Structured optical beams possess rich spatial features that are commonly characterized using entropic measures of field complexity. However, such measures do not directly quantify the operational usefulness of optical structure for parameter estimation and sensing. Here we introduce Fisher information as an operational metric to assess the metrological content of structured optical fields. By treating the measured intensity distribution as a statistical object, we define Fisher information with respect to physically relevant parameters, such as transverse displacement. We demonstrate that optical modes with comparable Shannon entropy can exhibit markedly different Fisher information, revealing sensitivity features associated with nodal structure and local curvature. Using Hermite--Gaussian modes as minimal test cases, we show that increasing modal order systematically enhances Fisher information. We then extend the analysis to two widely used families in structured light: Laguerre--Gaussian vortex beams and finite-energy Bessel--Gauss beams. Across these representative families, Fisher information provides a unified and experimentally accessible criterion for comparing structured optical fields in sensing applications.
Structured optical beams possess rich spatial features that are commonly characterized using entropic measures of field complexity. However, such measures do not directly quantify the operational usefulness of optical structure for parameter estimation and sensing. Here we introduce Fisher information as an operational metric to assess the metrological content of structured optical fields. By treating the measured intensity distribution as a statistical object, we define Fisher information with respect to physically relevant parameters, such as transverse displacement. We demonstrate that optical modes with comparable Shannon entropy can exhibit markedly different Fisher information, revealing sensitivity features associated with nodal structure and local curvature. Using Hermite--Gaussian modes as minimal test cases, we show that increasing modal order systematically enhances Fisher information. We then extend the analysis to two widely used families in structured light: Laguerre--Gaussian vortex beams and finite-energy Bessel--Gauss beams. Across these representative families, Fisher information provides a unified and experimentally accessible criterion for comparing structured optical fields in sensing applications.
While information is ubiquitously generated, shared, and analyzed in a modern-day life, there is still some controversy around the ways to assess the amount and quality of information inside a noisy optical channel. A number of theoretical approaches based on, e.g., conditional Shannon entropy and Fisher information have been developed, along with some experimental validations. Some of these approaches are limited to a certain alphabet, while others tend to fall short when considering optical beams with a nontrivial structure, such as Hermite-Gauss, Laguerre-Gauss, and other modes with a nontrivial structure. Here, we propose a new definition of the classical Shannon information via the Wigner distribution function, while respecting the Heisenberg inequality. Following this definition, we calculate the amount of information in Gaussian, Hermite-Gaussian, and Laguerre-Gaussian laser modes in juxtaposition and experimentally validate it by reconstruction of the Wigner distribution function from the intensity distribution of structured laser beams. We experimentally demonstrate the technique that allows to infer field structure of the laser beams in singular optics to assess the amount of contained information. Given the generality, this approach of defining information via analyzing the beam complexity is applicable to laser modes of any topology that can be described by well-behaved functions. Classical Shannon information, defined in this way, is detached from a particular alphabet, i.e., communication scheme, and scales with the structural complexity of the system. Such a synergy between the Wigner distribution function encompassing the information in both real and reciprocal space and information being a measure of disorder can contribute into future coherent detection algorithms and remote sensing.
We explore the use of higher-order Hermite-Gauss modes for sensing optically induced transverse displacements. In the small-displacement regime, we show that projective measurements onto the two neighboring spatial modes yield optimal Fisher information, linearly scaling with the mode order m. We further extend the analysis to arbitrary displacement values and derive general expressions for the Fisher information, demonstrating that higher-order modes continue to outperform the fundamental Gaussian mode even at larger separations. This approach enables enhanced displacement sensitivity with only a minimal number of measurements, offering a simple and scalable alternative to conventional Spatial Mode Demultiplexing schemes. We provide a proof-of-principle experimental demonstration using spatial light modulators, showing an order-of-magnitude reduction in estimation variance when employing Hermite-Gauss modes of order m=8 and m=17. These results highlight the potential of structured light for ultrasensitive displacement sensing and may enable new applications in birefringence measurements with broadband or low-coherence light sources.
Abstract Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote sensing, the parameter of interest is not only encoded in the quantum state of the field, but also in its spatio-temporal distribution, i.e. in its mode structure. In this mode-encoded parameter estimation setting, we derive an analytical expression for the quantum Fisher information valid for arbitrary multimode Gaussian fields. To illustrate the power of our approach, we apply our results to the estimation of the transverse displacement of a beam and to the temporal separation between two pulses. For these examples, we show how the estimation sensitivity can be enhanced by adding squeezing into specific modes.
Famously, the quantum Fisher information -- the maximum Fisher information over all physical measurements -- is additive for independent copies of a system and the optimal measurement acts locally. We are left to wonder: does the same hold when the set of accessible measurements is constrained? Such constraints are necessary to account for realistic experimental restrictions. Here, we consider a fully Gaussian scenario focusing on only Gaussian measurements. We prove that the optimal Gaussian measurement protocol remains local, if the information is encoded in either the displacement or the covariance matrix. However, when the information is imprinted on both, this no longer holds true: we construct a simple global Gaussian measurement where the Fisher information becomes super additive. These results can improve parameter estimation tasks via feasible tools. Namely, in quantum optical platforms our proposed global operation requires only passive global operations and single mode Gaussian measurements. We demonstrate this in two examples where we estimate squeezing and losses. While in the former case there is a significant gap between the Fisher information of the optimal Gaussian measurement and the quantum Fisher information for a single copy, this gap can be reduced with joint Gaussian measurements and closed in the asymptotic limit of many copies.
Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote sensing, the parameter of interest is not only encoded in the quantum state of the field, but also in its spatio-temporal distribution, i.e. in its mode structure. In this mode-encoded parameter estimation setting, we derive an analytical expression for the quantum Fisher information valid for arbitrary multimode Gaussian fields. To illustrate the power of our approach, we apply our results to the estimation of the transverse displacement of a beam and to the temporal separation between two pulses. For these examples, we show how the estimation sensitivity can be enhanced by adding squeezing into specific modes.
The emergence and development of quantum optics as a discipline in the latter half of the twentieth century has established photons as one of the most promising candidates for future technologies in computing, metrology, communication, and imaging. In imaging and sensing, a series of recent theoretical works and proof-of-concept experiments have shown that by examining the mode structure of photons, one can build optical systems with resolutions below the Rayleigh–Abbe limit. Building upon these developments, in one of our works, we investigate the use of higher-order Hermite–Gauss (HG) modes for sensing optically induced transverse displacements. We show that projective measurements onto neighboring modes are optimal and sufficient in the small-displacement regime, and that the sensitivity—quantified by the Fisher information—scales linearly with the order of the mode used. We generalize the calculations to arbitrary displacements and varying degrees of coherence between the displaced modes, and perform a proof-of-concept experiment with higher-order HG modes, obtaining an order-of-magnitude enhancement in sensitivity compared to the fundamental mode. This approach enables enhanced displacement sensitivity with minimal measurements and highlights the potential of structured light for ultrasensitive displacement sensing, particularly for birefringence measurements with broadband or low-coherence light sources. We also consider displacement sensing in the light field originating from a biphoton source, which possesses rich high-dimensional correlations in its biphoton mode structure. We show that the Fisher information is proportional to the degree of entanglement, or equivalently, its Schmidt rank. In addition to sensing, photons structured in their transverse degrees of freedom also provide a convenient toolkit for quantum computing and communication due to the high dimensionality of their Hilbert space. In one of the works presented, we introduce a technique for nonlocal transfer of high-dimensional computational results using spatial correlations in photon pairs. We expect these findings to be useful in future photonic quantum networks, where computational resources are distributed and users can access the results of complex computations via a centrally located quantum processor. We also experimentally implement the protocol in down-converted photon pairs and demonstrate the transfer of unitaries in one-dimensional and two-dimensional transverse momentum spaces. In another work, we address the noise inherent in quantum computing circuits and simulate the interaction between a qubit and its environment by manipulating transverse momentum modes. This study, performed by fabricating three liquid-crystal metasurfaces, provides a practical solution for quantum state purification, demonstrating a versatile approach for simulating open-qubit dynamics. Combining the transverse spatial structure with polarization yields the so-called vector modes of photons. Structuring two-qubit interference, or the Hong–Ou–Mandel (HOM) effect, offers significant potential to extend the applications of such modes beyond the classical regime. We demonstrate the simultaneous generation of all four Bell states in polarization by exploiting HOM interference of vector modes. These results represent a significant step toward manipulating HOM interference within structured photons, offering promising applications in high-dimensional quantum information processing, quantum communication, and sensing. On the algorithmic side of photonic information processing, we propose a quantum pattern recognition algorithm to identify images obtained from quantum imaging techniques with correlated photons—such as “interaction-free” or “ghost” imaging. Interfacing these imaging techniques with quantum pattern recognition promises a significantly improved image acquisition and identification system, with potential applications in medical diagnostics and biological imaging.