发表机构
BITS Pilani KK Birla Goa Campus; Harish-Chandra Research Institute; Homi Bhabha National Institute; Università di Trento; INFN-TIFPA, Trento Institute for Fundamental Physics and Applications（比拉戈亚校园; 哈里什-昌德拉研究所; 霍米·巴巴国立研究所; 特伦托大学; 意大利国家核物理研究所-基础物理与应用特伦托研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明无序环码哈密顿量下，初始可分离探针的量子Fisher信息在特定参数区间超过有序情况，并识别出最优乘积探针，其QFI呈瞬态四次标度且对局域噪声鲁棒。
AI 中文摘要
Kitaev环面码的拓扑序对其耦合中的无序不敏感，因为所有星算子和环算子都相互对易；因此，稳定子基态流形独立于各个耦合强度，并且该相在弱局域扰动下保持稳定。然而，这种不敏感性是特征态的性质，而非它们所产生的动力学的性质，我们表明，在特征基之外制备的探针的无序敏感性可以成为一种计量学资源。具体而言，我们研究了三种破坏拓扑序的扰动的强度估计，即非线性Castelnovo-Chamon形变、最近邻伊辛相互作用以及沿水平边缘的磁场，这些扰动通过无序环码哈密顿量下的幺正演化编码在初始可分离的探针上。我们证明，淬火平均量子Fisher信息（QFI）作为计量精度的品质因数，在适当的扰动强度和编码时间范围内超过其有序对应物。对于有序情况，我们进一步识别出最优乘积探针，对于这些探针，短时展开的二次和三次项完全消失，留下QFI的瞬态四次标度。有趣的是，只要编码产生的多体纠缠持续增加，这个窗口就持续存在，并且在每个位点上独立作用的局域退相、比特翻转和振幅阻尼噪声下也能存活，其中非幺正通道的危害最小。
英文摘要
The topological order of the Kitaev toric code is insensitive to disorder in its couplings since all star and plaquette operators commute; consequently, the stabilizer ground-state manifold is independent of the individual coupling strengths, and the phase remains stable against weak local perturbations. This insensitivity, however, is a property of the eigenstates and not of the dynamics they generate, and we show that the disorder sensitivity of a probe prepared outside that eigenbasis can be a metrological resource. In particular, we investigate the estimation of the strength of three topological-order-breaking perturbations, the nonlinear Castelnovo-Chamon deformation, nearest-neighbor Ising interactions, and a magnetic field along horizontal edges, encoded on an initially separable probe through unitary evolution under the disordered toric code Hamiltonian. We demonstrate that the quenched average quantum Fisher information (QFI), a figure of merit for metrological precision, exceeds that of its ordered counterpart in suitable regimes of perturbation strength and encoding time. For the ordered case, we further identify optimal product probes, for which the quadratic and cubic terms of the short-time expansion vanish identically, leaving a transient quartic scaling of QFI. Interestingly, this window persists as long as the multipartite entanglement generated by the encoding continues to increase, and it survives under local dephasing, bit-flip, and amplitude damping noise acting independently on each site, with the non-unital channel being the least detrimental.
Comments12 pages, 5 figures
