The perturbative method for quantum correlations

• URL: http://arxiv.org/abs/2603.26875v1
• Date: Fri, 27 Mar 2026 18:00:08 GMT
• Title: The perturbative method for quantum correlations
• Abstract summary: The set $mathcalQ$ of quantum correlations is the collection of all possible probability distributions on measurement outcomes achievable by space-like separated parties sharing a quantum state.<n>We introduce a perturbative method using Lie-theoretic tools for the unitary group to analyze the response of the evaluations of Bell functional perturbations under infinitesimal unitarys of quantum strategies.
• Score: 0.6187780920448871
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The set $\mathcal{Q}$ of quantum correlations is the collection of all possible probability distributions on measurement outcomes achievable by space-like separated parties sharing a quantum state. Since the original work of Tsirelson [Tsirelson, Lett. Math. Phys. 4, 93 (1980)], this set has mainly been studied through the means algebraic and convex geometry techniques. We introduce a perturbative method using Lie-theoretic tools for the unitary group to analyze the response of the evaluations of Bell functionals under infinitesimal unitary perturbations of quantum strategies. Our main result shows that, near classical deterministic points, an $(n, 2, d)$ Bell operator decomposes into a direct sum of $(k, 2, d-1)$ Bell operators which we call \emph{subset games}. We then derive three key insights: (1) in the $(n, 2, 2)$ case, if $p_0$ is classically optimal, it remains locally optimal even among 2-dimensional quantum strategies, implying in turn that the boundary of $\mathcal{Q}$ is flat around classical deterministic points; (2) it suggests a proof strategy for Gisin's open problem on correlations in $\mathcal{Q}(D)$ unattainable by projective strategies of the same dimension; and (3) it establishes that the Ansatz dimension is a critical resource for learning in distributed scenarios, even when the optimal solution admits a low-dimensional representation.

Related papers

• Quantum Speedups for Stochastic Optimization with Heavy-Tailed Noise [49.730496294398726]
  We develop a novel quantum mean estimator for heavy-tailed random variables.<n>We derive stronger lower bounds for tail index>4/3$, showing that a nontrivial dependence on a dimension is unavoidable.<n>For a convex objective function, we propose a quantum projected gradient descent method.
  arXiv  Detail & Related papers  (2026-07-28T09:29:37Z)
• Learning the closest Slater determinant [0.0]
  We study the task of learning the Slater determinant with maximum fidelity to an arbitrary fermionic many-body state.<n>We apply the algorithm to the Fermi-Hubbard model, extracting the closest Slater determinant from neural quantum state solutions.
  arXiv  Detail & Related papers  (2026-07-22T18:00:04Z)
• Average-case quantum complexity from glassiness [45.57609001239456]
  Glassiness -- a phenomenon in physics characterized by a rough free-energy landscape -- implies hardness for stable classical algorithms.<n>We prove that the standard notion of quantum glassiness based on replica symmetry breaking obstructs stable quantum algorithms for Gibbs sampling.
  arXiv  Detail & Related papers  (2025-10-09T17:37:33Z)
• KPZ scaling from the Krylov space [83.88591755871734]
  Recently, a superdiffusion exhibiting the Kardar-Parisi-Zhang scaling in late-time correlators and autocorrelators has been reported. Inspired by these results, we explore the KPZ scaling in correlation functions using their realization in the Krylov operator basis.
  arXiv  Detail & Related papers  (2024-06-04T20:57:59Z)
• A quantum-classical performance separation in nonconvex optimization [7.427989325451079]
  We prove that the recently proposed Quantum Hamiltonian (QHD) algorithm is able to solve any $d$dimensional queries from this family. On the other side, a comprehensive empirical study suggests that representative state-of-the-art classical algorithms/solvers would require a superpolynomial time to solve such queries.
  arXiv  Detail & Related papers  (2023-11-01T19:51:00Z)
• Approximation Algorithms for Quantum Max-$d$-Cut [42.248442410060946]
  The Quantum Max-$d$-Cut problem involves finding a quantum state that maximizes the expected energy associated with the projector onto the antisymmetric subspace of two, $d$-dimensional qudits over all local interactions. We develop an algorithm that finds product-state solutions of mixed states with bounded purity that achieve non-trivial performance guarantees.
  arXiv  Detail & Related papers  (2023-09-19T22:53:17Z)
• Guidable Local Hamiltonian Problems with Implications to Heuristic Ansätze State Preparation and the Quantum PCP Conjecture [0.0]
  We study 'Merlinized' versions of the recently defined Guided Local Hamiltonian problem. These problems do not have a guiding state provided as a part of the input, but merely come with the promise that one exists. We show that guidable local Hamiltonian problems for both classes of guiding states are $mathsfQCMA$-complete in the inverse-polynomial precision setting.
  arXiv  Detail & Related papers  (2023-02-22T19:00:00Z)
• The Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) Equation for Two-Dimensional Systems [62.997667081978825]
  Open quantum systems can obey the Franke-Gorini-Kossakowski-Lindblad-Sudarshan (FGKLS) equation. We exhaustively study the case of a Hilbert space dimension of $2$.
  arXiv  Detail & Related papers  (2022-04-16T07:03:54Z)
• The complexity of quantum support vector machines [1.7887848708497243]
  Quantum support vector machines employ quantum circuits to define the kernel function. We show that the dual problem can be solved in $O(M4.67/varepsilon2)$ quantum circuit evaluations.
  arXiv  Detail & Related papers  (2022-02-28T19:01:17Z)
• On the relation between completely bounded and $(1,cb)$-summing maps with applications to quantum XOR games [65.51757376525798]
  We show that given a linear map from a general operator space into the dual of a C$*$-algebra, its completely bounded norm is upper bounded by a universal constant times its $(''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''''
  arXiv  Detail & Related papers  (2021-12-09T21:06:52Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Random quantum circuits anti-concentrate in log depth [118.18170052022323]
  We study the number of gates needed for the distribution over measurement outcomes for typical circuit instances to be anti-concentrated. Our definition of anti-concentration is that the expected collision probability is only a constant factor larger than if the distribution were uniform. In both the case where the gates are nearest-neighbor on a 1D ring and the case where gates are long-range, we show $O(n log(n)) gates are also sufficient.
  arXiv  Detail & Related papers  (2020-11-24T18:44:57Z)

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.