Photonic System Rotation Clarifies Superresolution Origin

Byoung S. Ham, of the Gwangju Institute of Science and Technology, in collaboration with Oregon State University, have thoroughly analysed a multi-pass photonic scheme, determining the source of its observed superresolution and supersensitivity. Ham and colleagues, using a Jones-matrix formalism, show that phase accumulation within the linear-optical interferometer results from coherent rotation of the polarization state. This geometrical interpretation clarifies the physical mechanisms behind the enhanced measurement performance, validating the theoretical model with a classical-wave implementation and comparison to a recently proposed coherence de Broglie wavelength framework. The findings offer a deeper understanding of photonic interferometry and its potential for achieving measurement precision beyond classical limits.

Polarisation dynamics, Fisher information and superresolution via coherent wave propagation

A progressive realignment of the polarization state occurs during successive forward and backward propagations. Experimentally, a classical-wave implementation validated the theoretical model, with results analysed and compared to the corresponding Jones-matrix solution. Subsequently, the scaling behaviour of the Fisher information was analysed to examine the origin of the claimed supersensitivity, mirroring results from a recently developed coherence de Broglie wavelength framework that achieves identical superresolution through repeated coherent interactions in a cascaded interferometric architecture.

In coherence optics, coherence arises from a well-defined relative phase between optical fields, consistent with Maxwell’s equations. Although both coherence optics and quantum information science originate from wave phenomena, the interpretation of quantum superposition often differs from that of coherence. This distinction is commonly associated with wave-particle duality, where wave-like and particle-like properties provide complementary descriptions of the same physical system.

The coherence of a light source is limited by its finite spectral bandwidth, resulting in a localized wave packet characterised by a finite coherence time and coherence length. This wave-packet description closely resembles the particle concept represented by Schrödinger’s wave function in quantum mechanics. Consequently, the wavelength associated with a quantum particle may be understood as an effective property emerging from an ensemble of monochromatic wave components.

Within this framework, the uncertainty relation between conjugate variables, such as position and momentum, or photon number and phase, follows naturally from Fourier analysis. A decrease in uncertainty in photon number corresponds to an increase in the uncertainty in phase. In the limiting case of a Fock state with a well-defined photon number, a well-defined absolute optical phase cannot be assigned. This observation raises fundamental questions regarding the physical interpretation of phase in quantum measurements and motivates a careful distinction between absolute phase, relative phase, and phase correlations established between multiple particles or optical modes.

Over the last century, quantum mechanics has been largely developed from the particle interpretation of Schrödinger’s wave equation, emphasizing measurement outcomes associated with discrete quantum particles. Within this framework, the role of phase has often been discussed primarily through probability amplitudes rather than through direct physical phase relations between individual particles. As a result, quantum phenomena such as nonlocal correlation, quantum rubbers, and Hong-Ou-Mandel interference have traditionally been interpreted within the standard quantum-mechanical formalism.

More recently, alternative approaches have been explored to reexamine these phenomena from the perspective of optical coherence and phase correlations. These studies employ the phase degree of freedom to analyse effects otherwise regarded as uniquely quantum. For example, the wave-packet description has been used to investigate interference fringes in second-order intensity correlations. First-order interference between orthogonal basis states is forbidden in conventional coherence optics, but phase coherence can be recovered through selective projection measurements at the output ports, at the cost of a deterministic 50% reduction in available measurement resources.

A recent quantum-mechanical analysis provided a general description of superresolution in coherence de Broglie waves, where N00N-like superresolution originates from the Nth power of a unitary transformation of a Mach-Zehnder interferometer. This mechanism differs conceptually from conventional resolution enhancement techniques employed in optical sensors, such as wavelength metres, gyroscopes, and LIGO, where improved resolution is typically achieved through geometric scaling, amplitude superposition and increased interaction length via resonant enhancement, rather than through repeated coherent application of a unitary phase operator. A previous publication was revisited to analyse the origin of the reported superresolution and claimed supersensitivity in a simple multi-pass structure composed entirely of linear optical elements.

Each round trip within the linear optics unit equates to a double reflection in polarization space, effectively rotating the polarization and accumulating phase. The associated phase-accumulation mechanism was then examined through the coherent evolution of polarization bases, demonstrating that the round-trip Jones-matrix analysis is equivalent to a rotation of the polarization-state vector. Classical Fisher information was also calculated for the claimed supersensitivity and compared with the recently proposed coherence de Broglie wavelength method.

Particular attention was paid to the role of the scaling parameter used in the previous publication and to the interpretation of the random variable and resource counting in Fisher information analysis. This geometrical interpretation clarifies how the observed superresolution and associated supersensitivity originate, validating the theoretical model with a classical-wave implementation and offering a new perspective on photonic interferometry. The purpose of this work is not to challenge the validity of quantum mechanics, but to provide additional physical insight into the origin of superresolution and supersensitivity.

A deeper understanding of these mechanisms may help bridge coherence optics and quantum information science, thereby contributing to the development of scalable quantum technologies, especially in quantum sensing limited by the rapidly decreasing generation efficiency and unavoidable fringe degradation of higher-order N00N states. The input light consists of single photons generated from an attenuated laser, whose photon statistics follow a Poisson distribution. A polarizing beam splitter prepares the incident photons in the horizontal polarization state.

Subsequently, a half-wave plate transforms the photons into a coherent superposition state of horizontal and vertical polarization bases: |ψ⟩ = 1/√2 (|HH⟩ + |VV⟩). To maintain a multi-pass resulting phase accumulation structure, a quarter-wave plate is inserted symmetrically between the half-wave plate and the mirror. The resulting Q-M-Q configuration on both sides of the half-wave plate realigns the polarization basis of the photon between successive interactions. In particular, the reversal of the propagation direction of the photon by the mirror plays an essential role in the phase accumulation process through the double-pass configuration.

Without the Q-M-Q configuration, the double-pass scheme cannot satisfy the phase accumulation due simply to a toggle switch-like function in phase shift. Thus, the unit-phase shift generated by the elementary H-Q-M-Q cell is coherently added during successive passes, yielding the final state |ψ⟩ = 1/√2 (|HH⟩ + e^(iN(φ − ξ))|VV⟩). To measure the accumulated phase N(φ − ξ) in |ψ⟩, a polarization projection measurement is performed using an additional half-wave plate, resulting in a coherent superposition of the orthogonal basis components of |ψ⟩ onto both projection axes. This coherent superposition in the projection process results in interference fringes, 1 ± sin[2N(φ − ξ)]. Finally, the superimposed out-of-phase fringes are spatially separated by a polarization beam dispenser, where measurements are for the first-order intensity correlation.

The forward-propagating Jones matrices for a half-wave plate and quarter-wave plate oriented at an arbitrary angle α from the horizontal axis are represented by J_H(α) = cos(2α) sin(2α) sin(2α) −cos(2α) and J_Q(α) = cos(2α) + i sin(2α) (1 − i) sin(2α) (1 − i) sin(2α) + i cos(2α), where J_H(α) = R(α) 1 0 0 −1R(−α), J_Q(α) = R(α) 1 0 0 iR(−α), and R(α) = cos(α) −sin(α) sin(α) cos(α) is a rotation matrix. A normal-incidence mirror reflection flips the horizontal coordinate frame relative to the direction of propagation, acting as a transformation matrix J’M = 1 0 0 −1. When the photon reverses its spatial propagation vector, any physical orientation angle α transforms to −α relative to the travelling wave’s local frame. This reverse feature by the mirror is key to making the Nth power of J_H(α), resulting in the N-accumulated phase observed in the previous publication.

Polarisation rotation explains superresolution in a multi-pass photonic system

The multi-pass photonic scheme, initially reported in Nature 450, 393, achieves identical superresolution to a coherence de Broglie wavelength framework, but through a fundamentally different mechanism. This research reveals it arises from the coherent rotation of polarization states within a simple linear optical system. With each complete pass, the linear optics unit, dubbed HQMQ, undergoes a transformation equivalent to two reflections in polarization space, effectively rotating the polarization of light and accumulating phase.

This rotation is visualized on a geometrical model called the Poincaré sphere, illustrating how the polarization state realigns with each propagation. To validate their theoretical model, the team built a classical-wave system, mirroring the photonic setup, and compared the results obtained with calculations derived using Jones-matrix formalism. Analysis of the Fisher information, a measure of how much information a measurement provides, revealed the scaling behaviour underpinning the reported supersensitivity, which was then compared with a coherence de Broglie wavelength framework achieving identical superresolution through cascaded interferometry.

Classical wave optics achieve superresolution without quantum entanglement

The team’s demonstration of superresolution via coherent polarization rotation offers a compelling alternative to approaches demanding complex quantum states and architectures. However, the researchers acknowledge their classical-wave implementation does not definitively surpass the performance of the recently developed coherence de Broglie wavelength framework, leaving open the question of practical advantage. This raises a critical tension; while elegantly mirroring the superresolution achieved through quantum means, the current work doesn’t yet establish whether this classical analogue offers improved efficiency or scalability. Nevertheless, even if this classical implementation currently lacks a demonstrable edge over the coherence de Broglie wavelength framework in terms of quantifiable performance gains, the demonstration of superresolution through coherent polarization rotation remains significant, expanding the set of tools for achieving sub-diffraction-limit imaging.

Researchers demonstrated that superresolution, imaging beyond the classical diffraction limit, can be achieved using a classical wave optics system involving coherent polarization rotation. This finding clarifies the physical origin of previously observed superresolution in a multi-pass photonic scheme and shows it is not necessarily reliant on quantum entanglement. The system utilises a linear optics unit, dubbed HQMQ, which rotates the polarization of light with each pass, accumulating phase and realigning the polarization state. The team validated their theoretical model with a classical-wave implementation and compared the results with a coherence de Broglie wavelength framework achieving identical superresolution.