Faculty of Physics, University of Warsaw, Warszawa, Poland.
Nat Commun. 2012;3:1063. doi: 10.1038/ncomms2067.
Quantum precision enhancement is of fundamental importance for the development of advanced metrological optical experiments, such as gravitational wave detection and frequency calibration with atomic clocks. Precision in these experiments is strongly limited by the 1/√N shot noise factor with N being the number of probes (photons, atoms) employed in the experiment. Quantum theory provides tools to overcome the bound by using entangled probes. In an idealized scenario this gives rise to the Heisenberg scaling of precision 1/N. Here we show that when decoherence is taken into account, the maximal possible quantum enhancement in the asymptotic limit of infinite N amounts generically to a constant factor rather than quadratic improvement. We provide efficient and intuitive tools for deriving the bounds based on the geometry of quantum channels and semi-definite programming. We apply these tools to derive bounds for models of decoherence relevant for metrological applications including: depolarization, dephasing, spontaneous emission and photon loss.
量子精度增强对于先进计量光学实验的发展至关重要，例如引力波探测和原子钟的频率校准。这些实验的精度受到实验中使用的探针（光子、原子）数量 N 的 1/√N 散粒噪声因素的强烈限制。量子理论提供了使用纠缠探针克服这一限制的工具。在理想化的情况下，这会导致精度呈 Heisenberg 缩放，即 1/N。在这里，我们表明，当考虑退相干时，在无限 N 的渐近极限中，最大可能的量子增强通常是一个常数因子，而不是二次改进。我们提供了基于量子通道几何和半定规划的有效且直观的工具来推导这些界限。我们将这些工具应用于推导与计量应用相关的退相干模型的界限，包括：去极化、相消、自发发射和光子损耗。
