Quantum waste management: Utilizing residual states in quantum information processing

TL;DR

This paper introduces a framework for managing residual states in quantum resource protocols, enabling secondary resource extraction like private randomness from discarded states to improve overall quantum information processing efficiency.

Contribution

It proposes a novel approach to reuse residual states in quantum resource theories, demonstrated through private randomness extraction after quantum key distribution protocols.

Findings

Residual states can be used to extract private randomness after QKD.

Achievable private randomness rates are quantified for specific QKD protocols.

The framework generalizes resource utilization across sequential quantum tasks.

Abstract

Quantum resource theories use distillation protocols to convert less resourceful states into fully resourceful ones. However, these protocols often also generate an additional, unused output-referred to as a residual. We propose a framework for the quantum residual management, in which states discarded after a resource distillation protocol are repurposed as inputs for subsequent quantum information tasks. This approach extends conventional quantum resource theories by incorporating secondary resource extraction from residual states, thereby enhancing overall resource utility. As a concrete example, we investigate the distillation of private randomness from the residual states remaining after quantum key distribution (QKD). More specifically, we quantitatively show that after performing a well-known coherent Devetak-Winter protocol, one can locally extract private randomness from its residual. We further consider the Gottesman-Lo QKD protocol and provide the achievable rate of private randomness from the discarded states that are left after its performance. We also provide a formal framework that highlights a general principle for improving quantum resource utilization across sequential information processing tasks.