Polarization-based sensing is a powerful technique in remote sensing, material characterization, and biomedical diagnostics^[1–4]. It enables the extraction of valuable information about the investigated sample, including morphology^[5], chirality^[6], and birefringence^[7] with enhanced performance. Currently, the employment of non-classical states of light pushes the frontiers in photonic sensing. Advantages such as enhanced sensitivity and precision^[8–10], reduced noise^[11–13], and improved measurement strategies^[14] come to the fore. These developments have gained increasing attention and inspired comprehensive reviews covering different modalities of quantum sensing^[15,16] and imaging^[17–22].

Since the first experimental demonstration of ellipsometric measurements using correlated photon beams 20 years ago^[23], polarization-based sensing and imaging with non-classical states of light have demonstrated significant advancements^[24–28]. Especially in recent years, there has been an increase in research activities on quantum-enhanced polarization-based sensing. Proof-of-concept experiments in quantum polarimetry have been demonstrated using both local^[29] and non-local configurations^[25,30], revealing enhanced precision in parameter estimation^[31]. Polarization microscopy has been demonstrated with photonic NOON states to achieve superb sensitivity in phase measurements^[32]. The preservation of polarization entanglement after propagating through bio-tissue has been investigated^[33,34]. Last year, the potential of quantitative polarization-sensitive imaging of small biological species was demonstrated using polarization-entangled photons^[27].

Despite this progress, the full potential of quantum polarimetry is not yet fully unlocked, and this rapidly evolving field continues to expand. At the same time, a comprehensive review of methods and applications that leverage either the polarization properties of non-classical sources or target the polarization-sensitive properties of investigated samples is not yet available. This review endeavors to address this critical gap.

We begin our review by tracing the historical evolution of quantum polarization-based sensing as a separate field in combination with a summary of the theoretical framework for quantum polarimetry. We provide a brief overview of the non-classical states of light used for the purpose of polarization-based sensing, cover the approaches for the appropriate data acquisition, and discuss the main features and advantages of employing quantum light for polarization-based sensing. Subsequently, we present a comprehensive review of the advancements and breakthroughs in the application of polarization for quantum photonic sensing, highlighting seminal works and emerging trends in the field. Here, we address details of the above-mentioned applications and further examples. Upon a comprehensive survey of the state of the art, we conclude our review with a discussion on current challenges that quantum polarimetry is facing as well as potential areas for further development, offering insights into the future directions of this emerging field.

Back in 1947, Pryce and Ward investigated the polarization correlation of gamma-quanta resulting from the annihilation of a slow moving positron-electron pair^[35]. The two generated photons were polarized perpendicularly and their subsequent Compton scattering distributions were demonstrated to be correlated in the azimuthal angle. The authors supplemented the experiment with derivation of the analytical description for the expected magnitude of this correlation. In fact, it became one of the earliest theoretical treatments of polarization-based characterization of quantum systems.

Since then, the polarization of light has been tightly interwoven with quantum optics development. It was instrumental, e.g.,  in seminal works on demonstration of non-classical correlations between photons generated via spontaneous parametric down-conversion (SPDC) in the 1960s^[36,37] and later, when in 1989, Bohm revisited the Einstein-Podolsky-Rosen (EPR) argument using the concept of entangled photon polarization states^[38], which provided greater clarity on non-local measurements with quantum correlations.

The importance of polarization in quantum optical experiments motivated the theoretical exploration of its treatment. In classical optics, the polarization state of light can be comprehensively described with the Stokes parameters^[39]$$\begin{gathered} S0=EH*EH+EV*EV, \\ S1=Sz=EH*EH−EV*EV, \\ S2=Sx=EHEV*+EH*EV, \\ S3=Sy=i(EHEV*−EH*EV), \end{gathered}$$where EH and EV denote the complex amplitudes of the corresponding mode. Quantum counterparts of these are Stokes operators, which are introduced using creation α^H†, α^V† and annihilation α^H, α^V operators of horizontal and vertical polarization modes of the electromagnetic field^[40–42] as $$\begin{gathered} S^0=α^H†α^H+α^V†α^V, \\ S^1=Sz=α^H†α^H−α^V†α^V, \\ S^2=Sx=α^Hα^V†+α^H†α^V, \\ S^3=Sy=i(α^Hα^V†−α^H†α^V). \end{gathered}$$

These operators satisfy SU(2)-like commutation relations and their expectation values can transform similarly to Stokes parameters guided by 4×4 Mueller matrices. This framework is instrumental for describing polarization in quantum optics as well as translation of classical polarimetric tasks to the quantum paradigm. Using this, analogous to classical optical polarimetry, also known as Mueller polarimetry^[43], the Mueller matrix of a sample under study can be reconstructed from measured Stokes operators^[44]. Also, parameter estimation problems can be addressed^[45].

If pure polarization states are in focus, application of the Jones calculus can be advantageous. The components of the classical Jones vector are similarly the complex amplitudes EH and EV, so that, e.g.,  the horizontal and vertical polarization states can be expressed as [EHEV]=[10]and[EHEV]=[01],correspondingly. In this case, only the classical fully polarized states of light (S02=S12+S22+S32)^[39] are considered, which correspond to pure polarization states of single photons.

This framework is especially useful in quantum communication and computation where the Dirac notation is widely adopted and horizontal |H⟩=α^H†|0⟩ and vertical |V⟩=α^V†|0⟩ polarization states are preferred as basis states for decomposition of any arbitrary pure polarization state (|0⟩ stands for vacuum state). It is also used to describe generation and manipulation of multiphoton states like biphotons, or photon pairs, generated via SPDC and entangled states, e.g.,  Bell states in the form 1/2(|HV⟩±|VH⟩) or 1/2(|HH⟩±|VV⟩), with |H⟩ and |V⟩ indicating horizontal and vertical polarization states.

For problems dealing with ensembles of photons and their interaction with different media, another representation of polarization—Wolf’s coherency matrix^[39]—becomes useful. The latter can describe both fully and partially polarized states (S02≥S12+S22+S32), and can be related to the density matrix (or density operator) formalism of the quantum photonic states^[40,46]. This relation in turn enables application of numerical simulation methods for predicting the behavior of quantum photonic states such as modeling photon transport in a turbid medium with Monte Carlo methods^[46].

A comprehensive introduction to the theoretical treatment of polarization within classical and quantum paradigms is however beyond this review and the readers are highly encouraged to refer to the fundamental work by Mandel and Wolf^[40] as well as to Refs. [41,42,47,48], and more recent elaborations like Refs. [44,45]. Beyond this review is also the broad topic of the generation of non-classical states of light, while for states that are currently mostly used for quantum sensing with polarization, we provide a brief overview in Appendix A.

Similar to other quantum-enhanced sensing and imaging modalities, there are several strategies within which the quantum technologies are used in sensing with polarization.

The first one, and the most used one, is straightforward employment of quantum light to realize the measurement principles known from classical polarimetry but with enhanced performance. The latter includes, e.g.,  improved sensitivity, signal-to-noise ratio (SNR), accuracy, and possibility for deeper penetration of the probing light into the complex sample. In this scenario, the general framework of classical optical polarimetry is followed, where the full Mueller matrix of the sample is found^[44] or the full tomographic characterization is performed^[49], polarization-sensitive responses are directly monitored^[50] or certain parameters are retrieved within a parameter estimation problem^[31,45]. The most used photonic quantum states within this niche are photon pairs correlated in polarization and/or momentum, NOON states, and polarization-entangled photon states, usually pairs. Probing the sample with states mentioned benefits from their statistical properties and correlations.

The discussed strategy proposes to either herald the photon interacting with the sample (signal photon) with its partner from the SPDC event (idler or also reference photon)^[30] or directly use both partner photons to propagate through the sample^[9,32,51]. In the former case, the detection of one of the photons (herald or reference photon) signals the presence and timing of its correlated partner photon, which interacts with the sample. In the latter case, the photons are separated into two channels after interaction with the sample [most commonly distinct pixels on a two-dimensional (2D) sensor]. In both configurations, the coincidences counted between the signal and heralding channel within a narrow temporal window of no more than several ns represent the useful signal for analysis and allow filtering the accidental counts and thus improve the SNR and reduce the uncertainty of the measurement^[52]. This is especially useful when dealing with complex samples like biological tissues^[33] or for applications restricted to the usage of a low number of photons as in the case of delicate samples^[9].

Leveraging statistical distribution of photons is one of the arguments also when employing NOON states. This state can enable multiphoton probing, which results in a faster modulation of the response function. This in turn allows enhanced sensitivity and SNR of the measurement^[32], similar to modulation compression obtained with optical angular momentum (AOM) in photonic gears^[53].

For the already described methods with correlated and NOON states the collection of the signal can be performed with single-pixel single-photon counting modules in each optical mode and coincidence measurement between them, 2D sensors directly capable of spatial correlations detection like single-photon avalanche diode (SPAD) arrays^[54], or highly sensitive low-noise cameras supplemented with special signal processing algorithms^[55].

The second strategy to realize quantum-enhanced polarization-based sensing relies on the development of new measurement configurations and identification of new sensing mechanisms.

The first example to mention here is the non-local polarimetric measurement, a direct analogy of ghost imaging^[20,21] with photon pairs. In the non-local, or ghost, measurement configuration the correlated partner photons are spatially separated into two optical channels. One of the photons (sample or signal) interacts with the sample, while its partner (reference or idler) remains unmodified. Instead of the spatially resolved intensity or phase signal collection in ghost imaging, a polarization state analyzer is introduced into the idler channel to characterize the polarization properties of the sample^[56] or classify the samples by their polarization-based response^[26,57]. This distinguishes the approach from the heralding configuration, where only the temporal information on photon arrival times to the detectors is used for SNR improvement and the information on the sample is obtained locally, in the channel of interaction. In the introduced non-local measurement approach, the information about the sample is obtained from the non-local channel, where photons do not interact with the sample.

For characterization tasks, the polarization-state analyzer in the non-local spatially separated channel directly follows the native techniques of classical Stokes polarimetry, but the detection of the light transmitted by the sample is performed without a polarization-sensitive detector. To perform this measurement, photon pairs with classical polarization correlations are sufficient. However, when implemented with polarization-entangled states, also the information about the phase between the horizontally and vertically polarized photons can be reconstructed, which paves the path towards comprehensive characterization without necessity for generation of different probing states to be incident on the sample^[27] and for measurements that do not require calibration with reference samples^[58,59].

Besides spatial separation, the spectral separation between the optical channels, corresponding to the photons of the used photon pairs, is also possible. Wavelength non-degenerate photon pairs provide signal and idler photons at different wavelengths, i.e., in the visible and infrared. This allows for probing the sample at a different wavelength range than is used for the polarization-resolved detection, alleviating the need for polarization optics at the probing wavelength, which may not always be available.

Another noteworthy track for quantum-enabled measurement scenarios deals with exploration of substantially new mechanisms for light-matter interaction, e.g.,  identifying new diagnostics metrics^[46] and new measurement scenarios^[26,57]. Especially for the latter, the motivation for the studies is detection of polarization-sensing parameters, which would allow sensitivity levels not accessible with classical methods, also beyond SNR improvement already enabled by coincidence-based detection or specific photon statistics of probing states. Here, e.g.,  resources of quantum light like the level of entanglement are studied for quantitative sensing^[34,46]. Identifying such metrics often requires initial comprehensive analysis of light-matter interaction within the quantum experiment. This is provided by quantum process tomography (QPT)^[60], which in a straightforward scenario requires d2×d2 measurements (with Hilbert space dimension d=2 for one channel or photon, i.e., qubit). Already for a photon pair used for probing, this implies 16×16 measurements per sample or its point, which in turn results in enormous time consumption for any spatially resolved measurement. This motivates the search for possible optimized measurement scenarios with the maximized level of information obtainable with the minimum number of measurements needed. This problem has been addressed by studying the possibility of reasonable sensing with incomplete measurements when only quantum state tomography (QST)^[61] is used. This can be achieved, e.g.,  by translating the measurement problem into a parameter estimation problem^[31], performing tomographically incomplete measurements at customized projections for classification tasks^[26,57], or direct employment of parameters of the non-classical states as the sensing parameters^[34,46].

In the following section, we describe the main advancements in quantum polarization-based sensing in detail.

Following the strategies for realizing quantum-enhanced polarization-based sensing that we described in Sec. 3, in this section, we review the key advancements in the field in a chronological manner. Here, the reported solutions are often based on implementing classical measurement strategies with non-classical light, but often introduce modifications that enable leveraging quantum advantages. For this reason, we group the works in the discussion below by similarities in their implementation. Additionally, we briefly discuss the polarization-based sensing realized in the imaging mode.

In 1999, precision phase measurement and simultaneous measurement of Stokes parameters with non-classical light were proposed, which paved the way towards enhanced-precision non-classical polarimetry^[62].

Within the next few years, an approach for ellipsometric measurements using correlated photons^[23] (heralding configuration; see Sec. 3 for explanation) and polarization-entangled^[58,63] (ghost, or non-local, configuration; see Sec. 3) photon pairs was proposed.

The authors have realized the method with correlated photons experimentally. It allowed for reducing system sensitivity to instrumental imperfections with a more simplified optical setup (Fig. 1) while its performance was compared to a conventional ellipsometer using SNR and accuracy of the retrieved ellipsometric parameters measurements. The results proved enhancement enabled by quantum light on both SNR and accuracy [Fig. 1(b)].

In the case of ghost configuration with entangled photon pairs [Fig. 1(c)], the authors suggested introducing most of the optical components including polarization optics for general unitary polarization projections in the reference channel of the measurement system. Hereby, it would enable easy and repeatable changing of the incidence angle of the probing light onto the sample, which is a prerequisite for null, or absolute, measurements, and moreover, to eliminate the necessity of the reference sample, which in turn is required for such measurements in classical ellipsometry.

It was, however, only in 2020, when ghost polarimetry for complete polarization-based characterization of the sample was introduced as a standalone method. First with classical light, Hannonen et al.^[56] and Magnitskiy et al.^[64] explored polarization state correlations in the experimental arrangement of ghost imaging in order to characterize polarization-sensitive transmissive objects. The experimental arrangements studied within these works consider transmission of the probing light through the sample under investigation and imply retrieval of the complete polarization response of the sample instead of several ellipsometric parameters.

Here, instead of directly measuring intensity variations as it is performed in ghost imaging, correlated intensity fluctuations between the sample and reference beams were analyzed. For this, a spatially incoherent classical light source with adjustable polarization states was used to extract the four transmission amplitudes and three phase differences of the Jones matrix of the transmissive polarization-sensitive object, allowing full characterization of its polarization response^[56]. In parallel, ghost polarimetry using an unpolarized pseudo-thermal light was proposed, which enabled the measurement of the spatial distribution of anisotropy and azimuthal angles of polarization-sensitive objects^[64].

Later, Magnitskiy et al.^[25] expanded their analysis to using the entangled photons and investigated the advantages of polarimetry with quantum light^[65]. In particular, the authors emphasized that polarization-based sensing with non-classical states of light excels due to intrinsic quantum correlations and coherence. Specifically, non-classical states of light enable the ghost, or non-local, configuration of the measurement, allowing not only improved sensitivity and reduced noise but also the extraction of polarization information without introducing polarization optics into the sample arm and thus keeping the number of optical components in this path at a minimum.

In 2022, ghost polarimetry with polarization-entangled photon pairs was demonstrated in practice by Restuccia et al.^[30]. In the experiment (Fig. 2), the entangled photons were separated by a knife-edge prism into two channels, and thus both heralded configuration and non-local configuration could be realized and compared in performance. As test samples, the authors used solutions containing D-limonene, a chiral molecule known for exhibiting polarization rotation properties. Chirality parameters of D-limonene in cells of different lengths (1, 2, and 5 cm) were measured and compared for both studied configurations. The results confirmed that ghost polarimetry can provide optical activity measurements consistent with classical techniques but importantly without the need for polarized illumination incident on the sample, thus reducing disturbance of the sample in the case of its sensitivity to polarized light^[50].

Recently, the applicability of polarization-entangled photons to classical polarimetry has been revisited, particularly for probing samples in transmission^[59]. The authors achieved nanoscale accuracy with increased measurement stability and studied the achievable quantum advantage in terms of Fisher information. By sample translation, they demonstrated 2D characterization of anisotropic media, also under perturbation with an external light source^[66].

As discussed in Sec. 3, besides direct leveraging correlations of non-classical states of light and resultant heralding and ghost measurement configuration, there is a quest for quantum-enabled metrics in polarization-based sensing.

In this pursuit, in 2012, Wolfgramm et al. demonstrated application of polarization-entangled NOON states to probing the ensemble of Rb85 atoms as an example of a delicate sample^[9]. Matter-resonant NOON states of left- and right-circularly polarized photons with N=2 were passing through the sample and then split by polarization into two optical channels between which coincidence counts were measured for different polarization projection combinations (HH, HV, and VV). These coincidence counts were also used to reconstruct the quantum state of the photons after interacting with the sample. Hereby, this represents another example for leveraging the photon statistics of quantum light discussed in Sec. 3. The authors demonstrated the possibility to detect absorption—light induced damage to the sample and at the same time loss of information in the transmitted state estimated by Fisher information (FI)—as well as Faraday rotation within the sample due to an externally applied magnetic field. The results showed twice faster oscillation of the coincidence counts dependent on the magnetic field thus improving resolution twice with respect to the single-photon probing. Moreover, the method allowed the authors to surpass the standard quantum limit, with a 30%±5% improvement for information gained per photon and 23%±4% for damage to the sample (Fig. 3). In repeated probing, this means that fewer photons are needed to achieve the same measurement accuracy, causing less changes in the properties of the sample. The study showcased the method’s robustness under real-world conditions, including loss and noise, with an ensemble of atoms serving as a model of sensitive samples like biological specimens and nanostructures^[9].

In continuation, in 2024, Israel et al. demonstrated a proof-of-principle interferometric polarized light microscope using polarization NOON states (with N=2 and N=3)^[32]. The latter was generated by mixing coherent light with SPDC photons (see Appendix A), and thus the proposed instrument allowed to probe a model sample of low birefringence (crystalline quartz powder in the index matching oil, φ≪π) with both classical light and quantum light. The results confirmed improved phase sensitivity of the measurement with NOON states due to faster modulation by factors 2 and 3 for N=2 and N=3, respectively (Fig. 4). By sample scanning, the authors have realized spatially resolved measurement and the resultant images also proved enhanced SNR in the case of NOON probing (Fig. 4).

In 2022, bright polarization-squeezed lights was used to estimate the concentration of chiral media based on circular birefringence and circular dichroism. The authors analyzed the differential phase shift induced by chiral media on left- and right-circularly polarized lights to estimate the concentration of the chiral analyte. The results were quantified using quantum Fisher information (QFI) and demonstrated higher precision achievable with polarization-squeezed states than with classical strategies; moreover, with the potential of four-fold enhancement assuming the state-of-the-art squeezing levels^[67].

Recently, sensing scenarios that leverage polarization Bell states for characterization and classification purposes of samples by their polarization response have gained particular interest. A straightforward approach for the quantum counterpart of classical optical polarimetry^[43] can be realized by quantum process tomography^[60], which, as discussed in Sec. 3.2, requires d2×d2 measurements with Hilbert space dimension d=2 for one photon. However, when any of the partner photons of a polarization-entangled state is influenced by the respective quantum channel of propagation, this affects the state as a whole according to the principle of remote state preparation^[68]. Hereby, the entangled states are susceptible, or in other words, highly sensitive, to external disturbances impacting their entanglement. In this sense, even a pair of polarization-entangled photons, such as a Bell state, is expected to exhibit enhanced sensitivity to subtle changes in the sensed signal caused by changes in the sample’s properties.

In case that the mere detection of the sample’s presence or its change is the measurement goal, the complete characterization of the sample polarization properties is redundant, and the evolution of a single probing state might appear sufficient. For such applications, the measurement can be performed in the ghost configuration (see Sec. 3) and the information acquisition can be restricted to only quantum state tomography^[61] performed, e.g.,  for the basis of horizontal |H⟩ and vertical |V⟩ polarization states. The latter implies only d2 measurements, but due to the entanglement between the photons in the probing state, it appears sensitive to the information of interest.

Following this strategy, in 2016, preservation of polarization entanglement of photon pairs when one photon passed through a real biological tissue on an example of mouse brain tissue slides was studied^[33]. Similar to the previous example and in contrast to the already discussed works on ghost polarimetry described in Sec. 4.1, the coincidence counts between the two channels were used to reconstruct the quantum state via QST. Such metrics as fidelity, linear entropy, and tangle were retrieved from the measured density matrix of the state after interaction with the sample and analyzed to explore the entanglement degradation dependent on the tissue thickness, structure, and water content. In the experiment, it was ensured that predominantly ballistic photons were detected, and it was shown that non-classical correlations of the polarization-entangled photon pairs were maintained significantly better than classical correlations of photons upon multiple scattering events in the sample. One of the most important results was the demonstration of the entanglement preservation after passing through the cortex tissue of 400 µm thickness, promising deeper penetration into the real sample for diagnostics purposes in the future.

In continuation, in 2022, the applicability of polarization Bell states to distinguish different samples by scattering properties was investigated. In particular, the healthy brain tissues and brain tissues affected by Alzheimer’s disease of different thicknesses were studied^[34]. Besides monitoring tangle and linear entropy of the probing state, the authors analyzed the Werner curve, which represents a specific quantum decoherence pathway where an initially pure and maximally entangled quantum state progressively transitions into a maximally mixed state through scattering or other decoherence processes. The results showed that the entanglement decoherence followed the Werner curve, and importantly, the tissues affected by Alzheimer’s disease and healthy tissues could have been differentiated by the level of decoherence (Fig. 5).

In parallel and independent of the discussed studies, sensing with Bell states has been explored for polarization-based characterization and classification. In particular, this approach has been demonstrated for sensing of samples with subtle polarization response including monolayer cell cultures^[69] and aqueous solutions of microorganisms^[70]. The outcomes confirmed the ability of the method to identify qualitatively different polarization responses of minor discrepancy and little but comparable magnitude as well as to detect qualitatively similar responses but of different magnitudes.

In continuation and in pursuit of practical applications in biomedical diagnostics, Besaga et al. have systematically explored the applicability of the approach to sensing of complex turbid media and its feasibility for their quantitative characterization^[46]. As test samples, the authors used tissue-mimicking phantoms with varying scattering properties and revealed a clear proportionality of the entanglement level of the detected state to the scattering properties of the tested samples, which, moreover, was robust to variations of the initial probing state. For the interpretation and modeling of the experimental results, the authors proposed a Monte Carlo approach allowing for predicting the density matrix of the probing state after one of the partner photons interacted with the sample. The results of this study, together with already discussed demonstration of deeper penetration of entangled photons into the biological tissue^[33], underscore the diagnostic potential of quantum-enhanced polarimetry.

The performance of the quantum polarimetric approach utilizing polarization-entangled states has been thoroughly examined to assess the practically achievable quantum advantage. In particular, Pedram et al. have shown the improved precision of polarimetric measurements enabled by the information carried by the partner photon from the entangled pair compared to the heralded single-photon probing^[31]. The study has been performed using well-characterized conventional polarizing test objects such as polarizers and waveplates, and Fischer information from the experimental and theoretically modeled data has been used to demonstrate and quantitatively estimate the non-locality-enabled advantage.

Besides explicit sensing/detection of sample presence or its change, the task of identification/classification comes to the fore. Since a broad range of samples from nanostructures to biological specimens exhibit characteristic polarization properties, the polarization response can be employed for classification scenarios in a wide range of tasks. This includes distinguishing different types of tissues for diagnostics purposes and testing the state of a remote optical data link for ensuring secure communication. Here, the photonic entanglement in polarization offers special opportunities. Vega et al. proposed that in the non-local measurement scheme sketched in Fig. 6, it is possible to identify many different objects by employing a specifically tailored polarization projection in the arm of the photon that interacts with the object. It was shown that for a known set of objects, such a projection could be tailored to always lead to object-specific distinct reduced states of the idler photon after detection of the signal. Based on this, it is possible to find a set of polarization projections for the idler photon to distinguish the reduced states for each sample by a limited number of correlation measurements between the partner photons. Importantly, the number of needed projections and measurements can be less than required for a complete projective analysis of the idler photon^[57]. For implementing the polarization projections, metasurfaces have been suggested as a versatile platform, which can also implement projection onto partially polarized states. In their theoretical work, the authors have evaluated the impact of the degree of entanglement on object discrimination and demonstrated that higher degrees of entanglement improve the visibility of polarization-based patterns, enhancing measurement accuracy. They also compared the performance of thermal sources with entangled photons and concluded that the entangled case will show better contrast than the thermal source^[57].

This concept was also demonstrated experimentally^[26]. Moreover, it was shown that just two combinations of signal and idler projections allow for reliable distinguishing of more than 80 samples with only slightly different Mueller matrices using the example of different orientations of a linear polarizer and a quarter-wave plate (Fig. 7). With further refinement, e.g.,  in terms of the probing state preparation, this concept promises highly sensitive classification opportunities with a reduced number of measurements per sample for routine tasks, while also revealing new insights into unknown samples when classification is performed using features of interest.

Whereas we have so far discussed polarimetry in a single optical mode or beam, we will now briefly explore approaches that collect information about an object’s polarization properties with spatial resolution.

In 2018, polarization-based sensing in a ghost configuration (introduced in Sec. 3) was shown with polarization-correlated photon pairs and correlation measurement using a charge-coupled device (CCD) camera^[52]. Using a test sample with variable optical loss (1%–70%) and the instrument visualized in Fig. 8, the authors achieved unbiased and high-sensitivity optical loss estimation at the ultimate quantum limit. The achieved sensitivity exceeded the classical limit by 50% and doubled the sensitivity of the measurement with classically correlated beams.

In 2019, polarization-entangled photon pairs and an intensified CCD camera (ICCD) were employed for imaging polarization-sensitive samples in the ghost configuration^[71]. The test sample used in this study was a metasurface of superimposed two types of polarization-sensitive nanostructures, which acted as polarization filters to transmit either horizontally or vertically polarized light. Either type of nanostructure formed a different object (a triangle-shaped pattern and a star-shaped pattern). When the sample was illuminated by the pure entangled state, either a triangle or a star was reconstructed in the image, depending on the selected polarization of the photon in the reference channel. When illuminated with a mixed state, both shapes appeared in the image overlapped, showing the potential of non-local control of the polarization-encoded information. In 2021, similar experiments were demonstrated^[72] where the authors realized a polarization-sensitive pattern with a spatial light modulator (SLM).

Measurement of birefringent samples in the configuration where the probing photon pairs are split into two channels after interaction with the sample has been reported in Ref. [51]. The authors employed polarization NOON states with N=2 to realize phase-sensitive imaging with an SPAD array.

Correlations of the spatially separated photons were used for holographic reconstruction of phase images of the sample under study. The results showed enhanced sensitivity of the measurement thanks to the reduced noise. Quantitatively, the noise of the retrieved phase images was reduced by factors of 0.72±0.06 for birefringent and 0.80±0.04 for nonbirefringent samples^[51].

Last year, Zhang et al. demonstrated the imaging of biological organisms through spatial and polarization entanglement^[27]. The author employed the ghost configuration and for the first time realized polarization-based imaging with polarization-entangled photons. For the latter, spatially resolved measurement was realized by raster scanning of the sample. Besides a thorough analysis of quantum-enabled enhancement for imaging in terms of SNR and resolution, the authors could demonstrate quantitative reconstruction of birefringent properties of a thin low-absorption biological organism (Fig. 9).

The approach for polarization-sensitive imaging with polarization-entangled photons introduced in Ref. [27] was also explored in Ref. [73] and resonated with the entanglement-enabled ellipsometer^[58] and polarimeter^[59] that we discussed in Sec. 4.1. This emphasizes the weak boundaries between different approaches in quantum-enhanced polarization-based sensing and difficulties for categorizing the reported studies. Moreover, the brief overview of the key advancements reviewed in Sec. 4 cannot cover all recently introduced solutions. Besides already mentioned works, significant efforts have been made to study the fundamental limit of polarization-based sensing in parameter estimation tasks with light states of different levels of non-classicality^[74,75], apply polarization-entangled photons to sense^[76] and interact with^[77] the human retina, as well as address the polarization-based ghost measurement configuration in harsh environments like underwater conditions^[78].

The mentioned studies clearly support the high potential of quantum-enhanced polarization-based sensing for ensuring enhanced performance compared to classical measurement modalities in different aspects: from enhanced sensitivity or SNR to classically impossible measurement configurations. It is important to emphasize that quantum advantages in polarization-based sensing with relatively simple non-classical states involving mainly photon pairs have been demonstrated experimentally. It was shown that different non-classical states of light can provide higher sensitivity of the measurement either by changing the response function of the interaction with the samples or by improving the SNR. The latter is possible either immediately via the photon statistics of the used state, where fluctuations in the photon number can be below the classical shot-noise limit, or by temporal post-selection of the detected photons. The post-selection, in turn, is achieved by counting the coincidences between the partner photons propagating in spatially separated channels and can help mitigate the effects of different sources of noise, which is particularly advantageous in applications requiring high-precision sensing. This can find application in a broad range of problems, while the significance of quantum polarimetry becomes clear, especially for biomedical diagnostics. Here, the possibility to enhance sensing performance when dealing with highly scattering media is expected to pave the way for novel diagnostics tools for biological tissues.

Nevertheless, the proposed solutions have not yet achieved practicality. Besides the general complexity of generation of non-classical states of light, their manipulation, and delivery to the sample under study, the quantum enhanced sensing falls behind classical measurement in terms of duration of the measurement. The post-selection of the signal by coincidence counting, which allows filtering out the undesired noise background from the measurement output, results in the necessity for longer integration times for acquiring signals of sufficient strength as well as in the employment of often computationally heavy algorithms for post-processing and analysis of the data. This disadvantage compared to classical photonic sensing is valid so far for different modalities of quantum photonic sensing and imaging, also beyond polarization-based approaches, and is particularly important in practical measurement scenarios, where high losses in the samples under study exacerbate the situation.

An effective strategy to address this issue would involve the use of bright sources of photon pairs with generation rates approaching or exceeding the MHz range. For the SPDC process, which is most commonly used to generate polarization-entangled photons, such levels of the photon flux per second available for sensing purposes can be approached via painstaking optimization: selection of an appropriate nonlinear material with a large effective nonlinear coefficient (also as waveguide structures to exploit light confinement) and careful engineering of the phase-matching conditions^[79–81], as well as spectrally narrowband and efficient pumping^[82]. No less important is the efficient collection of the generated photons^[83,84]. Alternatively, solutions for bright sources of polarization-entangled photon pairs can include quantum dots with fast excitation^[85,86] and narrowband four-wave mixing^[87], while a comprehensive overview of approaches to increase source brightness and corresponding coincidence rates in detection is beyond the scope of this review. In addition, optimization of the measurement instruments through engineering fast polarization state switching for polarization projective measurements^[88] and increasing the number of single-photon counting detectors to perform measurements on orthogonal polarization projections in parallel^[89] can also be instrumental in speeding up the sensing routine.

The modifications to the experimental system mentioned above inevitably lead to an increase in the cost of such solutions. Addressing the hardware only would not be complete, however, and the commonly used tomographic reconstruction of the quantum states can be replaced by machine-learning-enabled state reconstruction^[90] or elaboration of sensing scenarios with the minimal required number of measurements^[26] to approach characterization and sensing tasks to real-time implementation. Methods for the polarization characterization of photonic quantum states are not covered in this review, where we encourage the reader to refer to, e.g.,  Refs. [91,92].

Nevertheless, this aspect is crucial for practical solutions in polarization-based quantum photonic sensing, since fast measurement approaches become even more critical when imaging modality is demanded, which in most cases is addressed currently by scanning the sample under study. Here, extended acquisition time hinder the broad adoption of quantum concepts already proved feasible and beneficial but also restrain the development of novel solutions. The latter applies to various fields, and especially to those dealing with complex or dynamic samples like biomedical imaging and remote sensing. The possibility for quantum-enhanced monitoring of the rapid changes in differential interference contrast microscopy enhanced with polarization NOON states^[12], entanglement-enabled birefringence quantification^[27,63,66], and other solutions discussed in Sec. 4.4 would advance practical polarization-based quantum sensing beyond the laboratory conditions. At the same time, various imaging modalities have not yet been studied for leveraging the polarization degree of freedom of non-classical states of light. Among others, it is yet to explore the feasibility and potential advantages of polarization-sensitive quantum optical coherence tomography^[93,94] and interferometry with shared polarization entanglement^[95].

Besides practical aspects of realizing the quantum-enhanced polarization-based sensing, there is a range of questions on optimal measurement approaches from the point of view of the retrievable information about the sample. Particularly interesting is the possibility for quantum polarization-based sensing with complex states of light. So far, mainly conventional polarization states like horizontal, vertical, diagonal, antidiagonal, circular, and other intermediate polarization states that can be mapped onto the Poincaré sphere have been employed for the quantum counterpart of the classical Mueller polarimetry. Such states are characterized with homogenous distribution of polarization over the spatial and temporal modes occupied by the photons, whereas in classical photonic sensing states with spatially and temporally structured intensity and phase, e.g., states with spin angular momentum (SAM) and optical angular momentum (OAM)^[96,97], have been shown to be advantageous^[98–101]. Also, states structured in the polarization itself, like topological states and optical polarization quasiparticles^[102], might be beneficial. Especially, the latter has been only recently demonstrated in free space optics and is expected to give rise to a standalone approach for metrology and sensing. This broad field of structured light has been recently reviewed, e.g.,  in Refs. [103,104].

To sum up, despite all the progress within the last several decades, quantum photonic sensing with polarization still remains an emerging technology. A range of promising results have been predicted theoretically and demonstrated experimentally. It is expected that further breakthroughs in the field will be reported in the coming years considering the increase in the research activity on polarization-based sensing with different non-classical states of light. In this review, we provided a brief overview of only the main advancements in the field, its current challenges, and possible directions for further development. At the same time, the current state of the art of quantum photonic sensing with polarization underscores its potential for applications spanning remote sensing, fundamental research, and biomedical diagnostics.