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arxiv: 2506.08521 · v4 · submitted 2025-06-10 · 🪐 quant-ph

Insightful Approach to Quantum Noise Suppression Below the Standard Quantum Limit Using a Single Mirror and Beam Splitter

Sun-Hyun Youn This is my paper

Pith reviewed 2026-05-19 10:58 UTC · model grok-4.3

classification 🪐 quant-ph
keywords quantum noise suppressionbeam splittermirrorstanding wavevacuum fluctuationsstandard quantum limitquantum optics
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The pith

A mirror at a beam splitter's unused port can reduce vacuum fluctuations below the standard quantum limit.

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

The paper shows how adding a mirror to form a standing wave at one input of a beam splitter affects the vacuum fluctuations in the output beams. Normally, quantum noise in split coherent light stays at the quantum limit regardless of intensity. Calculations show that the noise from the mirror side can be made to reach zero at certain output positions. This setup allows the split light's noise to fall below that limit. Feedback then extends the suppression to the second output port as well.

Core claim

By placing a mirror at the unused input port of the beam splitter, a standing wave is formed that causes the vacuum fluctuations at the beam splitter output to periodically reach zero, as calculated using semi-classical and quantum-mechanical methods, thereby reducing the vacuum noise of the split light below the quantum noise limit.

What carries the argument

The standing wave formed by the mirror at the unused input port, which periodically nulls the vacuum fluctuations at the beam splitter output.

Load-bearing premise

The standing wave formed by the mirror at the unused input port can be arranged so that vacuum fluctuations induced at the beam-splitter output periodically reach exactly zero.

What would settle it

Measuring the noise variance at the beam splitter outputs while varying the mirror position or phase, expecting drops to zero at specific periodic separations predicted by the standing wave.

Figures

Figures reproduced from arXiv: 2506.08521 by Sun-Hyun Youn.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of the beam splitter (BS) setup. One input port of the beam splitter is the [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Quantum noise characteristics divided by a beam splitter (BS). M denotes a mirror, and [PITH_FULL_IMAGE:figures/full_fig_p010_2.png] view at source ↗
read the original abstract

When a coherent electromagnetic wave passes through a beam splitter (BS), it is divided equally into two parts. However, the quantum noise associated with the resulting coherent states, despite being reduced in amplitude by half, remains fundamentally constrained by the quantum noise limit, independent of the intensity. By placing a mirror at the unused input port of the BS, a standing wave is formed in the vicinity of the mirror, which influences the vacuum fluctuations of the coherent state at the BS output. Using semi-classical and quantum mechanical approaches, we calculate the vacuum fluctuations induced by the mirror and demonstrate that the vacuum noise originating from the mirror side periodically reaches zero at the BS output. Leveraging this effect, we show that the vacuum fluctuations of the light split by the BS can be readily reduced below the quantum noise limit. Furthermore, through feedback mechanisms, the vacuum fluctuations of the electromagnetic field at the other output port can also be suppressed below the quantum noise limit. These findings provide a pivotal insight into the manipulation of electromagnetic noise, with broad implications for all experiments involving quantum noise control.

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

1 major / 1 minor

Summary. The paper claims that placing a mirror at the unused input port of a beam splitter creates a standing wave that causes the vacuum fluctuations from that port to periodically reach exactly zero at one output, allowing the split coherent light to have noise below the standard quantum limit (SQL). Semi-classical and quantum-mechanical calculations are said to demonstrate this periodic nulling, with feedback then used to suppress noise at the second output port as well.

Significance. If correct, the result would offer a resource-efficient route to sub-SQL noise in linear optical systems, with potential impact on interferometry and quantum sensing. The manuscript does not, however, supply the explicit operator derivations or commutation checks needed to evaluate whether the claim survives the standard input-output formalism.

major comments (1)
  1. [Abstract] Abstract: the assertion that vacuum fluctuations 'originating from the mirror side periodically reach exactly zero' at a BS output cannot be reconciled with the unitary BS transformation. For a lossless beam splitter the input-output map â_out1 = t â_in1 + r â_in2 (and conjugate) preserves [â, â†] = 1; replacing â_in2 by the reflected field from the mirror (including its vacuum fluctuations and phase e^{i k L}) yields a composite unitary whose output quadrature variances remain at or above vacuum level for coherent-state inputs. The semi-classical standing-wave null therefore does not lift to the operator level without either violating unitarity or reintroducing equivalent noise.
minor comments (1)
  1. [Abstract] The abstract mentions 'semi-classical and quantum mechanical approaches' but provides neither the explicit equations nor the error analysis that would allow verification of the periodic-zero claim.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for raising this important point about consistency with the unitary beam-splitter transformation. We address the concern directly below and will strengthen the manuscript by adding the requested explicit derivations.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the assertion that vacuum fluctuations 'originating from the mirror side periodically reach exactly zero' at a BS output cannot be reconciled with the unitary BS transformation. For a lossless beam splitter the input-output map â_out1 = t â_in1 + r â_in2 (and conjugate) preserves [â, â†] = 1; replacing â_in2 by the reflected field from the mirror (including its vacuum fluctuations and phase e^{i k L}) yields a composite unitary whose output quadrature variances remain at or above vacuum level for coherent-state inputs. The semi-classical standing-wave null therefore does not lift to the operator level without either violating unitarity or reintroducing equivalent noise.

    Authors: We agree that an explicit operator treatment is necessary to confirm the result. In our quantum-mechanical analysis the mirror imposes a propagation phase φ = 2kL on the field returning to the unused port, yielding the self-consistent relation â_in2 = e^{iφ} â_out2 (with â_out2 expressed via the beam-splitter relations). Solving the linear system for the two outputs in terms of the single independent input â_in1 shows that, for phases corresponding to standing-wave nodes at one output port, the coefficient of the vacuum quadrature in that port vanishes through destructive interference. Because the mirror correlates the fluctuations between the two output ports, the commutation relations [â_out, â_out†] = 1 remain satisfied and the total noise is merely redistributed; one quadrature variance falls below the SQL while the orthogonal quadrature is correspondingly increased. The semi-classical calculation illustrates the periodic nulling of the mean field, which is recovered as the expectation value of the full operator expression. We will insert the complete operator derivations together with the commutation checks in the revised manuscript. revision: partial

Circularity Check

1 steps flagged

Mirror distance selected to force standing-wave node at BS output, then presented as independent prediction of sub-SQL vacuum suppression

specific steps
  1. self definitional [Abstract]
    "By placing a mirror at the unused input port of the BS, a standing wave is formed in the vicinity of the mirror, which influences the vacuum fluctuations of the coherent state at the BS output. Using semi-classical and quantum mechanical approaches, we calculate the vacuum fluctuations induced by the mirror and demonstrate that the vacuum noise originating from the mirror side periodically reaches zero at the BS output. Leveraging this effect, we show that the vacuum fluctuations of the light split by the BS can be readily reduced below the quantum noise limit."

    The mirror distance L is chosen so the standing-wave phase places a node exactly at the BS output port; the resulting 'periodic zero' is therefore identical to the geometric input condition rather than a derived consequence. The subsequent claim of sub-SQL suppression is obtained simply by substituting this constructed null back into the output quadrature, making the reduction true by definition of the chosen L.

full rationale

The paper's central derivation begins by placing a mirror at the unused BS port to form a standing wave whose nodes are positioned (via choice of L) so that the mirror-port vacuum contribution is exactly zero at one output. This zero is then used to claim that the split coherent state's vacuum fluctuations fall below the SQL. Because the node location is fixed by the same mirror distance that defines the standing-wave phase, the null is tautological with the input assumption rather than an independent quantum prediction. The abstract's semi-classical/quantum calculation merely reproduces the classical interference pattern; lifting it to operator level while preserving unitarity is not shown. This matches the self-definitional pattern and justifies a moderate circularity score. No external benchmark or commutation-preserving derivation is supplied to break the loop.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5712 in / 1196 out tokens · 45793 ms · 2026-05-19T10:58:35.172193+00:00 · methodology

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Reference graph

Works this paper leans on

24 extracted references · 24 canonical work pages

  1. [1]

    Zhang, Y.-x

    J. Zhang, Y.-x. Liu, R.-B. Wu, K. Jacobs, F. Nori, Quantum feedback: theory, experiments, and applications, Phys. Rep. 679, 1 (2017)

    work page 2017

  2. [2]

    Yoshihisa Yamamoto, Nobuyuki Imoto, Susumu Machida, Amplitude squeezing in a semicon- ductor laser using quantum nondemolition measurement and negative feedback , Phys. Rev. A 33, 3243 (1986)

    work page 1986

  3. [3]

    S.-H. Youn, W. Jhe, J.-H. Lee, J.-S. Chang, Effect of vacuum fluctuations on the quantum- mechanical amplitude noise of a laser diode in feedback systems. J. Opt. Soc. Am. B 11, 20–26 (1994)

    work page 1994

  4. [4]

    R. E. Slusher,L. W. Hollberg, B. Yurke, J.C. Mertz, J. F. Valley,Observation of Squeezed States Generated by Four-Wave Mixing in an Optical Cavity , Phys. Rev. Lett. 55, 2409 (1985)

    work page 1985

  5. [5]

    L.-A. Wu, H. J. Kimble, J. L. Hall, H. Wu, Generation of squeezed states by parametric down conversion, Phys. Rev. Lett. 57, 2520 (1986)

    work page 1986

  6. [6]

    R. M. Shelby, M. D. Levenson, S. H. Perlmutter, R. G. DeVoe, and D. F. Walls, Broad-Band Parametric Deamplification of Quantum Noise in an Optical Fiber , Phys. Rev. Lett. 57, 691 (1986)

    work page 1986

  7. [7]

    C. M. Caves, Quantum-mechanical noise in an interferometer , Phys. Rev. D 23, 1693 (1981)

    work page 1981

  8. [8]

    S. L. Braunstein, P. van Loock, Quantum information with continuous variables , Rev. Mod. Phys. 77, 513 (2005)

    work page 2005

  9. [9]

    Giovannetti, S

    V. Giovannetti, S. Lloyd, L. Maccone, Quantum-enhanced measurements: beating the standard quantum limit, Science 306, 1330 (2004)

    work page 2004

  10. [10]

    Gagatsos , Saikat Guha, and Linran Fan, High-purity pulsed squeez- ing generation with integrated photonics , Phys

    Chaohan Cui, Christos N. Gagatsos , Saikat Guha, and Linran Fan, High-purity pulsed squeez- ing generation with integrated photonics , Phys. Rev. Research 3, 013199 (2021). High-purity pulsed squeezing generation with integrated photonics

    work page 2021

  11. [11]

    Chang-Woo Lee, Jae Hoon Lee, Hyojun Seok, Squeezed-light-driven force detection with an 14 optomechanical cavity in a Mach–Zehnder interferometer, Scientific Reports 10, 17496 (2020)

    work page 2020

  12. [12]

    A. A. Clerk, F. Marquardt, K. Jacobs, Back-action evasion and squeezing in a superconducting circuit, New J. Phys. 10, 095010 (2008)

    work page 2008

  13. [13]

    Aasi et al

    J. Aasi et al. (LIGO Scientific Collaboration), Advanced LIGO, Class. Quantum Grav. 32, 074001 (2015)

    work page 2015

  14. [14]

    Tse , Haocun Yu, N

    M. Tse , Haocun Yu, N. Kijbunchoo et al.,Quantum-Enhanced Advanced LIGO Detectors in the Era of Gravitational-Wave Astronomy , Phys. Rev. Lett., 123, 231107 (2019)

    work page 2019

  15. [15]

    Schnabel, N

    R. Schnabel, N. Mavalvala, D. E. McClelland, P. K. Lam, Quantum metrology for gravitational wave astronomy, Nat. Commun. 1, 121 (2010)

    work page 2010

  16. [16]

    Lu, B., Liu, L., Song, JY. et al. , Recent progress on coherent computation based on quantum squeezing., AAPPS Bull 33, 7 (2023)

    work page 2023

  17. [17]

    Ivan Derkach, Vladyslav C Usenko and Radim Filip, Squeezing-enhanced quantum key distri- bution over atmospheric channels , New J. Phys. 22, 053006 (2020)

    work page 2020

  18. [18]

    On the attraction between two perfectly conducting plates,

    H. B. G. Casimir, “On the attraction between two perfectly conducting plates,” Proc. Kon. Ned. Akad. Wetensch., B. 51, p. 793, 1948

    work page 1948

  19. [19]

    K. A. Milton, The Casimir Effect: Physical Manifestations of Zero-Point Energy . World Sci- entific, 2001

    work page 2001

  20. [20]

    Youn, J.-H

    S.-H. Youn, J.-H. Lee, J.-S. Chang, Modulation of the vacuum field in the beam splitter and mirror system. Opt. Quant. Electron. 27, 355 (1995)

    work page 1995

  21. [21]

    S. A. Wadood, J. T. Schultz, A. N. Vamivakas, C. R. Stroud Jr., Do remote boundary condi- tions affect photodetection? J. Mod. Opt. 66, 1116–1123 (2019)

    work page 2019

  22. [22]

    Sun-Hyun Youn, https://arxiv.org/abs/2504.11764 (2025)

    work page arXiv 2025

  23. [23]

    Loudon, The Quantum Theory of Light , 3rd ed

    R. Loudon, The Quantum Theory of Light , 3rd ed. (Oxford University Press, 2000)

    work page 2000

  24. [24]

    Engineering sub-Poisson light in a simple mirror and beam splitter system,

    Sun-Hyun Youn, “Engineering sub-Poisson light in a simple mirror and beam splitter system,” J. Kor. Phys. Soc. 83, 545 (2023). 15

    work page 2023