遍历动力学下量子资源的等价性
Equivalence of quantum resources under ergodic dynamics
AI总结：
该研究证明在遍历动力学下，多体量子系统中不同量子资源的演化并非独立，而是受少数共同自由度支配，强 scrambling 可实现不同量子资源间的等价性，为理解量子资源的动力学行为提供了关键简化机制。
AI中文摘要：
量子资源理论表征多体量子态中不同形式的非经典性，由此引出这些资源在一般遍历动力学下是否独立演化的问题。针对态的二次诊断，我们证明不同资源度量的动力学相互关联，且受少数共同自由度支配。对于Haar随机电路，纯度结合单个资源见证足以重构剩余资源度量，我们针对相干性、各类不对称性及数熵验证了这一点。相同关系在混沌Floquet动力学和连续时间哈密顿动力学下也近似成立，表明该动力学资源等价性超出随机电路范围。我们进一步推导了精确的相干性-虚部关系，其在Haar随机电路之外也具有极高精度。研究结果揭示了多体动力学的涌现简化：足够强的 scrambling（ scrambling 译为“ scrambling 即量子 scrambling，量子 scrambling 是指量子信息在多体系统中快速扩散的现象）将看似不同的量子资源简化为少数共同动力学自由度。
英文摘要：
Quantum resource theories characterize distinct forms of nonclassicality in many-body quantum states, raising the question of whether these resources evolve independently under generic ergodic dynamics. Considering diagnostics quadratic in the state, we show that the dynamics of different resource measures become mutually interdependent and are governed by a few common degrees of freedom. For Haar-random circuits, the purity together with a single resource witness suffices to reconstruct the remaining resource measures, as we demonstrate for coherence, various asymmetries, and number entropies. The same relations hold, to a good approximation, under chaotic Floquet and continuous-time Hamiltonian dynamics, establishing that this dynamical resource equivalence extends beyond random circuits. We further derive an exact coherence--imaginarity relation, remarkably accurate also beyond Haar-random circuits. Our results reveal an emergent simplification of many-body dynamics, in which sufficiently strong scrambling reduces seemingly distinct quantum resources to a few common dynamical degrees of freedom.
