Arbitrarily-high-dimensional reconciliation via cross-rotation for continuous-variable quantum key distribution

Multidimensional rotation serves as a powerful tool for enhancing information reconciliation and extending the transmission distance in continuous-variable quantum key distribution (CV-QKD). However, the lack of closed-form orthogonal transformations for high-dimensional rotations has limited the maximum reconciliation efficiency to channels with 8 dimensions over the past decade. This paper presents a cross-rotation scheme to overcome this limitation and enable reconciliation in arbitrarily high dimensions, constrained to even multiples of 8. The key treatment involves reshaping the string vector into matrix form and applying orthogonal transformations to its columns and rows in a cross manner, thereby increasing the reconciliation dimension by one order per cross-rotation while significantly reducing the communication overhead over the classical channel. A rigorous performance analysis is also presented from the perspective of achievable sum-rate. Simulation results demonstrate that 64-dimensional cross-rotation nearly approaches the upper bound, making it a recommended choice for practical implementations.

Joint parameter estimation and multidimensional reconciliation for CV-QKD

Accurate quantum channel parameter estimation is essential for effective information reconciliation in continuous-variable quantum key distribution (CV-QKD). However, conventional maximum likelihood (ML) estimators rely on a large amount of discarded data (or pilot symbols), leading to a significant loss in symbol efficiency. Moreover, the separation between the estimation and reconciliation phases can introduce error propagation. In this paper, we propose a novel joint message-passing scheme that unifies channel parameter estimation and information reconciliation within a Bayesian framework. By leveraging the expectation-maximization (EM) algorithm, the proposed method simultaneously estimates unknown parameters during decoding, eliminating the need for separate ML estimation. Furthermore, we introduce a hybrid multidimensional rotation scheme that removes the requirement for norm feedback, significantly reducing classical channel overhead. To the best of our knowledge, this is the first work to unify multidimensional reconciliation and channel parameter estimation in CV-QKD, providing a practical solution for high-efficiency reconciliation with minimal pilots.

Towards Heisenberg limit without critical slowing down via quantum reinforcement learning

Critical ground states of quantum many-body systems have emerged as vital resources for quantum-enhanced sensing. Traditional methods to prepare these states often rely on adiabatic evolution, which may diminish the quantum sensing advantage. In this work, we propose a quantum reinforcement learning (QRL)-enhanced critical sensing protocol for quantum many-body systems with exotic phase diagrams. Starting from product states and utilizing QRL-discovered gate sequences, we explore sensing accuracy in the presence of unknown external magnetic fields, covering both local and global regimes. Our results demonstrate that QRL-learned sequences reach the finite quantum speed limit and generalize effectively across systems of arbitrary size, ensuring accuracy regardless of preparation time. This method can robustly achieve Heisenberg and super-Heisenberg limits, even in noisy environments with practical Pauli measurements. Our study highlights the efficacy of QRL in enabling precise quantum state preparation, thereby advancing scalable, high-accuracy quantum critical sensing.