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SPIE Quantum Information Science, Sensing, and Computation

A novel approach of macroscopic N-fold superresolution using phase-controlled divided signals

Byoung Seung HAM

Published Jun 12, 2026• 0 citations
Publisher

Abstract

Although quantum sensing theoretically offers an N-fold fringe enhancement at the Heisenberg limit, its practical realization has been limited by the difficulty of achieving high-order N in N00N states. Furthermore, quantum sensing systems are highly vulnerable to losses, especially in remote target detection applications. To address these challenges, I introduce a novel approach that enables potentially unlimited, N-proportional superresolution for laser-based remote sensing, even in lossy environments. This method builds upon new physics of quantum sensing rooted in the wave nature of photons. In particular, it employs the intensity product of N-divided signals with N phase controls. As a result, this approach opens the door toward achieving unrestricted N-fold superresolution in the macroscopic regime - surpassing both classical sensors constrained by first-order intensity correlations and conventional quantum sensors limited by N00N state requirements.

DOI
10.1117/12.3095515

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Although quantum sensing theoretically offers an N-fold fringe enhancement at the Heisenberg limit, its practical realization has been limited by the difficulty of achieving high-order N in N00N states. Furthermore, quantum sensing systems are highly vulnerable to losses, especially in remote target detection applications. To address these challenges, I introduce a novel approach that enables potentially unlimited, N-proportional superresolution for laser-based remote sensing, even in lossy environments. This method builds upon new physics of quantum sensing rooted in the wave nature of photons. In particular, it employs the intensity product of N-divided signals with N phase controls. As a result, this approach opens the door toward achieving unrestricted N-fold superresolution in the macroscopic regime - surpassing both classical sensors constrained by first-order intensity correlations and conventional quantum sensors limited by N00N state requirements.
Recently, the delayed-choice quantum eraser has been applied for coherently excited superresolution using phase-controlled projection measurements of laser light to overcome the diffraction limit in classical physics as well as to solve the limited order N of the N00N state in quantum physics. Here, a general scheme of the phase-controlled quantum eraser-based superresolution is proposed for quantum sensing satisfying the Heisenberg limit, and its general solution is derived for an arbitrary Nth-order intensity correlation. Furthermore, phase quantization of the proposed superresolution is discussed to better understand the wave nature of quantum mechanics. Unlike other methods of superresolution in quantum sensing, the proposed method is for the intensity products between phase-controlled quantum erasers and thus is compatible with most conventional sensing metrologies.
Superresolution is a unique quantum feature generated by N00N states or phase-controlled coherent photons via projection measurements in a Mach-Zehnder interferometer (MZI). Superresolution has no direct relation with supersensitivity in quantum sensing and has a potential application for the precision measurement of an unknown signal frequency. Recently, phase-controlled quantum erasers have been demonstrated for superresolution using classical light of a continuous-wave laser to overcome the diffraction limit in classical physics and to solve the limited scalability in N00N state-based quantum sensing. Here, a quantum spectrometer is presented for the macroscopic superresolution using phase-controlled spatial light modulators (SLMs) in MZI. For validity, a general solution of the superresolution is derived from the SLM-based projection measurements and an unprecedented resolution is numerically confirmed for an unknown frequency of light.
Recently, the delayed-choice quantum eraser has been applied for coherently excited superresolution using phase-controlled projection measurements of laser light to overcome the diffraction limit in classical physics as well as to solve the limited photon number of the N00N state in quantum physics. Unlike other methods of phase-controlled superresolution in a noninterferometric system, the proposed method is for the intensity products between phase-controlled quantum erasers, resulting in superresolution compatible with the most conventional sensing metrologies. Here, a general scheme of the phase-controlled quantum eraser-based superresolution is proposed and its general solution is derived for an arbitrary Nth-order intensity correlation, where the superresolution shows the photonic de Broglie wave-like quantum feature. Furthermore, phase quantization of the superresolution is discussed to better understand quantum mechanics.
Quantum sensing and metrology have been extensively investigated over the past several decades to surpass the classical shot noise limit and approach the Heisenberg limit. The hallmark of N00N state based quantum sensing is superresolution, characterized by the interference fringe pattern (1+cosNphi). However, practical implementations are severely constrained by the achievable photon number N, reduced fringe visibility, and vulnerability to photon loss. Recently, several coherence-based approaches without using N00N states have been explored as alternative routes to superresolution. Among them, the coherence de Broglie wavelength (CBW) approach is fully compatible with coherence optics. Here, we experimentally demonstrate CBW based superresolution up to N=3. In contrast to N00N state based schemes, the observed CBW fringes exhibit near unity visibility that is essentially independent of N and remain robust against photon loss. Although CBW does not attain the Heisenberg limited phase sensitivity, its phase sensitivity exhibits an N fold enhancement over conventional classical interferometric approaches. These results suggest that CBW provides a practical and scalable platform for superresolution based sensing and metrology.
Abstract Recently, the delayed-choice quantum eraser has been applied for coherently excited superresolution using phase-controlled projection measurements of laser light to overcome the diffraction limit in classical physics as well as to solve the limited photon number of the N00N state in quantum physics. Unlike other methods of phase-controlled superresolution in a noninterferometric system, the proposed method is for the intensity products between phase-controlled quantum erasers, resulting in superresolution compatible with the most conventional sensing metrologies. Here, a general scheme of the phase-controlled quantum eraser-based superresolution is proposed and its general solution is derived for an arbitrary Nth-order intensity correlation, where the superresolution shows the photonic de Broglie wave-like quantum feature. Furthermore, phase quantization of the superresolution is discussed to better understand quantum mechanics.
Quantum sensing exploits nonclassical states of light, including multiphoton entangled states and squeezed states, to achieve superresolution and/or super-sensitivity. However, its practical implementation is constrained by state-generation complexity, photon loss, and detection efficiency. Here, we present a quantum-operator analysis of coherence de Broglie wavelength (CBW) in an anti-symmetrically coupled Mach-Zehnder interferometer (MZI) architecture and clarify the origin of its superresolution and enhanced phase sensitivity. The two-mode SU(2) structure of the MZI, represented by Pauli operators, shows that successive basis-realigned transformations produce an Nth-order unitary U^N(phi), yielding N-fold phase accumulation (1+cosNphi). The quantum-operator description is particularly significant at the single-photon level, where even a single photon undergoes the Nth-order unitary evolution through its coherent evolution in the two-mode state space. This differs from entanglement-based quantum sensing based on photonic de Broglie wavelength interferometry, where N-fold phase accumulation is associated with an N-photon entangled state. The same SU(2) transformation also applies to coherent classical fields, establishing a classical-quantum correspondence of the CBW phase evolution. Fisher-information analysis further shows that the architecture-induced phase transformation yields an order-dependent enhancement of phase sensitivity without increasing the photon number or statistical sampling. CBW therefore provides an architecture-controlled route to high-order interferometric superresolution, accompanied by enhanced phase sensitivity, with potential applications to fringe-counting wavemetry and Fourier-transform-based sensing.