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New multiphoton suppression laws and a generating-function treatment of partial distinguishability show that phase-and-loss sensing can remove probe incompatibility, yet measurement incompatibility persists at high photon number.

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2026-07-12 01:01 UTC pith:N3Z2GC56

load-bearing objection Solid thesis-level work: new suppression families outside permutation symmetry, a usable overlap-matrix generating function for partially distinguishable GBS, and a clean asymptotic split showing measurement incompatibility survives for the probes that kill probe incompatibility. the 2 major comments →

arxiv 2607.03636 v1 pith:N3Z2GC56 submitted 2026-07-03 quant-ph

From the Hong-Ou-Mandel Effect to Quantum Sensing: Interference of Nonclassical Light with Partial Distinguishability and Noise

Matheus Eiji Ohno Bezerra This is my paper
classification quant-ph PACS 42.50.St42.50.Dv03.65.Ta03.67.-a
keywords quantum interferenceboson samplingGaussian statespartial distinguishabilitysuppression lawsquantum multiparameter estimationphase and loss estimationHong-Ou-Mandel effect
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This thesis develops a unified generating-function description of nonclassical light interfering in linear multiports that may be noisy or only partially indistinguishable. For Fock states it finds whole families of exact zero-probability output events that lie outside the earlier permutation-symmetry rule, and shows how partial distinguishability lifts those zeros. For single-mode squeezed states it extends the hafnian formula of Gaussian boson sampling so that the internal-state overlap matrix enters the generating function, recovering known limits and giving a clean model of distinguishability as noise. The same interference setting is then used for simultaneous estimation of optical phase and photon loss. Optimized non-Gaussian probes and certain two-mode Gaussian probes can make the two quantum Fisher informations approach their single-parameter ultimate bounds at once, eliminating probe incompatibility; yet the symmetric logarithmic derivatives remain incompatible, so no single measurement can saturate both bounds even in the large-photon-number limit.

Core claim

Probe incompatibility between simultaneous phase and loss estimation can be removed by carefully chosen non-Gaussian states or by certain two-mode Gaussian states that keep an ancillary reference mode, but measurement incompatibility, quantified by a non-vanishing expectation value of the commutator of the two symmetric logarithmic derivatives, survives as a fundamental constraint even asymptotically at high photon number.

What carries the argument

Generating functions obtained from phase-space integrals (or from contingency-table averages of permanents) that encode both the multiport unitary and the photon-overlap matrix; their derivatives yield amplitudes, probabilities, and the matrices whose roots produce the new suppression laws and the extended hafnian expressions.

Load-bearing premise

The claim that measurement incompatibility is fundamental rests on a restricted family of Kraus operators for the lossy phase channel together with the large-photon-number limit; a different Kraus representation or a finite-N protocol that saturates both bounds with commuting derivatives would overturn it.

What would settle it

Exhibit a probe state and a single joint POVM for which both the phase and the loss quantum Cramér–Rao bounds are simultaneously saturated at large mean photon number, or show that the expectation value of the SLD commutator vanishes for that state while both diagonal quantum Fisher informations remain maximal.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

2 major / 5 minor

Summary. This thesis develops a unified phase-space and generating-function framework for multiphoton interference of Fock and Gaussian states in linear interferometers subject to partial distinguishability and loss. Chapter 3 derives new families of zero-probability (suppression) laws for beamsplitters and tritters that lie outside the permutation-symmetry principle of Dittel et al., obtained from recurrence relations on the permanent generating function; the laws are shown to degrade under partial distinguishability. Chapter 4 extends the Hafnian description of Gaussian Boson Sampling to a general internal-state overlap matrix, recovers the ideal hafnian and torontonian limits, and analyzes homogeneous-overlap noise and Gaussian temporal-mode models. Chapter 5 studies simultaneous phase-and-loss estimation, showing that optimized non-Gaussian and certain two-mode Gaussian probes can asymptotically eliminate probe incompatibility (F o1), while the SLD commutator expectation I_φη remains nonzero for all such probes, so that measurement incompatibility persists even at high photon number.

Significance. The work supplies concrete, analytically tractable extensions of two central photonic protocols (suppression laws beyond permutation symmetry; GBS with a general overlap matrix) and a carefully scoped multiparameter-metrology result that cleanly separates probe from measurement incompatibility. Strengths include explicit generating-function derivations checked against known HOM and balanced-tritter cases, tabulated analytic roots (Table 3.1), publicly available code for the ISS optimizer and GBS generating function, and asymptotic QFI expressions for the Gaussian families that attain the single-parameter bounds. The measurement-incompatibility claim is correctly limited to the examined optimal probes and the standard lossy-phase channel; within that scope it is a useful, falsifiable statement for optical multiparameter sensing.

major comments (2)
  1. Chapter 3, Sec. 3.3 and Table 3.1: the new suppression families are derived only for |n_S|≤2 and for two specific interferometers (beamsplitter, triangular tritter). The claim that “similar suppression laws … should arise for arbitrarily large multiports” (Conclusions) is plausible from multilinearity but is not demonstrated. A single higher-mode or larger-|n_S| example (or an explicit statement that the method becomes permanent-hard beyond the cases shown) would make the scope of the central claim precise.
  2. Chapter 5, Eqs. (5.70)–(5.73) and Appendix B: the assertion that measurement incompatibility “remains a fundamental constraint even in this limit” rests on I_φη eq0 for every probe that saturates both single-parameter QFIs under the standard lossy-phase channel. The necessary conditions of App. B are obtained by minimization over a restricted Kraus family parametrized by α,β. While no counter-example is known, the manuscript should state explicitly that the claim is scoped to this channel model and the examined optimal probes, rather than as a representation-independent theorem.
minor comments (5)
  1. Abstract and Resumo: “structures that is degraded” → “structures that are degraded”; several other minor grammatical slips appear in the English abstract and in Sec. 3.1.
  2. Chapter 4, Eq. (4.40) and surrounding text: the recovery of the ideal GBS probability is clear, but a short remark on how the general-overlap generating function reduces to the blocked-loop-hafnian expressions of the coarse-grained model would help readers familiar with that literature.
  3. Figures 3.3–3.4 and 5.2–5.5: axis labels and legends are readable, yet the caption of Fig. 5.5 should state the precise energy partition (p,q) used for the Gaussian curves so that the asymptotic claims can be checked without consulting the appendix.
  4. Code-availability statements appear in Ch. 4 and Ch. 5; a single consolidated repository link (or DOI) in the front matter would improve reproducibility.
  5. Bibliography: a few arXiv identifiers are given without final journal citations (e.g., the author’s own 2023 NJP paper is correctly cited, but some concurrent GBS-distinguishability works could be updated).

Circularity Check

0 steps flagged

No significant circularity: analytic derivations from phase-space generating functions, permanents/hafnians, and standard multiparameter QFI/SLD formulas stand independently of inputs; self-citations are only to the thesis chapters themselves.

full rationale

The thesis compiles three self-contained analytic chapters. Suppression laws (Ch. 3) follow by extracting roots of the multivariate polynomials that appear after repeated application of the permanent recurrence (Eqs. 3.20–3.22) to low-occupation output modes; the roots are not inserted by hand. The partial-distinguishability GBS generating function (Ch. 4, Eq. 4.35) is obtained by inserting the Gram matrix V into the anti-normally ordered expectation and evaluating the resulting Gaussian integral; the hafnian limit is recovered when V = 1, not assumed. Probe- and measurement-incompatibility results (Ch. 5) are obtained by (i) numerical ISS maximization of the normalized QFI quantifier (Eq. 5.10) over Fock coefficients and (ii) direct evaluation of the SLD commutator expectation I_φη (Eqs. 5.70–5.73 and Gaussian formula (5.71)) on the resulting states; both calculations use only the standard lossy-phase Kraus channel and the known single-parameter bounds F_max. Appendix B’s necessary conditions are derived from the multiparameter operator-norm bound of Ref. [65] after minimization over a two-parameter family of Kraus operators; they are necessary, not definitional. Self-citations point only to the author’s own published chapters that contain the same independent derivations. No fitted parameters are re-labeled as predictions, no uniqueness theorem is imported from prior author work to forbid alternatives, and no ansatz is smuggled via citation. The central claim that measurement incompatibility survives for all probes that saturate both single-parameter QFIs is therefore a genuine computation, not a tautology.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 0 invented entities

The thesis rests on standard quantum-optical and quantum-estimation axioms plus a few modeling choices (homogeneous overlap, Gaussian temporal wave-packets, restricted Kraus family for the multiparameter bound). No new physical entities are postulated; free parameters are ordinary experimental knobs (transmissivities, squeezing strengths, distinguishability ϵ) rather than fitted constants that define the claims.

free parameters (3)
  • distinguishability parameter ϵ (homogeneous model)
    Controls the weight of the orthogonal internal-mode component; used to interpolate between fully indistinguishable and fully distinguishable limits, not fitted to external data.
  • energy-partition exponents p, q for Gaussian probes
    Define how displacement vs squeezing and how τ_in approach their asymptotic values; chosen to explore regimes, not fitted to measurements.
  • Gaussian temporal width σ_t and central frequency Ω_0
    Model parameters for internal-state overlap; used for illustrative plots of phase-sensitive distinguishability, not claimed as universal constants.
axioms (5)
  • domain assumption Bosonic commutation relations and canonical quantization of the free electromagnetic field
    Foundation of Ch. 2; standard quantum optics.
  • domain assumption Linear interferometers implement passive unitaries generated by quadratic Hamiltonians; loss is modeled by a fictitious beamsplitter to vacuum
    Used throughout for state evolution and Kraus maps.
  • domain assumption Photon-counting probabilities for Gaussian states are given by hafnians of the appropriate submatrices of B = U D_r U^t (indistinguishable limit)
    Standard GBS result recovered as a consistency check.
  • standard math Quantum multiparameter Cramér–Rao bound and SLD commutator condition for measurement compatibility
    Standard quantum estimation theory (Helstrom, Holevo, Matsumoto).
  • ad hoc to paper Upper bounds on multiparameter QFI obtained by minimization over a restricted Kraus family parametrized by α, β
    Appendix B; the bound is valid but not proven tight for every possible Kraus representation.

pith-pipeline@v1.1.0-grok45 · 70072 in / 3193 out tokens · 33055 ms · 2026-07-12T01:01:50.339298+00:00 · methodology

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read the original abstract

This thesis explores the interference of nonclassical states of light, particularly Fock and Gaussian states, in noisy linear interferometers, with applications to quantum information and quantum sensing. Using the phase-space formalism, analytical tools based on generating functions are developed to describe quantum optical interference in a unified way. For multiphoton Fock states, new zero probability events (suppression laws) are identified beyond the previously derived symmetry permutation principle, revealing rich interference structures that is degraded with photon distinguishability. For Gaussian states, the Hafnian-based description of Gaussian Boson Sampling is extended to include partial distinguishability via the overlap matrix of the internal state of the photons. Finally, the link between these interference effects and quantum multiparameter estimation is examined for the simultaneous estimation of phase and loss. This study shows that while probe incompatibility can vanish for optimized non-Gaussian states and some two-mode Gaussian states, at high photon number, measurement incompatibility remains a fundamental constraint even in this limit.

Figures

Figures reproduced from arXiv: 2607.03636 by Matheus Eiji Ohno Bezerra.

Figure 2.1
Figure 2.1. Figure 2.1: Representation of the construction of a M-mode interferometer in terms of el￾ements of linear optics: beamsplitters (blue) and phase shifters (red). Indeed, the entire interferometer is represented by a matrix that is an element of the group U(M), while the elements are matrices belonging to the groups SU(2) and U(1) respectively. unitary [51, 72]: Uˆ BS = exph −i(ϕt − ϕr)Lˆ z i exph −2i arccos√ τ  Lˆ y… view at source ↗
Figure 2.2
Figure 2.2. Figure 2.2: Illustration of the operators acting on the phase space (a) Displacement operator [PITH_FULL_IMAGE:figures/full_fig_p024_2_2.png] view at source ↗
Figure 3.1
Figure 3.1. Figure 3.1: (a) Illustration of the scheme for the interference of [PITH_FULL_IMAGE:figures/full_fig_p034_3_1.png] view at source ↗
Figure 3.2
Figure 3.2. Figure 3.2: Schematic representation of the two interferometers used to illustrate the proposed [PITH_FULL_IMAGE:figures/full_fig_p043_3_2.png] view at source ↗
Figure 3.3
Figure 3.3. Figure 3.3: Suppression laws for the tritter T(τ1, φ) defined in Eq. (3.33). In both graphs is shown value of the transmissivity τ1 that suppresses the corresponding amplitudes. Panel (a) presents the suppression laws for the amplitudes b⟨n1, nS|n1, 1, 1⟩a = 0 while panel (b) presents the suppression laws for the amplitudes b⟨n1, nS|m, m, m⟩a = 0. respective suppression functions: f (n1,2,0) (n1,1,1) T(τ1, φ)  = √ … view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: Suppression laws for the tritter T(τ2, φ) defined in Eq. (3.39). In both graphs is shown value of the transmissivity τ2 that suppresses the corresponding amplitudes. Panel (a) presents the suppression laws for the amplitudes b⟨n1, nS|n1, 1, 1⟩a = 0 while panel (b) presents the suppression laws for the amplitudes b⟨n1, nS|m, m, m⟩a = 0. matrix T(τ2, φ) = 1 2   √ 2τ2, −i − √ρ2e iφ, i − √ρ2e iφ √ 2τ2, i … view at source ↗
Figure 3.4
Figure 3.4. Figure 3.4: (b), resulting in b⟨n1, 1, 1|m, m, m⟩a = 0. 3.4 Effects of the partial distinguishability on the sup￾pression laws In the previous discussion, we investigated suppression laws under the assumption of com￾pletely indistinguishable photons. However, as discussed at the beginning of this chapter in the context of the HOM effect, photon distinguishability affects quantum interference by degrading the destruc… view at source ↗
Figure 4.1
Figure 4.1. Figure 4.1: Schematic representation of the M-mode GBS setup considered in this work. Each input mode k = 1, . . . , M of a linear optical interferometer (multiport) described by a unitary matrix U is injected with a single-mode squeezed vacuum state |rψk ⟩, whose photons occupy an internal state |ψk⟩. The output modes are measured by PNR detectors with efficiencies η1, . . . , ηM. expression for the generating func… view at source ↗
Figure 4.2
Figure 4.2. Figure 4.2: Probabilities at the output for the interference of single-mode squeezed states [PITH_FULL_IMAGE:figures/full_fig_p072_4_2.png] view at source ↗
Figure 5.1
Figure 5.1. Figure 5.1: Illustration of the scheme considered. At the input, a two-mode pure probe [PITH_FULL_IMAGE:figures/full_fig_p076_5_1.png] view at source ↗
Figure 5.2
Figure 5.2. Figure 5.2: Panels (a) and (b) show the probe incompatibility quantifier [PITH_FULL_IMAGE:figures/full_fig_p086_5_2.png] view at source ↗
Figure 5.3
Figure 5.3. Figure 5.3: Panel (a) shows the photon number variance [PITH_FULL_IMAGE:figures/full_fig_p087_5_3.png] view at source ↗
Figure 5.4
Figure 5.4. Figure 5.4: The top panels show the photon-number distribution of the optimal single () [PITH_FULL_IMAGE:figures/full_fig_p088_5_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (b). The intuition is that the separation of the teeth allows one to better determine [PITH_FULL_IMAGE:figures/full_fig_p088_5.png] view at source ↗
Figure 5.5
Figure 5.5. Figure 5.5: Panels (a) and (b) show the measurement incompatibility for the independent [PITH_FULL_IMAGE:figures/full_fig_p101_5_5.png] view at source ↗

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