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Photonics Research

Quantum-enhanced postselected phase measurement with thermal light

Junfan Zhu, An Wang, Yurong Liu, Zhiyou Zhang

Published Jun 23, 2026• 0 citations
Publisher

Abstract

Postselected metrology provides technical advantages such as signal amplification and noise suppression by retaining only the quantum states that satisfy specific criteria. However, its precision remains fundamentally constrained by the shot noise limit. Here, we propose and experimentally demonstrate a quantum-enhanced postselected measurement scheme for phase estimation by leveraging the second-order correlations of thermal light. The failed-postselected photons that would otherwise be discarded are further utilized to condition and transform the detection probability of the postselected photons. Our results show that, at a fixed number of incident photons, the correlation improves the per-detection signal-to-noise ratio beyond that of a coherent probe operating at the shot noise limit. This enhancement arises at the detection stage and does not reduce the number of photons interacting with the sample, providing a robust and accessible strategy for high-precision phase measurement without sophisticated quantum operations.

DOI
10.1364/prj.604969

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Postselected metrology provides technical advantages such as signal amplification and noise suppression by retaining only the quantum states that satisfy specific criteria. However, its precision remains fundamentally constrained by the shot noise limit. Here, we propose and experimentally demonstrate a quantum-enhanced postselected measurement scheme for phase estimation by leveraging the second-order correlations of thermal light. The failed-postselected photons that would otherwise be discarded are further utilized to condition and transform the detection probability of the postselected photons. Our results show that, at a fixed number of incident photons, the correlation improves the per-detection signal-to-noise ratio beyond that of a coherent probe operating at the shot noise limit. This enhancement arises at the detection stage and does not reduce the number of photons interacting with the sample, providing a robust and accessible strategy for high-precision phase measurement without sophisticated quantum operations.
The quantum statistical fluctuations of electromagnetic fields establish a limit, known as the shot-noise limit, on the sensitivity of optical measurements performed with classical technologies. However, quantum technologies are not constrained by this shot-noise limit. In this regard, the possibility of using every photon produced by quantum sources of light to estimate small physical parameters, beyond the shot-noise limit, constitutes one of the main goals of quantum optics. Here, we experimentally demonstrate a scalable protocol for quantum-enhanced optical phase estimation across a broad range of phases, with neither pre- nor post-selected measurements. This is achieved through the efficient design of a source of spontaneous parametric downconversion in combination with photon-number-resolving detection. The robustness of two-mode squeezed vacuum states against loss allows us to outperform schemes based on N00N states, in which the loss of a single photon is enough to remove all phase information from a quantum state. In contrast to other schemes that rely on N00N states or conditional measurements, the sensitivity of our technique could be improved through the generation and detection of high-order photon pairs. This unique feature of our protocol makes it scalable. Our work is important for quantum technologies that rely on multiphoton interference such as quantum imaging, boson sampling, and quantum networks.
Quantum techniques, developed in recent decades, provide new approaches to achieving high-precision measurements beyond the classical bounds. In this paper, we theoretically demonstrate a metrology method for improving the sensitivity of the interferometric optical gyroscope, robust against the loss, by using coherent-light stimulated two-mode squeezed beams as the light source. The detection protocol is based on a simple intensity measurement, and the quantum noise is far below the shot-noise limit. The enhancement factors for different coherent light fields are analyzed in detail. Additionally, the influence of loss during the propagation in the optical path is studied, and the conditions for achieving sub-shot-noise measurement sensitivity are obtained. We also find that the phase sensitivity of the proposed gyroscope scheme becomes closer to the quantum Cramér-Rao bound with increasing of the photon number of the coherent beams.
In theory, quantum states of lights can be used to perform measurements with a level of precision beyond that which can be attained with their classical counterparts.In practice, they can only do so when the components that we use to generate, manipulate and measure them, operate beyond specific thresholds.In this thesis, we seek to address different obstacles that hinder our ability to fully exploit quantum-metrological schemes.We mainly focus our attention in quantum-enhanced optical transmission measurements.For this we make use of photon pair sources and take advantage of the photon number correlations of the sources to suppress noise in parameter estimation.With this approach we are able to reach a level of precision beyond the shot-noise limit without the use of postselection.We achieve this by implementing feed-forward and using a CCD camera with high detection efficiency.We have been able to obtain measurements of transmission with a maximum factor of advantage of 1.66 when compered to an ideal classical experiment using a noiseless coherent source and a 100% efficient detector.We have also studied the roll of photon distinguishability in quantum-enhanced phase estimation, where we have performed experiments with two and four-photons states controlling their level of distinguishability and we demonstrate that fully indistinguishable photons are not required to obtain quantum-enhanced measurements.I would also like to thank everyone else in QET Labs for their support and friendship.Gracias a Lorena por ser y por estar siempre presente.Y ante todo gracias a mi familia; sin ustedes nada de esto hubiese sucedido y nada de esto tendría sentido.
Quantum metrology exploits quantum correlations to perform measurements with precision higher than can be achieved with classical approaches [1]. Photonic approaches promise transformative advances in the family of interferometric phase measurement techniques, a vital toolset used to precisely determine quantities including distance, velocity, acceleration and materials properties. Without quantum enhancement, the precision limit in optical phase sensing (i.e. the minimum uncertainty) is the shot noise limit (SNL): 1/sqrt(N) where N is the number of resources (e.g. photons) used. Entangled photons promise sensitivity surpassing the shot noise limit achievable with classical probes. The maximally phase-sensitive state is the NOON state [2], a path-entangled state of definite photon number N. Despite theoretical proposals stretching back decades [3], no measurement using such photonic (i.e. definite photon number) states has unconditionally surpassed the shot noise limit: by contrast, all such demonstrations employed postselection to discount photon loss in the source, interferometer or detectors. Here, we use the state of art single photon generation and detection technology to respectively make and measure a two-photon NOON state, and use it to perform unconditional phase sensing beyond the shot noise limit — that is, without artificially correcting for loss or any other source of imperfection [4]. We performed a two-photon NOON state polarisation interferometry measurement on a birefringent test phase. We use photons generated from a high-heralding-efficiency, high purity source of telecom-wavelength photon pairs [5], and we employ high efficiency superconducting photon detectors. Unlike previous experiments, our apparatus does not require postselection to achieve phase uncertainty below that achievable in an ideal, lossless classical interferometer. Our results show a clear violation (for a range of phases) of the stringent SNL Fisher-information bound, F_{SNL} = 2.09635, that takes into account the information in unrecorded trials arising from loss and higher order terms — making our demonstration unconditional. We also performed a direct phase sensing measurement and observed phase uncertainties more than 10 standard deviations below the SNL [4]. Our results enable quantum-enhanced phase measurements at low photon flux and open the door to the next generation of optical quantum metrology advances. References [1] V. Giovannetti, S. Lloyd, and L. Maccone, “Advances in quantum metrology,” Nat. Photon. 5, 222–229 (2011). [2] J. P. Dowling, “Quantum optical metrology–the lowdown on high-N00N states,” Contemp. Phys. 49, 125–143 (2008). [3] R. Demkowicz-Dobrzanski, M. Jarzyna, and J. Kołodynski, “Quantum limits in optical interferometry,” Prog. Opt. 60, 345–435 (2015). [4] S. Slussarenko, M. M.Weston, H. M. Chrzanowski, L. K. Shalm, V. B. Verma, S.W. Nam, and G. J. Pryde, “Unconditional violation of the shot noise limit in photonic quantum metrology,” Nat. Photon. 11, 700-703 (2017). [5] M. M. Weston, H. M. Chrzanowski, S. Wollmann, A. Boston, J. Ho, L. K. Shalm, V. B. Verma, M. S. Allman, S. W. Nam, R. B. Patel, S. Slussarenko, and G. J. Pryde, “Efficient and pure femtosecond-pulse length source of polarization-entangled photons,” Opt. Express 24, 10,869–10,879 (2016).
We investigated precision measurements in a two-level system coupled to a single-photon-added coherent state (SPACS) under postselected weak measurement. We analyzed strategies for improving measurement precision, including parameter estimation and the signal-to-noise ratio (SNR) in postselected weak measurements, using the photon statistics of SPACS as the meter. Our results demonstrate that SPACS-based postselected weak measurements can outperform conventional measurement schemes in terms of precision. Additionally, we explicitly introduced an alternative weak measurement method, which is commonly applied in dispersive light-atom interactions. Our work presents a novel approach to addressing fundamental issues in quantum precision measurement based on photon statistics, and it provides a method for extracting the photon and phase shifts of radiation fields through the weak values of system observables.
Quantum-enhanced interferometers utilize non-classical states of light in order to surpass the limitations imposed by classical physics on phase measurement sensitivity and resolution. We review key scientific developments in this growing field of research and derive fundamental metrology concepts, namely the Cram\'{e}r-Rao bound and the Fisher information, which are used to analyze the metrological performance of quantum states of light. We propose a supersensitive quantum interferometry protocol that can be amplified to the macroscopic realm (i.e. the mean number of photons of the probe state can reach approximately 100,000 photons) using contemporary techniques of spontaneous parametric down conversion. The parity measurement on the output field asymptotically saturates the quantum Cram\'{e}r-Rao bound, which scales like the Heisenberg limit. We uncover the role of photon statistics on phase sensitivity and rule out the necessity of mode entanglement for quantum-enhanced interferometry. Based on these insights we outline a practical metrology technique (independent of mode entanglement) that measures a phase delay of a single-mode anti-squeezing operation. This scheme can also be scaled macroscopically using contemporary techniques and is shown to significantly surpass the shot-noise limit (SNL) in the presence of realistic losses. Finally, the physical resources that enable quantum-enhanced interferometry is studied by analyzing the quantum Fisher information (QFI) using the first quantization and the second quantization formalisms of quantum mechanics. It is shown that increasing the intra-mode correlations of an interferometer (as quantified by the second order Glauber coherence function) can be conducive to attaining a quantum advantage in phase estimation; whereas, introducing mode entanglement can reduce phase sensitivity. Using the first quantization description, we derive a formula for the QFI that shows explicitly how the Heisenberg scaling term depends on particle entanglement.