Achieving Heisenberg limit of quantum metrology in non-Markovian dissipative noises

Yi Peng, Heng Fan

Zachary Mann, Ningping Cao, Raymond Laflamme +1 more

Quantum metrology aims to maximize measurement precision on quantum systems, with a wide range of applications in quantum sensing. Achieving the Heisenberg limit (HL)—the fundamental precision bound set by quantum mechanics—is often hindered by noise-induced decoherence, which typically reduces achievable precision to the standard quantum limit (SQL). While quantum error correction (QEC) can recover the HL under Markovian noise, its applicability to non-Markovian noise remains less explored. In this work, we analyze a hidden Markov model (HMM) in which a quantum probe, coupled to an inaccessible environment, undergoes joint evolution described by Lindbladian dynamics, with the inaccessible degrees of freedom serving as a memory. We derive generalized Knill-Laflamme conditions for the HMM and establish three types of sufficient conditions for achieving the HL under non-Markovian noise using QEC. Additionally, we demonstrate the attainability of the SQL when these sufficient conditions are violated, by analytical solutions for special cases and numerical methods for general scenarios. Our results not only extend prior QEC frameworks for metrology but also provide new insights into precision limits under realistic noise conditions.

Sang Woo Park, Changsuk Noh, Hyunchul Nha

Bruno M. Escher, R. L. de Matos Filho, L. Davidovich

Kai Bai, Hong‐Gang Luo, Wenxian Zhang +1 more

Quantum metrology utilizes quantum effects to reach higher-precision measurements of physical quantities compared with their classical counterparts. However, the ubiquitous decoherence obstructs its application. Recently, non-Markovian effects are shown to be effective in performing quantum optical metrology under locally dissipative environments [Phys. Rev. Lett. 123, 040402 (2019)]. However, the mechanism is still rather hazy. Here, we uncover the reason why forming a bound state can protect the quantumness against a dissipative ambient via the quantum Fisher information of entangled coherent states. An exact analytical expression of the quantum Fisher information in the long-encoding-time condition is derived, which reveals that the dynamics of precision can asymptotically reach the ideal-case-promised one easily when the average photon number is small. Meanwhile, the scaling exhibits a transition from the weak Heisenberg limit to the subclassical limit with increasing average photon number. Our work provides a recipe to realize ultrasensitive measurements in the presence of noise by utilizing non-Markovian effects.

Kai Bai, Zhen Peng, Hong‐Gang Luo +1 more

Quantum metrology employs quantum effects to attain a measurement precision surpassing the limit achievable in classical physics. However, it was previously found that the precision returns the shot-noise limit (SNL) from the ideal Zeno limit (ZL) due to the photon loss in quantum metrology based on Mech-Zehnder interferometry. Here, we find that not only can the SNL be beaten, but also the ZL can be asymptotically recovered in a long-encoding-time condition when the photon dissipation is exactly studied in its inherent non-Markovian manner. Our analysis reveals that it is due to the formation of a bound state of the photonic system and its dissipative noise. Highlighting the microscopic mechanism of the dissipative noise on the quantum optical metrology, our result supplies a guideline to realize the ultrasensitive measurement in practice by forming the bound state in the setting of reservoir engineering.