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arxiv: 2605.00021 · v2 · submitted 2026-04-19 · ⚛️ physics.med-ph · quant-ph

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Quantum Entanglement Degree, Mean Positronium Lifetime, and the 3γ/2γ Annihilation-Rate Ratio as Novel PET Biomarkers for Hypoxia -- Concept, Challenges, and Predictions

Pawel Moskal
Authors on Pith no claims yet

Pith reviewed 2026-05-10 04:41 UTC · model grok-4.3

classification ⚛️ physics.med-ph quant-ph
keywords quantum entanglementpositronium lifetimePET biomarkershypoxiaoxygen concentrationannihilation rate ratio3 gamma decaypositron emission tomography
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The pith

The quantum entanglement degree of photons from positronium can indicate oxygen concentration in tissues for PET hypoxia detection.

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

This paper proposes two methods to assess tissue oxygen levels using positronium produced in positron emission tomography. The first combines measurements of the mean ortho-positronium lifetime and the three-gamma to two-gamma annihilation rate ratio. The second uses the degree of quantum entanglement of the emitted photons, which is hypothesized to depend on oxygen concentration through different annihilation processes. Formulas are derived relating these quantities to partial pressure of oxygen, with numerical estimates provided for various materials at different oxygen levels. If accurate, these could enable new ways to detect hypoxic regions in the body during standard PET scans.

Core claim

The authors introduce quantum sensing approaches for hypoxia assessment in PET by linking oxygen concentration to ortho-positronium decay rates and to the degree of quantum entanglement of annihilation photons. They derive a formula for pO2 in terms of the 3γ/2γ ratio and mean lifetime, and under the hypothesis that pick-off annihilation photons are unentangled, they calculate specific entanglement degrees at zero oxygen for adipose tissue (0.890), isopropanol (0.886), water (0.867), cyclohexane (0.818), and isooctane (0.784). Theoretical models are given for how these parameters vary with oxygen pressure in different tissues.

What carries the argument

The degree of quantum entanglement C_QE of photons from ortho-positronium annihilation, which varies with the relative contributions of pick-off and conversion processes depending on oxygen concentration.

If this is right

  • A formula is provided for calculating pO2 from measured R_oPs-3γ/2γ and τ_oPs.
  • Measurement accuracies needed are estimated to distinguish hypoxic from physoxic conditions.
  • Quantitative predictions for C_QE, lifetime, and rate ratio as functions of pO2 are made for five specific materials.
  • At zero oxygen, C_QE values range from 0.784 to 0.890 depending on the material.

Where Pith is reading between the lines

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

  • Validating these predictions experimentally could lead to integration of entanglement measurements into clinical PET systems.
  • This approach might complement existing hypoxia imaging methods by providing additional quantum information from the same scan.
  • The method could be tested first in vitro with controlled oxygen environments before in vivo applications.

Load-bearing premise

The working hypothesis that photons produced in the pick-off annihilation process are not quantum entangled.

What would settle it

Direct measurement of the quantum entanglement degree C_QE in controlled samples of water or adipose tissue at known zero oxygen concentration, to check if it matches the predicted values around 0.86-0.89.

Figures

Figures reproduced from arXiv: 2605.00021 by Pawel Moskal.

Figure 12
Figure 12. Figure 12: Entanglement witnesses CQE (left) and RQE (right) as a function of oxygen pressure pO2 estimated for water, isopropanol, cyclohexane, isooctane, and adipose. Right figure presents result of RQE obtained for θ= θ1 = θ2 = 81.7◦. Calculations were performed using earlier results for RQE and CQE as a function of α ( [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Pictorial illustration of the measure of quantum entanglement C(θS) in Compton scattering in the body, and the degree of quantum entanglement CQE depending on the annihilation mechanism. (Left) Photo of the modular J-PET scanner, the first Quantum Entanglement PET, with a superimposed patient and events illustrating annihilation photons (red￾yellow dashed arrows) and photons following scattering within th… view at source ↗
read the original abstract

This manuscript introduces a novel method to assess tissue oxygen concentration via the quantum entanglement (QE) of photons originating from positronium which is produced within the patient's body during positron emission tomography. We also investigate the possibility of assessing hypoxia by simultaneously detecting positronium lifetime and the positronium decay rate ratio. We introduce two distinct quantum sensing approaches. Method 1 utilizes the correlation between oxygen concentration and ortho-positronium (o-Ps) decay rates, relying on the simultaneous measurement of the mean o-Ps lifetime ($\tau_{\mathrm{oPs}}$) and the $3\gamma$-to-$2\gamma$ annihilation rate ratio of o-Ps ($R_{\mathrm{oPs-3\gamma/2\gamma}}$). Method 2 introduces a novel hypothesis: that the degree of QE is sensitive to the relative contribution of annihilation mechanisms (pick-off vs. conversion), which in turn depends on oxygen concentration. We derive a formula for partial pressure of oxygen ($p\mathrm{O}_2$) as a function of $R_{\mathrm{oPs-3\gamma/2\gamma}}$ and $\tau_{\mathrm{oPs}}$ and estimate the measurement accuracy required for these parameters - and for the degree of QE - to sense in-vivo oxygen pressure in the range between hypoxic and physoxic conditions. Theoretical models and quantitative estimates for $R_{\mathrm{oPs-3\gamma/2\gamma}}$, $\tau_{\mathrm{oPs}}$ and for the degree of QE ($C_{\mathrm{QE}}$ ) as a function of $p\mathrm{O}_2$ are provided for water, isopropanol, cyclohexane, isooctane, and adipose tissue. In particular, applying the formulas derived under the working hypothesis that in pick-off process the photons are not entangled, we estimated that for $p\mathrm{O}_2 = 0$, the degree of quantum entanglement $C_{\mathrm{QE}}$ is equal to 0.890 for adipose, 0.886 for isopropanol, 0.867 for water, 0.818 for cyclohexane, and 0.784 for isooctane.

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

3 major / 1 minor

Summary. The manuscript proposes two quantum-sensing methods for assessing tissue hypoxia via positronium in PET: Method 1 correlates pO2 with o-Ps lifetime τ_oPs and the 3γ/2γ rate ratio R_oPs-3γ/2γ; Method 2 introduces C_QE (degree of quantum entanglement of annihilation photons) as a biomarker, deriving pO2 formulas under the explicit working hypothesis that pick-off annihilation produces unentangled photons. It supplies theoretical models and numerical estimates for R_oPs-3γ/2γ, τ_oPs, and C_QE(pO2) in water, isopropanol, cyclohexane, isooctane, and adipose tissue, including specific C_QE values at pO2=0 (0.890 adipose, 0.886 isopropanol, 0.867 water, 0.818 cyclohexane, 0.784 isooctane) and required measurement accuracies.

Significance. If the non-entanglement hypothesis for pick-off can be independently validated, the work would introduce a genuinely new quantum observable (C_QE) into hypoxia imaging, with the provided multi-medium predictions and accuracy estimates enabling direct experimental tests. The explicit framing of the hypothesis and the derivation of pO2 expressions from measurable quantities are constructive features that support falsifiability.

major comments (3)
  1. [Abstract] Abstract (Method 2 paragraph): The quoted C_QE values at pO2=0 are obtained by direct substitution of the assumption that pick-off photons carry zero entanglement into the branching-ratio formula; this renders the numerical outputs equivalent to the input hypothesis by construction rather than an independent prediction.
  2. [Abstract] Abstract and theoretical models: No QED derivation or cited experimental bound is supplied to justify why pick-off events are separable while conversion events remain entangled; without such support the claimed sensitivity of C_QE to the hypoxic-to-physoxic range rests on an untested axiom whose violation would collapse the entire C_QE(pO2) mapping.
  3. [Method 2] pO2 formula derivation (Method 2): The mapping from measured R_oPs-3γ/2γ and τ_oPs to C_QE should include an explicit propagation of uncertainty under alternative entanglement assumptions for pick-off; the current estimates do not quantify how robust the reported C_QE differences remain if the hypothesis is relaxed.
minor comments (1)
  1. [Abstract] Notation for R_oPs-3γ/2γ and τ_oPs should be standardized in all equations and figure captions to avoid ambiguity between o-Ps-specific and total annihilation quantities.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We are grateful to the referee for the detailed and constructive report. The comments accurately highlight the central role of our working hypothesis in Method 2 and the need for greater clarity on its implications. We respond to each major comment below and have revised the manuscript to improve transparency and robustness where possible.

read point-by-point responses

  1. Referee: [Abstract] Abstract (Method 2 paragraph): The quoted C_QE values at pO2=0 are obtained by direct substitution of the assumption that pick-off photons carry zero entanglement into the branching-ratio formula; this renders the numerical outputs equivalent to the input hypothesis by construction rather than an independent prediction.

    Authors: We agree that the reported C_QE values at pO2=0 follow directly from substituting the zero-entanglement assumption for pick-off into the branching-ratio expression. These are therefore conditional predictions under the stated hypothesis rather than independent results. We have revised the abstract to state explicitly that the values are obtained by applying the formulas derived under the working hypothesis of unentangled pick-off photons. revision: yes

  2. Referee: [Abstract] Abstract and theoretical models: No QED derivation or cited experimental bound is supplied to justify why pick-off events are separable while conversion events remain entangled; without such support the claimed sensitivity of C_QE to the hypoxic-to-physoxic range rests on an untested axiom whose violation would collapse the entire C_QE(pO2) mapping.

    Authors: The manuscript introduces the separability of pick-off photons as a novel working hypothesis motivated by the involvement of an uncorrelated medium electron, in contrast to the correlated pair in conversion annihilation. We acknowledge that no QED derivation or experimental bound is supplied to justify this distinction. The C_QE(pO2) sensitivity therefore depends on the validity of the hypothesis. We have added a dedicated paragraph in the discussion section that states the hypothesis explicitly, outlines its physical motivation, and calls for independent experimental tests to validate or refute it. revision: partial

  3. Referee: [Method 2] pO2 formula derivation (Method 2): The mapping from measured R_oPs-3γ/2γ and τ_oPs to C_QE should include an explicit propagation of uncertainty under alternative entanglement assumptions for pick-off; the current estimates do not quantify how robust the reported C_QE differences remain if the hypothesis is relaxed.

    Authors: We agree that quantifying robustness under relaxed assumptions would strengthen the analysis. The present derivation is performed under the zero-entanglement hypothesis for pick-off. We have revised the Method 2 section to include a qualitative assessment of how C_QE values would shift if pick-off photons carry a non-zero entanglement degree, parameterized by an additional factor. Full quantitative uncertainty propagation would require an a priori value for that factor, which is not currently available; we therefore note that experimental determination of pick-off entanglement is required for precise error estimates, while showing that moderate deviations from zero still preserve detectable C_QE differences within the stated accuracy targets. revision: partial

standing simulated objections not resolved
  • No QED derivation or cited experimental bound is supplied to justify why pick-off events are separable while conversion events remain entangled.

Circularity Check

1 steps flagged

C_QE estimates at pO2=0 reduce directly to the non-entanglement hypothesis for pick-off by construction

specific steps
  1. self definitional [Abstract]
    "applying the formulas derived under the working hypothesis that in pick-off process the photons are not entangled, we estimated that for pO2 = 0, the degree of quantum entanglement C_QE is equal to 0.890 for adipose, 0.886 for isopropanol, 0.867 for water, 0.818 for cyclohexane, and 0.784 for isooctane."

    The C_QE numbers are produced by inserting the zero-entanglement assumption for pick-off directly into the derived C_QE formula. The output values are therefore equivalent to the hypothesis by algebraic construction rather than an independent prediction or measurement.

full rationale

The paper's Method 2 derives formulas for C_QE under an explicit working hypothesis that pick-off annihilation photons carry zero entanglement (while conversion photons are entangled). The reported numerical C_QE values at pO2=0 for multiple tissues are obtained by direct substitution of this hypothesis into those formulas, with no independent derivation, external data, or QED justification supplied. This renders the central quantitative biomarker claims tautological with the input assumption. The separate Method 1 relating pO2 to measured R_oPs-3γ/2γ and τ_oPs retains independent modeling content from rate equations and is not circular on the evidence given.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The proposal rests on one central ad-hoc assumption about photon entanglement in pick-off and on theoretical decay models for specific media without external benchmarks or experimental anchors.

free parameters (1)
  • C_QE for pO2=0 in each medium
    Numerical values computed directly from the non-entanglement assumption for adipose, isopropanol, water, cyclohexane, and isooctane
axioms (1)
  • ad hoc to paper Photons from pick-off annihilation are not quantum entangled
    Explicitly invoked as working hypothesis to derive C_QE values and oxygen sensitivity
invented entities (1)
  • C_QE as hypoxia biomarker no independent evidence
    purpose: To sense oxygen concentration through changes in annihilation mechanism
    New postulated observable with no independent experimental evidence or falsifiable handle outside the model

pith-pipeline@v0.9.0 · 5715 in / 1376 out tokens · 57016 ms · 2026-05-10T04:41:29.277329+00:00 · methodology

discussion (0)

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Reference graph

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