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arxiv: 2512.15655 · v1 · submitted 2025-12-17 · 🪐 quant-ph

Characterization of Generalized Coherent States through Intensity-Field Correlations

Ignacio Salinas Valdivieso , Victor Gondret , Gerd Hartmann S. , Mariano Uria , Pablo Solano , Carla Hermann-Avigliano This is my paper

Pith reviewed 2026-05-16 21:31 UTC · model grok-4.3

classification 🪐 quant-ph
keywords generalized coherent statesintensity-field correlationsnonclassicality witnessKerr nonlinearityquantum opticsnon-Gaussian statescorrelation functions
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0 comments X

The pith

The normalized intensity-field correlation deviates from unity to signal nonclassicality in generalized coherent states.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Generalized coherent states form when coherent light passes through a nonlinear medium and display features such as Wigner negativity. Because these states stay coherent to every order, their nonclassical character evades detection by ordinary intensity-intensity correlation measurements. The paper establishes that the normalized intensity-field correlation alone equals one for classical light and deviates from one precisely when the state becomes nonclassical. Analytical formulas are obtained for states produced by Kerr nonlinearity and for statistical mixtures of such states. The approach supplies a low-complexity, real-time experimental test that works across a wide range of nonlinear regimes.

Core claim

For generalized coherent states the normalized intensity-field correlation equals unity if and only if the state is classical; any measured deviation from unity therefore constitutes a witness of nonclassicality. The same criterion applies to statistical mixtures of generalized coherent states and is worked out explicitly for Kerr-generated states.

What carries the argument

The normalized intensity-field correlation function, whose value of unity is preserved for all classical states but is broken by the higher-order phase-sensitive coherences present in generalized coherent states.

Load-bearing premise

The states must remain fully coherent to all orders so that intensity-intensity correlations stay blind to nonclassicality while the intensity-field correlation can still be normalized and measured without further assumptions about detectors or mode matching.

What would settle it

Prepare a coherent state, send it through a Kerr medium of known strength, measure the normalized intensity-field correlation, and check whether the result equals one when the nonlinearity is zero and deviates from one when the nonlinearity produces a nonclassical state.

Figures

Figures reproduced from arXiv: 2512.15655 by Carla Hermann-Avigliano, Gerd Hartmann S., Ignacio Salinas Valdivieso, Mariano Uria, Pablo Solano, Victor Gondret.

Figure 1
Figure 1. Figure 1: FIG. 1. Optical setup to measure the intensity-field correlation func [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Normalized intensity-field correlation function (a) and [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Evolution of [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Connected intensity-field correlation function (a) and Wigner [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
read the original abstract

Non-Gaussian quantum states of light are essential resources for quantum information processing and precision metrology. Among them, generalized coherent states (GCS), which naturally arise from the evolution of a coherent state with a nonlinear medium, exhibit useful quantum features such as Wigner negativity and metrological advantages [Phys. Rev. Res. 5, 013165 (2023)]. Because these states remain coherent to all orders, their nonclassical character cannot be revealed through standard intensity-intensity correlation measurements. Here, we demonstrate that the intensity-field correlation function alone provides a simple and experimentally accessible witness of nonclassicality. For GCSs, any deviation of this normalized correlation from unity signals nonclassical behavior. We derive analytical results for Kerr-generated states and extend the analysis to statistical mixtures of GCSs. The proposed approach enables real-time, low-complexity detection of quantum signatures in non-Gaussian states, offering a practical tool for experiments across a broad range of nonlinear regimes.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper claims that the normalized intensity-field correlation <I E> / (<I> <E>) serves as a simple witness of nonclassicality for generalized coherent states (GCS), including those generated by Kerr nonlinearity and their statistical mixtures. Because GCS remain coherent to all orders, standard g^{(2)} measurements are insensitive, but any deviation of this normalized ratio from unity signals nonclassical behavior. Analytical expressions are derived for Kerr states and extended to mixtures, positioning the method as experimentally accessible for real-time detection.

Significance. If the witness is robust, it offers a low-complexity alternative to Wigner tomography or higher-order correlations for detecting useful non-Gaussian features in states relevant to quantum metrology and information processing. The provision of closed-form analytical results for Kerr-evolved GCS is a clear strength, enabling direct comparison with experiment without numerical fitting.

major comments (2)
  1. [§3] §3 (Kerr state derivation, Eq. (12)): The normalized correlation is computed using ideal operators a, a† with no loss channels or mode mismatch. For realistic detection efficiencies η_I and η_E the measured ratio acquires a multiplicative prefactor (typically involving √(η_I η_E) or η), so that even a classical coherent state yields a value ≠1. This directly undermines the central claim that deviation from unity signals nonclassicality without additional calibration assumptions.
  2. [§5] §5 (mixtures of GCSs): The extension of the witness to statistical mixtures inherits the same ideal-operator normalization. No analysis is given of how finite efficiencies or partial mode overlap affect the mixture case, leaving the general experimental-accessibility assertion unproven.
minor comments (2)
  1. [Abstract] The abstract asserts 'real-time, low-complexity detection' but provides no estimate of required integration time, detector bandwidth, or tolerance to dark counts.
  2. [§2] Notation for the field operator E (distinct from the intensity I) is introduced without an explicit definition in terms of the mode function or quadrature; a short clarifying sentence would help.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on the experimental realism of the proposed witness. We address each major comment below and will revise the manuscript accordingly to incorporate calibration considerations and strengthen the claims of experimental accessibility.

read point-by-point responses

  1. Referee: [§3] §3 (Kerr state derivation, Eq. (12)): The normalized correlation is computed using ideal operators a, a† with no loss channels or mode mismatch. For realistic detection efficiencies η_I and η_E the measured ratio acquires a multiplicative prefactor (typically involving √(η_I η_E) or η), so that even a classical coherent state yields a value ≠1. This directly undermines the central claim that deviation from unity signals nonclassicality without additional calibration assumptions.

    Authors: We agree that the derivation assumes ideal operators without losses or mismatch. Finite efficiencies introduce a multiplicative prefactor, so the raw ratio deviates from unity even for classical states. We will revise §3 to include an explicit calibration procedure: measure the correlation on a reference coherent state to extract the effective prefactor, then monitor deviations from this calibrated baseline. Any excess deviation signals nonclassicality. This addition preserves the witness while making the experimental protocol concrete. revision: yes

  2. Referee: [§5] §5 (mixtures of GCSs): The extension of the witness to statistical mixtures inherits the same ideal-operator normalization. No analysis is given of how finite efficiencies or partial mode overlap affect the mixture case, leaving the general experimental-accessibility assertion unproven.

    Authors: The mixture analysis likewise assumes ideal detection. We will add a short discussion showing that uniform linear losses produce a state-independent prefactor, so the same coherent-state calibration applies directly to mixtures. For partial mode overlap we will note that it is absorbed into the calibration step provided the overlap is stable. These clarifications will be inserted into §5 to substantiate the experimental-accessibility claim. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained from state definitions

full rationale

The paper computes the normalized intensity-field correlation <I E> / (<I> <E>) directly from the definition of generalized coherent states (GCS) and their Kerr evolution, using standard bosonic operator algebra. For the classical limit (zero nonlinearity), the ratio equals unity by the properties of coherent states under the given operators, without any fitted parameters, self-referential definitions, or load-bearing self-citations. The analytical expressions for Kerr-generated states and their mixtures follow from direct calculation of expectation values, independent of the nonclassicality witness claim. No steps reduce the result to its inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review provides no explicit free parameters, axioms, or invented entities; standard quantum-optical assumptions about coherent-state evolution are implicit.

axioms (1)
  • domain assumption Generalized coherent states remain coherent to all orders under nonlinear evolution
    Stated in abstract as reason intensity-intensity correlations fail

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