Quantum metrology, such as quantum phase estimation, can surpass classical sensing limits, reaching the Heisenberg‐scaling precision. So far, this kind of metrology has been thought to be only implementable with the quantum systems, which, however, are fragile to environmental noise and hardly contribute to the practical detections. Herein, it is demonstrated both theoretically and experimentally that the parameter encoded by the optical phase can also be estimated at the Heisenberg scaling in classical optics. Inspired by the quantum‐entanglement‐enhanced sensing scheme, the estimation is performed by using classically correlated beams as probes, and obtaining the probes readout after their interaction with the target system. Because the correlated beams considered are spatially separable, a distributed phase estimation scheme is given, which can sense the linear combinations of the phase shifts induced by distinct systems. The results of our experiments show an error reduction up to 3.89 dB below the classical limit when the correlated beam number for probing is 6, approaching the Heisenberg limit. Compared with quantum strategies, the proposal shows a better robustness against the environmental disturbance and keeps their performances even when the correlated beam number is relatively large. Hence, it indicates promising practical applications in the future.
The distribution of quantum sensors on quantum networks is a key enabler of quantum technologies in interferometry, gravimetry, timekeeping, biological monitoring, and beyond. Yet, guaranteeing the security of these distributed sensors over noisy, insecure networks remains a formidable challenge. Previous efforts to combine quantum metrology and cryptography have encountered an apparently unavoidable tension, proposing bounds for security which are only loosely tied to the achievable measurement performance.
Here we introduce a quantum remote sensing protocol that can rigorously certify privacy and integrity of the estimation. By employing offline bilateral Pauli-twirling, our approach forces the effective quantum channel into a Bell-diagonal form, independently of the attack. Surprisingly, this also preserves metrological sensitivity without introducing additional experimental overhead. Relying solely on public communication alongside an insecure quantum link, the protocol enables legitimate users to exactly quantify their estimation error relative to an eavesdropper controlling the channels.
We experimentally demonstrate this framework by estimating an optical phase using entangled photons, observing that the users' precision consistently surpasses the eavesdropper's capabilities across a broad parameter regime. By unifying quantum cryptography and metrology, our results provide a practical pathway to achieve simultaneous quantum-limited precision and rigorous information security in real-world quantum networks.
The measurement of a phase difference between two optical modes in an interferometer has several important applications in metrology. This measurement can be useful in several contexts, such as in the detection of gravitational waves. The quantum nature of light imposes a limit on how accurately a phase difference can be measured, this limit being known as the Heisenberg limit (HL). On the other hand, photonic quantum metrology studies alternatives to reach the HL through entangled or squeezed quantum states. According to the theory of parameter estimation, the minimum uncertainty possible in the estimation of a phase
θ considering classical light scales with $1/\sqrt{\Bar{N}}$, where $\Bar{N}$ is the average number of photons. This dependence is known as the standard quantum limit. However, when considering quantum light sources, there is a significant improvement in the estimation of the phase parameter, as its minimum uncertainty can scale with $1/{\Bar{N}}$, known as HL. In this thesis, starting from the relative phase probability distribution P(
ϕ) introduced by Luis and S\'anchez-Soto in 1996, we obtained this distribution for several quantum states of light useful in photonic quantum metrology. We show that, within the numerical precision of our calculations, the Fisher information obtained via the relative phase distribution is equal to the quantum Fisher information for the considered states, such that the average differences between these quantities were on the order of
0,1%. Our results indicate that the relative phase distribution can be used to predict the minimum possible uncertainty in the phase detection process in quantum metrology, since this uncertainty depends on the quantum Fisher information, at least for pure states.