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arxiv: 2606.13286 · v1 · pith:OF43ITL7new · submitted 2026-06-11 · 💻 cs.IT · math.IT

Error Probability Analysis of Quantum Communication with Phase-squeezed M-PSK

Nikos A. Mitsiou , Ioannis Krikidis This is my paper

Pith reviewed 2026-06-27 05:41 UTC · model grok-4.3

classification 💻 cs.IT math.IT
keywords phase squeezingM-PSKsymbol error probabilityquantum communicationMark-II receiverphoton efficiencyphase measurement
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The pith

Phase squeezing reduces symbol error probability in M-PSK and nearly doubles photon efficiency.

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

The paper analyzes the symbol error probability of phase-squeezed M-ary phase-shift keying detected with an adaptive Mark-II receiver. It derives expressions from the phase probability operator measure in the Fock basis and introduces an effective tangential-variance model that produces a closed-form expression using Owen's T-function. Numerical evaluation shows that squeezing lowers error rates relative to coherent states, with larger improvements at higher constellation sizes, and that it can almost double photon efficiency as the average photon number grows. A reader would care because the work identifies a concrete physical mechanism for improving the efficiency of quantum optical links without added transmit power.

Core claim

The paper establishes that phase-squeezed M-PSK yields substantially lower symbol error probability than coherent-state M-PSK when detected via the adaptive Mark-II receiver, that the improvement increases with constellation order M, and that squeezing can almost double photon efficiency with rising mean photon number. The analysis proceeds from the phase POM of the Mark-II scheme, develops a phase-density convolution method, and supplies the tangential-variance approximation for tractable computation.

What carries the argument

The adaptive Mark-II receiver's phase probability operator measure (POM) together with the effective tangential-variance model that converts the squeezed-state phase statistics into a closed-form SEP expression via Owen's T-function.

If this is right

  • Phase squeezing substantially reduces SEP of M-PSK relative to coherent-state transmission.
  • The reduction grows with constellation order.
  • Squeezing nearly doubles photon efficiency of M-PSK as mean transmitted photon number increases.
  • The tangential-variance and convolution approximations match the exact POM calculation within 2-4 photons.

Where Pith is reading between the lines

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

  • The same receiver model could be applied to analyze squeezing benefits in other phase-sensitive quantum modulation formats.
  • System designers might use the closed-form SEP expression to optimize constellation size jointly with squeezing level.
  • Laboratory tests with real squeezed-light sources would directly test whether the predicted efficiency gain appears at practical photon numbers.

Load-bearing premise

The adaptive Mark-II receiver supplies the physically relevant phase observable and the tangential-variance model stays accurate over the photon-number range where the efficiency doubling is reported.

What would settle it

An experiment that measures symbol error probability for phase-squeezed 8-PSK or 16-PSK at increasing mean photon numbers and checks whether the observed photon efficiency approaches twice the coherent-state value.

Figures

Figures reproduced from arXiv: 2606.13286 by Ioannis Krikidis, Nikos A. Mitsiou.

Figure 2
Figure 2. Figure 2: Phase measurement viewpoint for phase-squeezed PSK [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: PSK constellations, M = 8, Ntot = 10. usual projective measurement description in a direct way. In a standard projective measurement, an observable is represented by a Hermitian operator. The possible measurement outcomes are the eigenvalues of that operator, while the associated eigenvectors, determine the projectors used to compute the probabilities of those outcomes through the Born rule. For example, p… view at source ↗
Figure 3
Figure 3. Figure 3: A schematic of the polar-domain SEP analysis. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: The effective variance assumption. VI. CLOSED-FORM SEP ANALYSIS WITH EFFECTIVE TANGENTIAL VARIANCE In this section, we get a closed form analysis for the M￾PSK scheme by considering the effect of the Mark-II phase error in the tangential domain instead, and then calculating the SEP in the polar domain. This way, we fold the Mark￾II phase uncertainty into an effective tangential variance and we avoid the ne… view at source ↗
Figure 5
Figure 5. Figure 5: SEP vs the squeezing factor r, M = 16, Ntot = 30. 5 10 15 20 25 30 35 40 Mean photon number per symbol 0 0.2 0.4 0.6 0.8 1 1.2 Optimal squeezing amplitude M = 4 M = 8 M = 16 M = 32 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Optimal squeezing factor r ∗ vs Ntot. comparing (i) the “Quantum exact” scheme which is calculated by (30) and (31) (ii) the “Quantum approximation” scheme which occurs from calculating SEP by (22) and (31) (iii) the “Analysis - polar domain” scheme which is calculated by (47)-(48) and Proposition 1 (iv) the “Analysis T -Owens” which is given by Proposition 2 and (v) the no squeezing scheme, which is M-PSK… view at source ↗
Figure 7
Figure 7. Figure 7: reports the SEP as a function of Ntot for M ∈ {8, 16, 32}. We note that for each Ntot, the optimal squeezing value was calculated based on an exhaustive search. First, we observe that, for all values of Ntot, the proposed approxima￾tion schemes remain consistent with the full quantum analysis, as they predict the SEP with an accuracy corresponding in gen￾eral to about 2 to 4 photons. Notably, for M = 8, th… view at source ↗
Figure 8
Figure 8. Figure 8: The quantum state phase & Mark-II phase noise distrib [PITH_FULL_IMAGE:figures/full_fig_p010_8.png] view at source ↗
read the original abstract

In this paper, we investigate the symbol error probability (SEP) of phase-squeezed M-ary phase-shift keying (M-PSK). Since the relevant observable for M-PSK detection is the optical phase, we adopt the adaptive Mark-II receiver which is a physically realizable phase measurement. First, we develop a theoretical analysis based on the phase probability operator measure (POM) of the Mark-II scheme in the Fock basis. Then, we develop two SEP methods based on the statistics of the received PSK symbol and the error introduced by the Mark-II measurement. The first method derives the phase probability density induced by the squeezed state noise and incorporates the additional Mark-II phase uncertainty through an angular convolution. Since this convolution does not admit a simple closed form, we also introduce an effective tangential-variance model, which yields a closed form SEP expression in terms of the Owen's T-function. Numerical results show that phase squeezing substantially reduces the SEP of M-PSK compared to coherent state transmission, with greater gains for higher constellation orders. Notably, for the investigated scenario, squeezing can almost double the photon efficiency of M-PSK as the mean number of transmitted photons increases. Finally, the proposed approximations closely follow the Mark-II POM analysis, typically within an accuracy of 2-4 photons, and therefore provide accurate and computationally efficient tools for analyzing phase squeezed quantum M-PSK communication.

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

0 major / 2 minor

Summary. The paper analyzes the symbol error probability (SEP) of phase-squeezed M-PSK using the adaptive Mark-II receiver as the phase observable. It develops a Fock-basis phase POM analysis, followed by two approximation methods: an angular convolution of the phase PDF induced by squeezed-state noise with Mark-II uncertainty, and an effective tangential-variance model that produces a closed-form SEP via Owen's T-function. Numerical results claim that squeezing substantially lowers SEP relative to coherent states (with larger gains at higher M) and can nearly double photon efficiency as mean photon number grows; the approximations track the exact POM within 2-4 photons.

Significance. If the reported accuracy of the tangential-variance model holds across the relevant photon-number range, the closed-form expression supplies a practical tool for squeezed-state M-PSK analysis and quantifies a potentially significant photon-efficiency gain. The explicit comparison to the Mark-II POM and the provision of both convolution and closed-form routes are positive features.

minor comments (2)
  1. [Abstract] Abstract: the statement that the approximations 'closely follow the Mark-II POM analysis, typically within an accuracy of 2-4 photons' should specify whether the error is measured in mean photon number, in SEP, or in the derived efficiency metric, and whether the bound remains uniform as mean photon number and M increase.
  2. The definition and normalization of the 'effective tangential variance' used to obtain the Owen's T-function expression should be stated explicitly so that readers can verify it does not introduce hidden fitting parameters.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive summary, significance assessment, and recommendation of minor revision. No specific major comments were provided in the report.

Circularity Check

0 steps flagged

No significant circularity; approximation explicitly validated against exact POM

full rationale

The derivation begins with the phase POM of the adaptive Mark-II receiver in the Fock basis, then forms two SEP expressions: one via angular convolution of the squeezed-state phase PDF with Mark-II uncertainty, and a second via an explicitly introduced effective tangential-variance model that yields a closed-form expression in Owen's T-function. The paper states that the model tracks the exact POM within 2-4 photons and presents the efficiency-doubling claim as a numerical outcome of this approximation. No quoted step reduces a prediction to its inputs by construction, no parameter is fitted and then relabeled as a prediction, and no self-citation chain is load-bearing. The central results therefore remain independent of the inputs they are derived from.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so free parameters, axioms, and invented entities cannot be identified with certainty; the tangential-variance model may introduce an effective variance parameter, but this cannot be confirmed.

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Reference graph

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