Disentanglement Provides a Unified Estimation for Quantum Entropies and Distance Measures

• URL: http://arxiv.org/abs/2401.07716v2
• Date: Mon, 29 Jul 2024 07:00:53 GMT
• Title: Disentanglement Provides a Unified Estimation for Quantum Entropies and Distance Measures
• Authors: Myeongjin Shin, Seungwoo Lee, Junseo Lee, Mingyu Lee, Donghwa Ji, Hyeonjun Yeo, Kabgyun Jeong,
• Abstract summary: This paper introduces a unified approach using Disentangling Quantum Neural Networks (DEQNN) for estimating quantum entropies and distances. Our mathematical proof demonstrates that DEQNN can preserve quantum entropies and distances in smaller partial states. This method is scalable to an arbitrary number of quantum states and is particularly effective for less complex quantum systems.
• Score: 2.14566083603001
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The estimation of quantum entropies and distance measures, such as von Neumann entropy, R\'enyi entropy, Tsallis entropy, trace distance, and fidelity-induced distances like Bures distance, has been a key area of research. This paper introduces a unified approach using Disentangling Quantum Neural Networks (DEQNN) for estimating these quantities, leveraging continuity bounds and disentanglement in the cost function design. Our mathematical proof demonstrates that DEQNN can preserve quantum entropies and distances in smaller partial states, making them suitable for further estimation. This method is scalable to an arbitrary number of quantum states and is particularly effective for less complex quantum systems. Numerical simulations validate our approach, and we also discuss strategies to enhance trainability and avoid barren plateaus.

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