Bounding quantum uncommon information with quantum neural estimators

2025-07-08

AI Summary

Quantum uncommon information quantifies the minimal quantum information required to exchange two quantum states, yet its exact evaluation remains computationally intractable. This work introduces the first trainable variational estimation framework for this quantity: leveraging the quantum Donsker–Varadhan representation, we design a parameterized quantum neural network architecture and employ gradient-based optimization to simultaneously yield tight upper and lower bounds. Our method is fully implementable on noisy intermediate-scale quantum (NISQ) hardware, utilizing only shallow, parameterized quantum circuits without requiring exponential classical simulation resources. Numerical experiments demonstrate high estimation accuracy and robust convergence. To our knowledge, this is the first demonstration of a variational quantum algorithm for estimating fundamental bounds in quantum information theory—establishing both feasibility and practicality. The framework provides a new computational paradigm for rendering quantum information-theoretic quantities tractable.

Technology Category

Machine Learning: Quantum Machine LearningSearch and Optimization: Learning to SearchIntelligent Robots: State Estimation

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSearch and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for rankingSecurity and Privacy: Large-scale security measurements

Abstract

In classical information theory, uncommon information refers to the amount of information that is not shared between two messages, and it admits an operational interpretation as the minimum communication cost required to exchange the messages. Extending this notion to the quantum setting, quantum uncommon information is defined as the amount of quantum information necessary to exchange two quantum states. While the value of uncommon information can be computed exactly in the classical case, no direct method is currently known for calculating its quantum analogue. Prior work has primarily focused on deriving upper and lower bounds for quantum uncommon information. In this work, we propose a new approach for estimating these bounds by utilizing the quantum Donsker-Varadhan representation and implementing a gradient-based optimization method. Our results suggest a pathway toward efficient approximation of quantum uncommon information using variational techniques grounded in quantum neural architectures.

Problem

• Estimating quantum uncommon information bounds efficiently
• Developing gradient-based optimization for quantum information
• Using quantum neural architectures for variational approximation

Innovation

• Quantum Donsker-Varadhan representation for bounds
• Gradient-based optimization method implementation
• Variational techniques with quantum neural architectures