Quantum Information-Theoretical Size Bounds for Conjunctive Queries with Functional Dependencies

• URL: http://arxiv.org/abs/2506.07552v1
• Date: Mon, 09 Jun 2025 08:46:56 GMT
• Title: Quantum Information-Theoretical Size Bounds for Conjunctive Queries with Functional Dependencies
• Authors: Valter Uotila, Jiaheng Lu,
• Abstract summary: We establish a connection between earlier work on estimating size bounds for conjunctive queries with classical information theory and quantum information theory.<n>We propose replacing the classical Shannon entropy with the quantum R'enyi entropy.<n>Although this is a promising modification, optimization with respect to the quantum states instead of classical distributions creates a new set of challenges.
• Score: 5.430093460802071
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Deriving formulations for computing and estimating tight worst-case size increases for conjunctive queries with various constraints has been at the core of theoretical database research. If the problem has no constraints or only one constraint, such as functional dependencies or degree constraints, tight worst-case size bounds have been proven, and they are even practically computable. If the problem has more than one constraint, computing tight bounds can be difficult in practice and may even require an infinite number of linear inequalities in its optimization formulation. While these challenges have been addressed with varying methods, no prior research has employed quantum information theory to address this problem. In this work, we establish a connection between earlier work on estimating size bounds for conjunctive queries with classical information theory and the field of quantum information theory. We propose replacing the classical Shannon entropy formulation with the quantum R\'enyi entropy. Whereas classical Shannon entropy requires infinitely many inequalities to characterize the optimization space, R\'enyi entropy requires only one type of inequality, which is non-negativity. Although this is a promising modification, optimization with respect to the quantum states instead of classical distributions creates a new set of challenges that prevent us from finding a practically computable, tight worst-case size bound. In this line, we propose a quantum version to derive worst-case size bounds. The previous tight classical worst-case size bound can be viewed as a special limit of this quantum bound. We also provide a comprehensive background on prior research and discuss the future possibilities of quantum information theory in theoretical database research.

Related papers

• One-Shot Min-Entropy Calculation Of Classical-Quantum States And Its Application To Quantum Cryptography [21.823963925581868]
  We develop a one-shot lower bound calculation technique for the min-entropy of a classical-quantum state.<n>It offers an alternative tight finite-data analysis for the BB84 quantum key distribution scheme.<n>It gives the best finite-key bound known to date for a variant of device independent quantum key distribution protocol.
  arXiv  Detail & Related papers  (2024-06-21T15:11:26Z)
• A quantum annealing approach to the minimum distance problem of quantum codes [0.0]
  We introduce an approach to compute the minimum distance of quantum stabilizer codes by reformulating the problem as a Quadratic Unconstrained Binary Optimization problem. We demonstrate practical viability of our method by comparing the performance of purely classical algorithms with the D-Wave Advantage 4.1 quantum annealer.
  arXiv  Detail & Related papers  (2024-04-26T21:29:42Z)
• Quantum algorithms: A survey of applications and end-to-end complexities [88.57261102552016]
  The anticipated applications of quantum computers span across science and industry.<n>We present a survey of several potential application areas of quantum algorithms.<n>We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• QSETH strikes again: finer quantum lower bounds for lattice problem, strong simulation, hitting set problem, and more [5.69353915790503]
  There are problems for which there is no trivial' computational advantage possible with the current quantum hardware. We would like to have evidence that it is difficult to solve those problems on quantum computers; but what is their exact complexity? By the use of the QSETH framework [Buhrman-Patro-Speelman 2021], we are able to understand the quantum complexity of a few natural variants of CNFSAT.
  arXiv  Detail & Related papers  (2023-09-28T13:30:20Z)
• Optimal lower bounds for Quantum Learning via Information Theory [3.093890460224435]
  We derive optimal lower bounds for quantum sample complexity in both the PAC and models via an information-theoretic approach. We then turn to a quantum analogue of the Coupon Collector problem, a classic problem from probability theory. All the aspects of the Quantum Coupon Collector problem we study rest on properties of the spectrum of the associated Gram matrix.
  arXiv  Detail & Related papers  (2023-01-05T18:55:04Z)
• Quantum Worst-Case to Average-Case Reductions for All Linear Problems [66.65497337069792]
  We study the problem of designing worst-case to average-case reductions for quantum algorithms. We provide an explicit and efficient transformation of quantum algorithms that are only correct on a small fraction of their inputs into ones that are correct on all inputs.
  arXiv  Detail & Related papers  (2022-12-06T22:01:49Z)
• Unbalanced penalization: A new approach to encode inequality constraints of combinatorial problems for quantum optimization algorithms [42.29248343585333]
  We present an alternative method that does not require extra slack variables. We evaluate our approach on the traveling salesman problem, the bin packing problem, and the knapsack problem. This new approach can be used to solve problems with inequality constraints with a reduced number of resources.
  arXiv  Detail & Related papers  (2022-11-25T06:05:18Z)
• Complexity-Theoretic Limitations on Quantum Algorithms for Topological Data Analysis [59.545114016224254]
  Quantum algorithms for topological data analysis seem to provide an exponential advantage over the best classical approach. We show that the central task of TDA -- estimating Betti numbers -- is intractable even for quantum computers. We argue that an exponential quantum advantage can be recovered if the input data is given as a specification of simplices.
  arXiv  Detail & Related papers  (2022-09-28T17:53:25Z)
• Resource Optimisation of Coherently Controlled Quantum Computations with the PBS-calculus [55.2480439325792]
  Coherent control of quantum computations can be used to improve some quantum protocols and algorithms. We refine the PBS-calculus, a graphical language for coherent control inspired by quantum optics.
  arXiv  Detail & Related papers  (2022-02-10T18:59:52Z)
• Stochastic approximate state conversion for entanglement and general quantum resource theories [41.94295877935867]
  An important problem in any quantum resource theory is to determine how quantum states can be converted into each other. Very few results have been presented on the intermediate regime between probabilistic and approximate transformations. We show that these bounds imply an upper bound on the rates for various classes of states under probabilistic transformations. We also show that the deterministic version of the single copy bounds can be applied for drawing limitations on the manipulation of quantum channels.
  arXiv  Detail & Related papers  (2021-11-24T17:29:43Z)
• Experimental violations of Leggett-Garg's inequalities on a quantum computer [77.34726150561087]
  We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
  arXiv  Detail & Related papers  (2021-09-06T14:35:15Z)
• On Applying the Lackadaisical Quantum Walk Algorithm to Search for Multiple Solutions on Grids [63.75363908696257]
  The lackadaisical quantum walk is an algorithm developed to search graph structures whose vertices have a self-loop of weight $l$. This paper addresses several issues related to applying the lackadaisical quantum walk to search for multiple solutions on grids successfully.
  arXiv  Detail & Related papers  (2021-06-11T09:43:09Z)
• R\'{e}nyi formulation of uncertainty relations for POVMs assigned to a quantum design [0.0]
  Information entropies provide powerful and flexible way to express restrictions imposed by the uncertainty principle. In this paper, we obtain uncertainty relations in terms of min-entropies and R'enyi entropies for POVMs assigned to a quantum design.
  arXiv  Detail & Related papers  (2020-04-12T09:44:44Z)

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.