Quantum entanglement and quantum squeezing are two typical approaches to beat the standard quantum limit (SQL) for the sensitive phase estimations in quantum metrology. Each of them has already been utilized individually and sequentially to improve the sensitivity of electric field sensing with the trapped ion platform. However, the upper bound of the demonstrated sensitivity gain is still limited, i.e., the theoretical 6 dB and experimental 3 dB over the corresponding SQL, for electric field sensing. By simultaneously using the internal (spin)-external (oscillator) state entanglement and the oscillator squeezing to effectively amplify the accumulation phase, we show here that such a theoretical sensitivity gain upper bound can be significantly surpassed. The proposal provides a novel approach to implement the stronger beat of the SQL and even approach the Heisenberg limit, for the sensitive sensings of the desired electric field and also the other metrologies.
Quantum entanglement and quantum squeezing are two typical approaches to beat the standard quantum limit (SQL) for the sensitive phase estimations in quantum metrology. Each of them has already been utilized individually and sequentially to improve the sensitivity of electric field sensing with the trapped ion platform. However, the upper bound of the demonstrated sensitivity gain is still limited, i.e., the theoretical 6 dB and experimental 3 dB over the corresponding SQL, for electric field sensing. By simultaneously using the internal (spin)-external (oscillator) state entanglement and the oscillator squeezing to effectively amplify the accumulation phase, we show here that such a theoretical sensitivity gain upper bound can be significantly surpassed. The proposal provides a novel approach to implement the stronger beat of the SQL and even approach the Heisenberg limit, for the sensitive sensings of the desired electric field and also the other metrologies.
Quantum entanglement and quantum squeezing are two most typical approaches to beat the standard quantum limit (SQL) of the sensitive phase estimations in quantum metrology. Each of them has already been utilized individually to improve the sensitivity of electric field sensing with the trapped ion platform, but the upper bound of the demonstrated sensitivity gain is very limited, i.e., the experimental 3dB and theoretical 6dB, over the SQL. Here, by simultaneously using the internal (spin)-external (oscillator) state entanglements and the oscillator squeezings to effectively amplify the accumulation phase, we show that these sensitivity gains can be effectively surpassed. Hopefully, the proposal provides a novel approach to the stronger beaten of the SQL for the sensitive sensings of the desired electric field and also the other metrologies.
Achieving measurement precision beyond the standard quantum limit (SQL) is a fundamental object in quantum metrology. In this manuscript, we propose a streamlined protocol for weak signal sensing in a trapped-ion spin-oscillator system that simultaneously exploits detuned motional squeezing and spin-oscillator entanglement. By combining these two quantum resources, the phase accumulation in this spin system is significantly accelerated, as a result achieving an exponential improvement in the sensitivity over unsqueezed cases. Remarkably, we show that the significant metrological gain provided by our protocol persists in noisy environments, with the sensitivity remaining below the SQL. In particular, our protocol retains a distinct advantage in the short interrogation time regime, thus demonstrating the practical potential in quantum-enhanced sensing.
Quantum entangled states have a potential to beat the standard quantum limit (SQL) and approach the Heisenberg limit (HL). We previously demonstrated that phase shifts induced by magnetic fields are coherently accumulated in a Ramsey protocol using an entangled Nitrogen-Vacancy (NV) pair. However, the sensitivity is limited to the order of ~µT/√Hz due to the various sources of error and noise, including classical readout noise, spin manipulation and initialization errors, and decoherence error. One of the most critical problems is that decoherence of entangled sensing proceeds more rapidly than ensemble-based sensing. When decoherence follows a Markovian process (i.e., when the environment noises behave as white noise without autocorrelation), the sensitivity of entangled sensing is limited to SQL3,4. Therefore, enhancement from entanglement cannot be achieved under the white noise conditions. To realize entanglement-enhanced sensing to beat SQL, it is essential to characterize the environment noise and prepare a suitable condition. In this study, we conducted noise spectroscopy to evaluate the environmental noise and demonstrated that diamond NV centers have the potential to beat SQL.
As a cornerstone of quantum science and technology, quantum precision measurement aims to transcend the standard quantum limit (SQL) and achieve sensitivities unattainable by classical approaches by harnessing distinctive quantum resources such as entanglement, squeezing and non-Gaussianity. Within this framework, Gaussian states have historically played a central role, underpinning a series of seminal experimental advances; however, their utility in metrology is fundamentally bounded by theoretical constraints that preclude unlimited gains in measurement precision. In contrast, a growing body of recent research has revealed that non-Gaussian states–endowed with stronger quantum correlations and more pronounced non-classical characteristics — can significantly surpass Gaussian counterparts in key tasks such as phase estimation, quantum imaging and quantum sensing. Under specific conditions, these states even exhibit the potential to approach or saturate the ultimate Heisenberg limit. This review offers a comprehensive overview of the theoretical underpinnings, representative preparation methodologies, experimental progress and emerging applications of non-Gaussian states in quantum metrology. Special attention is devoted to illustrating their transformative potential for the development of next-generation quantum sensors and high-precision measurement instruments, while also addressing prevailing challenges and delineating promising future research trajectories in this rapidly advancing field.
State of the art atomic sensors operate near the standard quantum limit (SQL) of projection noise, and overcoming this limit by using atom-atom entanglement such as spin squeezing is a major goal in quantum metrology. By coupling an ensemble of approximately 1000 Yb-171 atoms to a high-finesse asymmetric micromirror cavity with single-atom cooperativity of 1.8., we produce a near-unitary spin squeezed state. The observed spin noise suppression and metrological gain are limited by the state readout to 9.4(4) dB and 6.5(4) dB, respectively, while the generated states offer a spin noise suppression of 15.9(6) dB and a metrological gain of 12.9(6) dB over the standard quantum limit, limited by the curvature of the Bloch sphere. When requiring the squeezing process to be within 30% of unitarity, we demonstrate an interferometer that improves the averaging time over the SQL by a factor of 3.7(2).
The precision measurements provided by quantum sensing plays a significant role in fields of science. However, the sensitivity is limited by the standard quantum limit (SQL). Quantum entangled state have a potential to beat the SQL and to approach the Heisenberg limit (HL). In particular, entanglement sensors based on Nitrogen-Vacancy (NV) centers provide high spatial resolution at room temperature. In 2021, it was reported that the multi-spin sensor constituted by the NV electron spin (S=1), the 14N nuclear spin (I=1), and proximate 13C nuclear spin (I=1/2) beat the SQL1 . However, since the nuclear gyromagnetic ratio is ~MHz/T, it does not lead to a dramatic improvement of sensitivity. For enhancement of quantum sensing, it is required to utilize the entangled state among dipole coupled NV centers.