Approximating fixed size quantum correlations in polynomial time

• URL: http://arxiv.org/abs/2507.12302v1
• Date: Wed, 16 Jul 2025 15:01:45 GMT
• Title: Approximating fixed size quantum correlations in polynomial time
• Authors: Julius A. Zeiss, Gereon Koßmann, Omar Fawzi, Mario Berta,
• Abstract summary: We show that $varepsilon$-additive approximations of the optimal value of fixed-size two-player free games can be computed in time.<n>Our main result is based on novel Bose-symmetric quantum de Finetti theorems tailored for constrained quantum separability problems.
• Score: 8.099700053397278
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We show that $\varepsilon$-additive approximations of the optimal value of fixed-size two-player free games with fixed-dimensional entanglement assistance can be computed in time $\mathrm{poly}(1/\varepsilon)$. This stands in contrast to previous analytic approaches, which focused on scaling with the number of questions and answers, but yielded only strict $\mathrm{exp}(1/\varepsilon)$ guarantees. Our main result is based on novel Bose-symmetric quantum de Finetti theorems tailored for constrained quantum separability problems. These results give rise to semidefinite programming (SDP) outer hierarchies for approximating the entangled value of such games. By employing representation-theoretic symmetry reduction techniques, we demonstrate that these SDPs can be formulated and solved with computational complexity $\mathrm{poly}(1/\varepsilon)$, thereby enabling efficient $\varepsilon$-additive approximations. In addition, we introduce a measurement-based rounding scheme that translates the resulting outer bounds into certifiably good inner sequences of entangled strategies. These strategies can, for instance, serve as warm starts for see-saw optimization methods. We believe that our techniques are of independent interest for broader classes of constrained separability problems in quantum information theory.

Related papers

• Optimistic Online Learning in Symmetric Cone Games [3.124884279860061]
  We introduce the Optimistic Symmetric Cone Multiplicative Weights Update algorithm and establish an iteration complexity of $mathcalO (1/epsilon)$ to reach an $epsilon$-saddle point.<n>A key technical contribution is a new proof of the strong convexity of the symmetric cone negative entropy with respect to the trace-one norm.
  arXiv  Detail & Related papers  (2025-04-04T16:59:19Z)
• Computable entanglement cost under positive partial transpose operations [4.642647756403864]
  We consider the problem of computing the entanglement cost of preparing noisy quantum states under quantum operations.<n>To our knowledge, this is the first time that an entanglement measure is shown to be efficiently computable despite no closed-form formula being available.
  arXiv  Detail & Related papers  (2024-05-15T18:00:01Z)
• Projection by Convolution: Optimal Sample Complexity for Reinforcement Learning in Continuous-Space MDPs [56.237917407785545]
  We consider the problem of learning an $varepsilon$-optimal policy in a general class of continuous-space Markov decision processes (MDPs) having smooth Bellman operators. Key to our solution is a novel projection technique based on ideas from harmonic analysis. Our result bridges the gap between two popular but conflicting perspectives on continuous-space MDPs.
  arXiv  Detail & Related papers  (2024-05-10T09:58:47Z)
• Learning with Norm Constrained, Over-parameterized, Two-layer Neural Networks [54.177130905659155]
  Recent studies show that a reproducing kernel Hilbert space (RKHS) is not a suitable space to model functions by neural networks. In this paper, we study a suitable function space for over- parameterized two-layer neural networks with bounded norms.
  arXiv  Detail & Related papers  (2024-04-29T15:04:07Z)
• Reduced Contraction Costs of Corner-Transfer Methods for PEPS [0.0]
  We propose a pair of approximations that allows the leading order computational cost of contracting an infinite projected entangled-pair state to be reduced. The improvement in computational cost enables us to perform large bond dimension calculations, extending its potential to solve challenging problems.
  arXiv  Detail & Related papers  (2023-06-14T02:54:12Z)
• Pseudonorm Approachability and Applications to Regret Minimization [73.54127663296906]
  We convert high-dimensional $ell_infty$-approachability problems to low-dimensional pseudonorm approachability problems. We develop an algorithmic theory of pseudonorm approachability, analogous to previous work on approachability for $ell$ and other norms.
  arXiv  Detail & Related papers  (2023-02-03T03:19:14Z)
• A Newton-CG based barrier-augmented Lagrangian method for general nonconvex conic optimization [53.044526424637866]
  In this paper we consider finding an approximate second-order stationary point (SOSP) that minimizes a twice different subject general non conic optimization. In particular, we propose a Newton-CG based-augmentedconjugate method for finding an approximate SOSP.
  arXiv  Detail & Related papers  (2023-01-10T20:43:29Z)
• Stochastic Inexact Augmented Lagrangian Method for Nonconvex Expectation Constrained Optimization [88.0031283949404]
  Many real-world problems have complicated non functional constraints and use a large number of data points. Our proposed method outperforms an existing method with the previously best-known result.
  arXiv  Detail & Related papers  (2022-12-19T14:48:54Z)
• Explicit Second-Order Min-Max Optimization Methods with Optimal Convergence Guarantee [86.05440220344755]
  We propose and analyze inexact regularized Newton-type methods for finding a global saddle point of emphcon unconstrained min-max optimization problems. We show that the proposed methods generate iterates that remain within a bounded set and that the iterations converge to an $epsilon$-saddle point within $O(epsilon-2/3)$ in terms of a restricted function.
  arXiv  Detail & Related papers  (2022-10-23T21:24:37Z)
• On efficient algorithms for computing near-best polynomial approximations to high-dimensional, Hilbert-valued functions from limited samples [1.0650780147044159]
  Sparse approximation has become indispensable for approxing smooth, high-dimensional functions from limited samples. This paper introduces algorithms and theoretical guarantees that assert exponential or algebraic rates of convergence, along with robustness to sampling, algorithmic and physical discretization errors.
  arXiv  Detail & Related papers  (2022-03-25T20:56:07Z)
• Nonparametric approximation of conditional expectation operators [0.3655021726150368]
  We investigate the approximation of the $L2$-operator defined by $[Pf](x) := mathbbE[ f(Y) mid X = x ]$ under minimal assumptions. We prove that $P$ can be arbitrarily well approximated in operator norm by Hilbert-Schmidt operators acting on a reproducing kernel space.
  arXiv  Detail & Related papers  (2020-12-23T19:06:12Z)
• Learning Halfspaces with Tsybakov Noise [50.659479930171585]
  We study the learnability of halfspaces in the presence of Tsybakov noise. We give an algorithm that achieves misclassification error $epsilon$ with respect to the true halfspace.
  arXiv  Detail & Related papers  (2020-06-11T14:25:02Z)
• Quasi-polynomial time algorithms for free quantum games in bounded dimension [11.56707165033]
  We give a semidefinite program of size $exp(mathcalObig(T12(log2(AT)+log(Q)log(AT))/epsilon2big)) to compute additive $epsilon$-approximations on the values of two-player free games. We make a connection to the quantum separability problem and employ improved multipartite quantum de Finetti theorems with linear constraints.
  arXiv  Detail & Related papers  (2020-05-18T16:55:08Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.