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pro vyhledávání: '"Helton, J. William"'
Let $S_r(p,q)$ be the $r$-associated Stirling numbers of the second kind, the number of ways to partition a set of size $p$ into $q$ subsets of size at least $r$. For $r=1$, these are the standard Stirling numbers of the second kind, and for $r=2$, t
Externí odkaz:
http://arxiv.org/abs/2409.01489
Publikováno v:
Quantum 8, 1352 (2024)
The Quantum Max Cut (QMC) problem has emerged as a test-problem for designing approximation algorithms for local Hamiltonian problems. In this paper we attack this problem using the algebraic structure of QMC, in particular the relationship between t
Externí odkaz:
http://arxiv.org/abs/2307.15661
A spectrahedron is a convex set defined by a linear matrix inequality, i.e., the set of all $x \in \mathbb{R}^g$ such that \[ L_A(x) = I + A_1 x_1 + A_2 x_2 + \dots + A_g x_g \succeq 0 \] for some symmetric matrices $A_1,\ldots,A_g$. This can be exte
Externí odkaz:
http://arxiv.org/abs/2212.00748
Recent results showed it was possible to determine if a modest size 3XOR game has a perfect quantum strategy. We build on these and give an explicit polynomial time algorithm which constructs such a perfect strategy or refutes its existence. This new
Externí odkaz:
http://arxiv.org/abs/2209.04655
Autor:
Helton, J. William, Mousavi, Hamoon, Nezhadi, Seyed Sajjad, Paulsen, Vern I., Russell, Travis B.
We study synchronous values of games, especially synchronous games. It is known that a synchronous game has a perfect strategy if and only if it has a perfect synchronous strategy. However, we give examples of synchronous games, in particular graph c
Externí odkaz:
http://arxiv.org/abs/2109.14741
Autor:
Watts, Adam Bene, Helton, J. William
Publikováno v:
Communications in Mathematical Physics volume 400, pages 731-791 (2023)
We consider 3XOR games with perfect commuting operator strategies. Given any 3XOR game, we show existence of a perfect commuting operator strategy for the game can be decided in polynomial time. Previously this problem was not known to be decidable.
Externí odkaz:
http://arxiv.org/abs/2010.16290
Publikováno v:
Experimental Mathematics 2021. pp. (1-25)
Semidefinite programming is based on optimization of linear functionals over convex sets defined by linear matrix inequalities, namely, inequalities of the form $$L_A(X)=I-A_1X_1-\dots-A_g X_g\succeq0.$$ Here the $X_j$ are real numbers and the set of
Externí odkaz:
http://arxiv.org/abs/2006.02248
Publikováno v:
J. Math. Anal. Appl. 492 (2020) 124421, 23pp
A noncommutative (nc) function in $x_1,\dots,x_g,x_1^*,\dots,x_g$ is called plurisubharmonic (plush) if its nc complex Hessian takes only positive semidefinite values on an nc neighborhood of 0. The main result of this paper shows that an nc rational
Externí odkaz:
http://arxiv.org/abs/1908.01895
Publikováno v:
Int. Math. Res. Not. IMRN Issue 11 (2022) 343--372
This article gives a class of Nullstellens\"atze for noncommutative polynomials. The singularity set of a noncommutative polynomial $f=f(x_1,\dots,x_g)$ is $Z(f)=(Z_n(f))_n$, where $Z_n(f)=\{X \in M_n^g: \det f(X) = 0\}.$ The first main theorem of th
Externí odkaz:
http://arxiv.org/abs/1907.04328