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arxiv: 2606.19649 · v1 · pith:FRESVIEGnew · submitted 2026-06-17 · 🪐 quant-ph · physics.ins-det

Optimized Quantum States for Sensing in the Presence of Loss and Phase Noise

Shruti Maliakal , Zachary Mann , Christopher Wipf , Rana X Adhikari , Su Direkci , Yanbei Chen This is my paper

Pith reviewed 2026-06-26 20:04 UTC · model grok-4.3

classification 🪐 quant-ph physics.ins-det
keywords quantum sensingnon-Gaussian statesquantum Fisher informationphase noisephoton losssqueezed vacuumhomodyne detection
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The pith

Non-Gaussian states outperform squeezed vacuum by up to 2.2 dB in sensors with both photon loss and phase noise.

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

The paper numerically optimizes the quantum Fisher information to identify input states that deliver better sensitivity than any Gaussian state once phase noise joins photon loss. Squeezed vacuum is known to be optimal when loss is the only imperfection, but the addition of phase noise removes that optimality. For states limited to an average of five photons, at five percent loss and two hundred milliradians of phase noise, the identified non-Gaussian states reach an advantage of 2.2 decibels. The same states retain part of their edge even when the measurement is restricted to ordinary homodyne detection. Three families of states appear repeatedly: Fock-like, cubic-phase-like, and those possessing discrete rotational symmetry.

Core claim

Numerically optimizing the quantum Fisher information across the loss and phase-noise landscape, we identify non-Gaussian states that outperform any Gaussian state. These fall into three classes: Fock-like, cubic-phase-like, and states with discrete rotational symmetry. Limiting the average number of photons in the input state to ar{n}=5, with 1-η = 5% photon loss and 200 mrad phase noise, the non-Gaussian advantage reaches up to 2.2 dB. Furthermore, we observe that the non-Gaussian advantage can persist even when the measurement strategy is homodyne detection.

What carries the argument

Numerical maximization of the quantum Fisher information over families of non-Gaussian states subject to simultaneous photon loss and phase noise.

If this is right

  • Non-Gaussian states can deliver up to 2.2 dB better sensitivity than squeezed vacuum at five percent loss and two hundred milliradians phase noise.
  • The advantage appears in three recurring classes of states: Fock-like, cubic-phase-like, and discrete rotational symmetry.
  • Part of the non-Gaussian benefit survives when only homodyne detection is available.
  • Squeezed vacuum is no longer optimal once phase noise is added to loss.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same optimization procedure could be rerun for other values of loss and phase noise to map the full advantage landscape.
  • Realizing the reported states would require specific nonlinear operations whose experimental overhead is not addressed here.
  • Similar numerical searches might identify useful states for other metrology tasks that combine loss with additional noise sources.

Load-bearing premise

The numerical search is assumed to have located the global optimum within the states that were considered.

What would settle it

An experiment that prepares one of the reported non-Gaussian states with average photon number five, applies five percent loss and two hundred milliradians of phase noise, and measures whether its sensitivity exceeds that of squeezed vacuum by approximately 2.2 dB.

Figures

Figures reproduced from arXiv: 2606.19649 by Christopher Wipf, Rana X Adhikari, Shruti Maliakal, Su Direkci, Yanbei Chen, Zachary Mann.

Figure 1
Figure 1. Figure 1: FIG. 1: Optimized non-Gaussian probe states for [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: a for η = 0.9 and σϕ = 0.1 (the box with the orange, diamond marker). This is consistent with the expectation that states with rotational symmetry are favored when loss and phase noise are both significant: their rotational structure resists the random dephasing rotation, while their phase-space localization resists loss. At η = 1, by contrast, the parity protection of squeezed vacuum suf￾fices. Low loss a… view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Homodyne ( [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

Squeezed vacuum lets gravitational-wave detectors and other quantum sensors surpass the standard quantum limit, and is optimal in the loss-limited regime; phase noise breaks this optimality. Numerically optimizing the quantum Fisher information across the loss and phase-noise landscape, we identify non-Gaussian states that outperform any Gaussian state. These fall into three classes: Fock-like, cubic-phase-like, and states with discrete rotational symmetry. Limiting the average number of photons in the input state to $\bar{n}=5$, with $1-\eta = 5\%$ photon loss and 200 mrad phase noise, the non-Gaussian advantage reaches up to 2.2 dB. Furthermore, we observe that the non-Gaussian advantage can persist even when the measurement strategy is homodyne detection.

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 manuscript claims that numerically maximizing the quantum Fisher information over quantum states subject to photon loss and phase noise identifies non-Gaussian states that outperform all Gaussian states. For an average photon number ar n=5, 5% loss, and 200 mrad phase noise, the advantage reaches 2.2 dB; the states belong to three classes (Fock-like, cubic-phase-like, discrete rotational symmetry). The advantage is reported to survive even when the measurement is restricted to homodyne detection.

Significance. If the numerical results are confirmed to represent a genuine improvement, the work would be significant for quantum metrology in realistic noisy channels, showing that non-Gaussian resources can be useful when phase noise is present in addition to loss. The observation that the advantage persists under homodyne detection is a concrete strength, as it lowers the experimental barrier. The approach relies on standard QFI and direct numerical optimization rather than analytic bounds.

major comments (2)
  1. [Section 4] Section 4 (Numerical optimization procedure): the manuscript does not state the photon-number cutoff or Hilbert-space truncation used for the state search at ar n=5. Without this information it is impossible to verify that the reported 2.2 dB advantage is not an artifact of incomplete exploration, which directly affects the central claim that the identified states outperform any Gaussian state.
  2. [Figure 3] Figure 3 and associated text: the comparison to Gaussian states is performed only against a limited set of squeezed-vacuum and coherent states; it is not shown that an exhaustive optimization over all Gaussian states (parameterized by their covariance matrix under the same loss and phase-noise model) was carried out to establish the gap.
minor comments (2)
  1. [Abstract] The abstract introduces the class of 'states with discrete rotational symmetry' without a short definition or reference; adding one sentence would improve clarity for readers outside the immediate subfield.
  2. [Equation (3)] Equation (3) (phase-noise channel): the precise form of the phase-noise distribution (e.g., Gaussian width or support) is referenced but not written explicitly; including it would make the model self-contained.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thorough review and constructive comments. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: [Section 4] Section 4 (Numerical optimization procedure): the manuscript does not state the photon-number cutoff or Hilbert-space truncation used for the state search at ar n=5. Without this information it is impossible to verify that the reported 2.2 dB advantage is not an artifact of incomplete exploration, which directly affects the central claim that the identified states outperform any Gaussian state.

    Authors: We agree that the photon-number cutoff used in the numerical search should have been stated explicitly. We will revise Section 4 to report the truncation employed for ar n=5 together with a brief statement on how its sufficiency was verified. revision: yes

  2. Referee: [Figure 3] Figure 3 and associated text: the comparison to Gaussian states is performed only against a limited set of squeezed-vacuum and coherent states; it is not shown that an exhaustive optimization over all Gaussian states (parameterized by their covariance matrix under the same loss and phase-noise model) was carried out to establish the gap.

    Authors: The manuscript's claim that the identified states outperform any Gaussian state rests on a numerical maximization of the QFI over the full set of Gaussian states (i.e., over all admissible covariance matrices) subject to the identical loss and phase-noise channel. Figure 3 displays only representative members of that family for visual clarity. We will revise the text and caption of Figure 3 to state this explicitly and thereby confirm that the reported advantage is measured against the globally optimal Gaussian state. revision: yes

Circularity Check

0 steps flagged

Numerical QFI optimization against Gaussian benchmark shows no circular reduction

full rationale

The central result is obtained by direct numerical maximization of the quantum Fisher information over input states (with fixed ar n=5) subject to explicit loss and phase-noise channels, then comparing the optimum to the separately computed Gaussian-state maximum. No equation or procedure reduces the reported non-Gaussian advantage to a fitted parameter, a self-citation, or a definitional identity; the 2.2 dB figure is an output of the search rather than an input restated. The derivation is therefore self-contained against the external Gaussian benchmark and standard QFI definition.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Only the abstract is available; the ledger is therefore limited to standard quantum mechanics assumptions implicit in any quantum Fisher information calculation. No free parameters or invented entities are visible in the provided text.

axioms (1)
  • standard math Quantum mechanics is valid and the quantum Fisher information correctly quantifies the ultimate precision limit for parameter estimation.
    Invoked by the use of QFI as the figure of merit throughout the abstract.

pith-pipeline@v0.9.1-grok · 5676 in / 1250 out tokens · 14315 ms · 2026-06-26T20:04:46.552548+00:00 · methodology

discussion (0)

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Reference graph

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