Abstract We introduce a generalized algebraic framework for the bright–dark mode decomposition of a two-path quantum interferometer entangled with a path-sensitive detector. Within this formulation, the loss of interference visibility is reinterpreted not as a destruction of quantum coherence, but as a conserved, coherent redistribution of amplitude between a bright (interfering) sector and a dark (path-informative) sector of the joint quanton–detector state. Unlike previous bright–dark formulations restricted to bosonic field-mode algebra in optical or cavity-QED systems, our approach utilizes the universal SU (2) geometry of the two-path Hilbert space. This allows the formalism to be applied to any single-particle ( N = 1) interferometer, including massive fermions such as electrons or neutrons, where particle statistics introduce no additional constraints. We demonstrate that as detector distinguishability increases, amplitude flows continuously and predictably into the dark sector, providing a quantitative redistribution sum rule that governs the transition from interference to which-path information. This algebraic perspective offers a unified, platform-independent language for characterizing decoherence and complementarity, providing a direct operational framework for monitoring information flow in diverse quantum interferometric platforms.
Abstract We introduce a generalized algebraic framework for the bright–dark mode decomposition of a two-path quantum interferometer entangled with a path-sensitive detector. Within this formulation, the loss of interference visibility is reinterpreted not as a destruction of quantum coherence, but as a conserved, coherent redistribution of amplitude between a bright (interfering) sector and a dark (path-informative) sector of the joint quanton–detector state. Unlike previous bright–dark formulations restricted to bosonic field-mode algebra in optical or cavity-QED systems, our approach utilizes the universal SU (2) geometry of the two-path Hilbert space. This allows the formalism to be applied to any single-particle ( N = 1) interferometer, including massive fermions such as electrons or neutrons, where particle statistics introduce no additional constraints. We demonstrate that as detector distinguishability increases, amplitude flows continuously and predictably into the dark sector, providing a quantitative redistribution sum rule that governs the transition from interference to which-path information. This algebraic perspective offers a unified, platform-independent language for characterizing decoherence and complementarity, providing a direct operational framework for monitoring information flow in diverse quantum interferometric platforms.
Interference is conventionally attributed to path-accumulated phase differences, with measurement treated as a passive readout. Here we demonstrate that single-particle interference is governed by the relative phase between the prepared quantum state and the detector-defined measurement basis -- a joint quantity that is operationally inaccessible in any conventional interferometer. Using coherently seeded entangled nonlinear biphoton sources, we show that independently scanning the pump phase difference, the seed phase difference, or the signal interferometric phase each produces identical sinusoidal fringes (V≈0.99) -- a three-scan equivalence impossible in any two-mode interferometer. The fringe visibility is continuously controlled through the idler-state overlap, directly encoding quantum distinguishability without idler detection. The same measurement-defined interference law persists from the single-photon to the high-flux regime. The bright-dark collective-state structure demonstrated here unifies coherent population trapping and electromagnetically induced transparency in atomic Λ-systems, discrete photonic interference, and single-slit diffraction within a common framework differing only in dark-subspace dimensionality, establishing measurement-defined photonic modes as a fundamental resource for quantum photonics.
A quantum system (quanton) traverses an interferometer with N equally probable paths and interacts with another quantum system (detector) that stores path information in a set of symmetric states. In this framework, we present a systematic quantitative study of wave-particle duality based on entropic trade-off relations between quantum coherence, characterized by the relative entropy of coherence of the quanton state, and which-path knowledge, quantified by the mutual information obtained through detector-state discrimination. Unlike prior upper-bound-based formulations, we obtain an exact quantification of which-path knowledge for the discrimination strategies considered here, encompassing previous strategies and extending beyond them. A general optimal measurement is implemented through a state-separation map governed by a continuous parameter ξ∈[0,1], followed by minimum-error (ME) discrimination of either the successful outputs only (standard approach) or both successful and failure outputs (concatenated approach). Our framework identifies a strategy-dependent hierarchy that generally emerges in the tightness of the resulting duality relations. At ξ=0, both approaches reduce to the ME measurement, which typically yields the tightest relation. For ξ>0, each approach yields a distinct relation that generally becomes less tight as ξ increases, with the concatenated strategy always yielding a relation at least as tight as its standard counterpart. We further characterize saturation of these relations by identifying the detector-state sets that lead to it and show that nontrivial saturation occurs only for interferometers with a nonprime number of paths. From these sets, we elucidate how the underlying structure of the quanton-detector correlations gives rise to this behavior and explains the lack of universal saturation in multipath duality relations for pure states.
In this paper, we study the effect of a which-path memory ancilla on the three-slit interference pattern within the framework of the bright--dark state description [Phys. Rev. Lett. 134, 133603 (2025)]. Whereas two slits give one bright mode, a photonic mode that couples to the detector atoms, and one dark mode, which does not couple to the detector atoms, three slits lead to one detector-coupled bright mode and a two-dimensional dark-mode subspace in the three-dimensional path space. We first discuss the classical three-slit interference pattern in terms of probability leakage into the dark subspace. We then study the von Neumann entropy SD of the dark subspace and the coherence measures of the reduced photonic state obtained by tracing out the memory: dark-sector coherence CD and bright--dark coherence CBD. These quantities bring out the internal quantum structure of the two-dimensional dark subspace. We show that, whereas CD is not by itself a basis-independent physical observable, CBD is basis-invariant. We establish that, for two paths, CBD is fixed entirely by the populations and the single pairwise coherence, whereas for multiple paths, M≥3, it acquires a genuinely multipath contribution generated by asymmetry among the pairwise which-path overlaps. Finally, we distinguish the part of the path-coherence loss that is recoverable through a suitable measurement of the memory from the irreducible coherence deficit imposed by an uncontrolled environment.
Abstract Quantum entanglement between an interfering particle and a detector for acquiring the which-path information plays a central role for enforcing Bohr’s complementary principle, but the quantitative relation between this entanglement and the fringe visibility remains untouched upon for an initial mixed state. Here we find an equality for quantifying this relation. Our equality characterizes how well the interference pattern can be preserved when an interfering particle, initially carrying a definite amount of coherence, is entangled with a which-path detector to a certain degree. This equality provides a connection between entanglement and interference in the unified framework of coherence, revealing the quantitative entanglement-interference complementarity. We experimentally demonstrate this relation with a superconducting circuit, where a resonator serves as a which-path detector for an interfering qubit. The results demonstrate quantum entanglement is the mechanism for prohibiting any detector from acquiring which-path information without deteriorating the interference pattern, which was not confirmed previously.
Abstract The relation between interference visibility and path distinguishability is a core pillar of quantum complementarity and decoherence theory. In standard quantum mechanics, all coherence decay in interferometric systems is attributed exclusively to path information leakage, which establishes a one-to-one relation between environmental distinguishability and fringe visibility. However, a fundamental question remains experimentally untested: whether discrete quantized energy exchange between light and matter can degrade quantum coherence independently of path distinguishability. In this work, we propose a high-precision cavity-QED experiment based on a Mach–Zehnder interferometer to decouple interaction modality from path information. A single trapped Rb atom inside an optical cavity is placed in one interferometer arm, enabling fully switchable light–matter interaction regimes: resonant discrete energy exchange and far-detuned continuous dispersive interaction. To eliminate systematic artifacts, we employ environmental state tomography to rigorously equalize the path distinguishability in both operational regimes. Furthermore, we systematically compensate all linear dynamical differences between resonant and dispersive cavity responses, including group delay, spectral distortion, and temporal mode mismatch. With all standard decoherence and dynamical contributions precisely calibrated, standard quantum mechanics predicts identical interference visibility for resonant and dispersive interactions. In contrast, a physically motivated alternative conjecture suggests that discrete energy exchange can induce intrinsic coherence suppression even at fixed path distinguishability. The two scenarios yield experimentally distinguishable visibility differences. Our scheme utilizes mature single-atom cavity quantum optics techniques without low-temperature superconducting devices, providing a robust and accessible platform to resolve this long-standing open question in quantum interferometry. The complete optical layout, timing sequence, tomography calibration, statistical criteria, and error suppression strategies are presented. This experiment offers a decisive experimental benchmark for the fundamental relationship between light–matter interaction type and quantum coherence.
In the FIGID framework (Field Intrinsic Gravity Induced Density), mass is condensed quantum field and gravity is a density gradient. This paper extends the framework to quantum interference, decoherence, and the quantum eraser. A particle in superposition is described as a single coherent field configuration extended across multiple paths, with interference encoded in the field density itself before any measurement occurs. The field amplitude at a point is the coherent sum of Yukawa-sourced contributions from each path, and the detection probability is proportional to the squared magnitude of that amplitude. When a which-path probe interacts with the configuration at one path, the probe’s field creates an asymmetric gradient that entangles the particle’s configuration with the probe’s state. The interference term transfers from the particle alone into the joint particle-probe field configuration. Tracing over the probe eliminates the cross term from the particle’s reduced state — decoherence. The quantum eraser is then shown to recover the interference by applying a symmetric transformation to the probe that erases path information, restoring the cross term in conditioned subsets. The entire sequence is presented in both standard quantum formalism and FIGID field language side by side. A visibility function V(η) = exp(−d/λ) is derived from the physical overlap of the probe’s field configuration with the particle’s two-path superposition, reproducing the observed wavelength dependence of decoherence and providing a physical mechanism absent from the standard account. The central claim is falsifiable: if coherence were destroyed rather than redistributed, the quantum eraser would not work. It does.