider
    semidefinite programs (SDPs) that approximate the maximum acceptance probability
    of a measurement over separable states, the optimization problem underlying QMA(2).
    In the extended-formulation model of Harrow, Natarajan, and Wu (HNW), all measurements
    share a common feasible region and an objective-independent embedding of product
    states that exactly reproduces their acceptance probabilities. For every $0<θ<2/7$,
    there are constants $c_θ,a_θ>0$ such that, for sufficiently large $d$, any such
    SDP with uniform additive error $0<a\le a_θ$ has size at least $d^{c_θ\min\{a^{-1/3},d^θ\}}$.
    The bound applies at sufficiently small constant error, is superpolynomial in
    $d$ whenever $a=o(1)$, and becomes $d^{Ω(d^θ)}$ when $a\le d^{-3θ}$, improving
    HNW's quasipolynomial bound at inverse- square error. The same bound holds for
    any SDP-representable convex set of states that contains all separable states
    and lies within trace distance $a$ of them, giving a quantitative counterpart
    to Fawzi's theorem that the separable set has no exact semidefinite representation.
    Our proof combines the quantitative pseudo-density theorem of Lee, Raghavendra,
    and Steurer with explicit block-positive operators and Chebyshev amplification.
    Our main results are supported by Lean proofs.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Sevag
      foaf_name: Gharibian, Sevag
      foaf_surname: Gharibian
      foaf_workInfoHomepage: http://www.librecat.org/personId=71541
    orcid: 0000-0002-9992-3379
  - foaf_Person:
      foaf_givenName: Carsten
      foaf_name: Hecht, Carsten
      foaf_surname: Hecht
  - foaf_Person:
      foaf_givenName: Dorian
      foaf_name: Rudolph, Dorian
      foaf_surname: Rudolph
      foaf_workInfoHomepage: http://www.librecat.org/personId=57863
  dct_date: 2026^xs_gYear
  dct_language: eng
  dct_title: Semidefinite extension complexity of the separable set, with applications
    to approximate disentanglers@
...