Query complexities of quantum channel discrimination and estimation: A unified approach

2025-11-13

AI Summary

This work addresses the query complexity of quantum channel discrimination and parameter estimation—i.e., identifying an unknown channel from a discrete set or estimating a continuous parameter with minimal oracle queries under a given error tolerance. We propose a unified modeling framework based on isometric extension, embedding both discrimination and estimation into a common geometric structure, thereby removing reliance on specific query models (parallel vs. adaptive) or task types (discrete vs. continuous). Innovatively combining the squared Bures distance with upper bounds on the symmetric logarithmic derivative (SLD) Fisher information, we derive universal lower bounds on query complexity. Our framework not only yields concise, unified proofs of several classical results but also significantly enhances theoretical scalability and analytical flexibility. It establishes a new foundation for characterizing resource requirements in quantum black-box algorithms.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements

Abstract

The goal of quantum channel discrimination and estimation is to determine the identity of an unknown channel from a discrete or continuous set, respectively. The query complexity of these tasks is equal to the minimum number of times one must call an unknown channel to identify it within a desired threshold on the error probability. In this paper, we establish lower bounds on the query complexities of channel discrimination and estimation, in both the parallel and adaptive access models. We do so by establishing new or applying known upper bounds on the squared Bures distance and symmetric logarithmic derivative Fisher information of channels. Phrasing our statements and proofs in terms of isometric extensions of quantum channels allows us to give conceptually simple proofs for both novel and known bounds. We also provide alternative proofs for several established results in an effort to present a consistent and unified framework for quantum channel discrimination and estimation, which we believe will be helpful in addressing future questions in the field.

Problem

• Establishing query complexity bounds for quantum channel discrimination tasks
• Developing unified framework using isometric channel extensions for proofs
• Analyzing both parallel and adaptive access models for quantum estimation

Innovation

• Using isometric extensions for simpler proofs
• Establishing query complexity lower bounds
• Applying Bures distance and Fisher information bounds