Bounding quantum uncommon information with quantum neural estimators

TL;DR

This paper introduces a novel variational approach using quantum neural architectures to estimate bounds on quantum uncommon information, a quantum analogue of a classical information measure, which previously lacked direct computation methods.

Contribution

It proposes a new method employing quantum Donsker-Varadhan representation and gradient-based optimization to approximate quantum uncommon information bounds.

Findings

Demonstrates the feasibility of using variational techniques for quantum information estimation

Provides a pathway for efficient approximation of quantum uncommon information

Suggests potential for quantum neural architectures in quantum information theory

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.