---
title: "Semantic Fidelity: An Operational Measure for Borrowed Quantum Terms and Their Scale of Failure"
slug: "semantic-fidelity-an-operational-measure-for-borrowed-quantum-terms-and-the-scal"
url: https://papers.qnfo.org/papers/semantic-fidelity-an-operational-measure-for-borrowed-quantum-terms-and-the-scal
authors: ["Rowan Brad Quni-Gudzinas"]
version: "2.0.0"
published: "2026-10-11"
updated: "2026-10-26"
license: "QNFO-ULA-2.1"
status: "published"
quality_label: "High-quality scholarly research"
quality_basis: "QNFO publisher classification for open-access, versioned research with a public revision history and reader correction channel; this is not a claim of independent peer review."
peer_review_status: "Not independently peer-reviewed"
quality_evidence_url: "https://qnfo.org/about"
quality_tags: ["High-quality scholarly research", "open-access scholarly work", "versioned research publication"]
---

# Semantic Fidelity: An Operational Measure for Borrowed Quantum Terms and Their Scale of Failure

Quantum‑computing projects routinely import terminology from quantum optics, condensed‑matter physics, and high‑energy theory. When the ontological commitments of a borrowed term diverge from the circuit‑model formalism, engineers may make design decisions that are sub‑optimal or infeasible, contributing to multi‑billion‑dollar delays. We formalize **operational semantic fidelity** $F_S^{(n)}(T,C)=1-D_{TV}^{(n)}(T,C)$, where $D_{TV}^{(n)}$ is the total‑variation distance between the outcome distributions generated by a term’s native ontology $O_T$ and the target circuit context $C$ on the decision‑relevant observable set $\mathcal O_C$. For the prototypical term “photon”, we compute a per‑element divergence of $1/2$ at a balanced two‑boson beamsplitter, derive the compounding law $D_{TV}^{(k)}=1-2^{-k}$ for $k$ independent interference elements, and show that a decision‑relevance threshold $\varepsilon=0.9$ is crossed at $k^{*}=4$ ($\approx$ 8 photonic qubits).  A sensitivity analysis explores how $k^{*}$ varies with per‑element divergence $\delta$ and threshold $\varepsilon$. The measure converts ontological drift into a quantitative engineering specification, enabling systematic validation and falsification. Limitations, required assumptions, and a concrete next‑step experiment are discussed.

# Semantic Fidelity: An Operational Measure for Borrowed Quantum Terms and Their Scale of Failure

## Abstract

Quantum‑computing projects routinely import terminology from quantum optics, condensed‑matter physics, and high‑energy theory. When the ontological commitments of a borrowed term diverge from the circuit‑model formalism, engineers may make design decisions that are sub‑optimal or infeasible, contributing to multi‑billion‑dollar delays. We formalize **operational semantic fidelity** $F_S^{(n)}(T,C)=1-D_{TV}^{(n)}(T,C)$, where $D_{TV}^{(n)}$ is the total‑variation distance between the outcome distributions generated by a term’s native ontology $O_T$ and the target circuit context $C$ on the decision‑relevant observable set $\mathcal O_C$. For the prototypical term “photon”, we compute a per‑element divergence of $1/2$ at a balanced two‑boson beamsplitter, derive the compounding law $D_{TV}^{(k)}=1-2^{-k}$ for $k$ independent interference elements, and show that a decision‑relevance threshold $\varepsilon=0.9$ is crossed at $k^{*}=4$ ($\approx$ 8 photonic qubits).  A sensitivity analysis explores how $k^{*}$ varies with per‑element divergence $\delta$ and threshold $\varepsilon$. The measure converts ontological drift into a quantitative engineering specification, enabling systematic validation and falsification. Limitations, required assumptions, and a concrete next‑step experiment are discussed.

## 1. Introduction

Large‑scale quantum‑computing programmes allocate billions of dollars to hardware that must interoperate across disciplinary boundaries. Engineers who design photonic interferometers, superconducting processors, or trapped‑ion chains regularly encounter terms such as “photon”, “quasiparticle”, or “measurement” that originated in quantum‑optical, condensed‑matter, or high‑energy contexts. The native ontology of such a term may imply indistinguishability, copyability, or number conservation that the circuit‑model formalism does not guarantee. When these commitments conflict, design teams can pursue architectures that are fundamentally incompatible with the underlying hardware, inflating budgets and delaying commercial delivery.

A quantitative criterion that tells a hardware architect whether a borrowed term remains trustworthy at a given system size would allow the architect either to retain the term (saving documentation effort) or to replace it with a vocabulary‑neutral description before costly redesigns occur. This paper provides exactly such a criterion.

**Contributions.**
1. Formal definition of operational semantic fidelity $F_S^{(n)}$ based on total‑variation distance (Section 3).
2. Analytic derivation of $D_{TV}^{(1)}=1/2$ for the “photon” term at a balanced beamsplitter and the compounding law $D_{TV}^{(k)}=1-2^{-k}$ (Section 4.1–4.2).
3. Determination of the crossing scale $k^{*}=4$ ($\approx$ 8 photonic qubits) for a decision‑relevance threshold $\varepsilon=0.9$ (Section 4.2).
4. Sensitivity analysis showing how $k^{*}$ depends on per‑element divergence $\delta$ and threshold $\varepsilon$ (Section 4.3).
5. Comprehensive discussion of limitations, falsification conditions, and a concrete validation experiment (Sections 6–7).

## 2. Background and Related Work

Several of the cited works provide methodological foundations that inform the present analysis. [1] presents a formalism for quantifying contextuality in quantum optics, demonstrating that interference visibility can be expressed as a probability difference; this informs our use of outcome distributions. [2] derives the total‑variation distance for distinguishable versus indistinguishable particles in a beamsplitter, reporting a value of $0.5$, which we adopt as the per‑element divergence. [3] introduces an operational measure of semantic mismatch in quantum communication protocols, showing how decision‑relevant observables can be mapped to engineering actions. [4] discusses the impact of mode‑matching errors on interference outcomes, providing a quantitative loss model that underlies our independence assumption. [5] offers a compositional framework for aggregating independent error sources, yielding the product form used in Eq. (3). [6] reports experimental benchmarks for photon‑pair sources, establishing realistic values for indistinguishability that motivate our idealised analysis. [7] critiques the use of particle‑based terminology in circuit models, arguing for vocabulary‑neutral descriptions, which motivates our motivation. [8] surveys design‑space‑exploration tools for quantum hardware, highlighting the need for quantitative fidelity metrics such as the one introduced here. These works collectively demonstrate that quantitative assessment of ontological drift is feasible and motivate the specific definitions and thresholds employed in this paper.

## 3. Methods

### 3.1 Formal definitions

Let $C$ denote a computational context characterised by a family of circuits parameterised by a size $n$, a set of decision‑relevant observables $\mathcal O_C$, and a deterministic decision rule that maps measurement outcomes to engineering actions. Let $T$ be a borrowed term with a native ontology $O_T$ that specifies a set of commitments (e.g., indistinguishability, copyability, number conservation). Both $O_T$ and the circuit formalism induce probability distributions over the outcome space $\mathcal X^{(n)}$ of $\mathcal O_C$:

\[
P_T^{(n)}(x),\qquad P_C^{(n)}(x),\qquad x\in\mathcal X^{(n)} .
\]

The **operational divergence** is the total‑variation distance

\[
D_{TV}^{(n)}(T,C)=\frac12\sum_{x\in\mathcal X^{(n)}}\bigl|P_T^{(n)}(x)-P_C^{(n)}(x)\bigr| .
\]

The **semantic fidelity** is defined as

\[
F_S^{(n)}(T,C)=1-D_{TV}^{(n)}(T,C) .
\]

Total‑variation distance upper‑bounds the advantage any decision rule can obtain by using one description instead of the other; thus $F_S$ directly quantifies the decision‑relevance of the ontological mismatch.

### 3.2 Decision threshold and failure scale

A design team selects a decision‑relevance threshold $\varepsilon\in(0,1)$ that reflects the maximum tolerable probability of making a wrong engineering choice due to semantic drift. The term $T$ is **semantically faithful** at size $n$ if $D_{TV}^{(n)}\le\varepsilon$ and becomes **provably misleading** at the smallest $n^{*}$ satisfying

\[
D_{TV}^{(n^{*})}>\varepsilon .
\]

### 3.3 Compounding across independent elements

If the context decomposes into $k$ statistically independent loci where $T$ is invoked, each with per‑element divergence $\delta_i$, and the joint outcome distribution factorises, then

\[
D_{TV}^{(k)}=1-\prod_{i=1}^{k}\bigl(1-\delta_i\bigr) .
\]

For identical elements $\delta_i=\delta$ this reduces to

\[
D_{TV}^{(k)}=1-(1-\delta)^{k} .
\]

The crossing index $k^{*}$ follows from $(1-\delta)^{k^{*}}\le 1-\varepsilon$:

\[
k^{*}= \left\lceil\frac{\ln(1-\varepsilon)}{\ln(1-\delta)}\right\rceil .
\]

### 3.4 Projection assumptions

All numerical results in Sections 4.1–4.4 are derived analytically from the stated inputs. The sensitivity analysis (Section 4.3) treats $\delta$ and $\varepsilon$ as free parameters and reports the resulting $k^{*}$ as a projection.

## 4. Analysis

All input numbers are cited with their source or labelled as an assumption, and every arithmetic step is shown.

### 4.1 Per‑element divergence for “photon”

**Setup.** Consider a balanced $50/50$ beamsplitter with one particle in each input port. The decision‑relevant observable is whether the two output particles exit the same port (“bunch”) or different ports (“split”).

**Native‑ontology prediction.** In the bosonic ontology of a photon, two indistinguishable bosons interfere destructively in the split amplitudes, yielding

\[
P_T(\text{same})=1,\qquad P_T(\text{split})=0 .
\]

**Circuit‑model prediction.** Treating the two particles as distinguishable qubits routed independently through the beamsplitter gives

\[
P_C(\text{same})=\tfrac12,\qquad P_C(\text{split})=\tfrac12 .
\]

**Divergence.** With outcome space $\mathcal X=\{\text{same},\text{split}\}$:

\[
\begin{aligned}
D_{TV}^{(1)} &=\frac12\Bigl(\bigl|1-\tfrac12\bigr|+\bigl|0-\tfrac12\bigr|\Bigr) \\
&=\frac12\Bigl(\tfrac12+\tfrac12\Bigr)=\frac12 .
\end{aligned}
\]

Thus

\[
F_S^{(1)}=1-\frac12=\frac12 .
\]

### 4.2 Compounding law and threshold crossing

Assume $k$ independent beamsplitter elements, each with per‑element divergence $\delta=\tfrac12$ (derived above). Applying the identical‑element compounding law:

\[
D_{TV}^{(k)}=1-\bigl(1-\tfrac12\bigr)^{k}=1-2^{-k}.
\]

We tabulate the first six values:

| $k$ | $D_{TV}^{(k)}$ | $F_S^{(k)}$ |
|---|---|---|
| 1 | $0.5$ | $0.5$ |
| 2 | $0.75$ | $0.25$ |
| 3 | $0.875$ | $0.125$ |
| 4 | $0.9375$ | $0.0625$ |
| 5 | $0.96875$ | $0.03125$ |
| 6 | $0.984375$ | $0.015625$ |

We adopt a decision‑relevance threshold $\varepsilon=0.9$ (a design‑team stipulation). The smallest $k^{*}$ with $D_{TV}^{(k)}>\varepsilon$ satisfies

\[
1-2^{-k^{*}} > 0.9 \;\Longrightarrow\; 2^{-k^{*}} < 0.1 .
\]

Taking natural logarithms:

\[
\begin{aligned}
- k^{*}\ln 2 &< \ln 0.1 \\
k^{*} &> \frac{\ln 0.1}{-\ln 2}
      = \frac{-2.302585\ldots}{-0.693147\ldots}
      \approx 3.3219 .
\end{aligned}
\]

Hence $k^{*}=4$. Since each element involves two particles, the crossing occurs at $2\times4=8$ photonic particles (or equivalently eight qubits of a two‑mode interferometric hardware).

### 4.3 Sensitivity analysis (projection)

Using the general compounding formula $D_{TV}^{(k)}=1-(1-\delta)^{k}$, the crossing index for arbitrary per‑element divergence $\delta$ and threshold $\varepsilon$ is

\[
k^{*}= \left\lceil\frac{\ln(1-\varepsilon)}{\ln(1-\delta)}\right\rceil .
\]

We evaluate $k^{*}$ for selected $\delta$ values while keeping $\varepsilon=0.9$:

| $\delta$ | $\ln(1-\delta)$ | $k^{*}$ |
|---|---|---|
| $0.10$ | $\ln 0.9 = -0.105360$ | $\lceil \frac{\ln 0.1}{-0.105360}\rceil = \lceil 21.86\rceil = 22$ |
| $0.25$ | $\ln 0.75 = -0.287682$ | $\lceil \frac{-2.302585}{-0.287682}\rceil = \lceil 8.01\rceil = 9$ |
| $0.50$ | $\ln 0.5 = -0.693147$ | $\lceil \frac{-2.302585}{-0.693147}\rceil = \lceil 3.32\rceil = 4$ |
| $0.75$ | $\ln 0.25 = -1.386294$ | $\lceil \frac{-2.302585}{-1.386294}\rceil = \lceil 1.66\rceil = 2$ |

Thus, for more modest per‑element divergences the crossing scale grows rapidly, while highly divergent elements reach the threshold after only a few repetitions.

## 5. Results

- **R1.** Per‑element divergence for “photon” at a balanced beamsplitter: $D_{TV}^{(1)}=1/2$, $F_S^{(1)}=1/2$ (Section 4.1).
- **R2.** Compounded divergence for $k$ independent elements: $D_{TV}^{(k)}=1-2^{-k}$ (Section 4.2).
- **R3.** Decision‑relevance crossing at $k^{*}=4$ elements ($\approx$ 8 photonic particles) for $\varepsilon=0.9$ (Section 4.2).
- **R4.** Projection: under the assumption of perfect independence, “photon” becomes misleading at $n^{*}=8$ qubits of photonic‑interference hardware (Section 4.2).

- **R6.** Sensitivity analysis showing $k^{*}$ as a function of per‑element divergence $\delta$ (Section 4.3).

## 6. Discussion

### 6.1 Limitations

1. **Idealised ontologies.** The divergence calculations compare two perfect theoretical models (bosonic photons vs. distinguishable qubits) rather than noisy physical devices. Real beamsplitters exhibit partial indistinguishability and loss, which would reduce the observed $D_{TV}$.
2. **Independence assumption.** The compounding law presumes statistical independence and factorisation of the $k$ elements. Shared sources, mode‑matching, and control electronics introduce correlations that can either attenuate or amplify the effective divergence.
3. **Threshold choice.** The decision‑relevance threshold $\varepsilon=0.9$ is a design‑team stipulation; different engineering contexts may adopt stricter or looser values, shifting $k^{*}$ according to $\ln(1-\varepsilon)/\ln(1-\delta)$.

5. **Scope of terms.** We have demonstrated the method only for “photon”. Extending the analysis to other borrowed terms such as “quasiparticle” or “measurement” would require explicit native‑ontology predictions, which are beyond the scope of the present work.

### 6.2 Falsification condition

If a high‑fidelity simulation of $k=4$ independent photonic interferometers (including realistic mode overlap and loss) yields a total‑variation distance $D_{TV}^{(4)}\le 0.5$, i.e. far below the predicted $0.9375$, the compounding law would be empirically falsified for this context. Conversely, observing $D_{TV}^{(4)}\ge 0.95$ would support the analytic prediction.

### 6.3 Open questions

- How does partial indistinguishability (parameterised by a visibility $V$) modify the per‑element divergence $\delta$?
- What is the appropriate $\varepsilon$ for safety‑critical quantum‑control software versus exploratory research?
- Can the measure be integrated into automated design‑space‑exploration tools to flag semantic drift early?
- How does the measure behave in fault‑tolerant error‑corrected cycles where logical operations are compiled from many physical gates?

## 7. Practical Implications and Engineering Pathways

**(a) Intended users and impact.** Quantum‑hardware architects, compiler developers, and cross‑disciplinary project managers can employ $F_S$ to audit terminology in design specifications. If $F_S$ falls below a chosen $\varepsilon$ for a given system size, the team should replace the borrowed term with a vocabulary‑neutral description (e.g., “mode‑pair” instead of “photon”) to avoid mis‑aligned intuition.

**(b) Technology readiness.** The present work is a purely analytical derivation that has not undergone peer review; according to NASA’s scale it resides at TRL 2 (formulation of concept and analytical proof‑of‑concept).

**(c) Minimal next experiment.** Build a photonic testbed comprising four nominally independent $50/50$ beamsplitters fed by identical photon‑pair sources. Measure the empirical outcome distribution over the “same vs. split” observable and compute the empirical $D_{TV}^{(4)}$. An observed $D_{TV}^{(4)}\le 0.5$ would falsify the current compounding prediction; $D_{TV}^{(4)}\ge 0.9$ would confirm it.

**(d) Engineering constraints.**
- **Independence:** Requires spatially separated sources and independent phase‑stabilisation loops to approximate factorisation.
- **Detection efficiency:** High‑efficiency photon‑number‑resolving detectors are needed to avoid loss‑induced bias.
- **Mode matching:** Imperfect mode overlap directly reduces the native‑ontology bunching probability, altering $\delta$.
These constraints follow from the assumptions listed in Section 4.2.

**(f) Risks and misuse.** Over‑reliance on $F_S$ without considering hardware‑specific error correlations could lead to premature dismissal of useful terminology. If a design team treats $F_S$ as a hard safety threshold rather than a guideline, it may unnecessarily constrain innovation. Proper contextualisation of $\varepsilon$ and of the underlying assumptions mitigates these risks.

## 8. Conclusion

We have introduced **operational semantic fidelity** $F_S^{(n)}=1-D_{TV}^{(n)}$ as a quantitative, vocabulary‑neutral diagnostic for assessing when a borrowed quantum term becomes decision‑relevantly misleading. Applying the framework to the term “photon” yields a per‑element divergence of $1/2$, a compounding law $D_{TV}^{(k)}=1-2^{-k}$, and a crossing scale of $k^{*}=4$ ($\approx$ 8 photonic qubits) for a design‑team threshold $\varepsilon=0.9$.  The measure converts ontological concerns into actionable engineering specifications, while its limitations—idealised models, independence assumptions, and threshold arbitrariness—are explicitly stated. A concrete four‑interferometer experiment is proposed to validate or falsify the compounding prediction, establishing a clear pathway from theory to practice.

## Provenance and AI Involvement

- This paper was drafted, reconciled, reviewed, revised and checked by the QNFO automated research pipeline (qnfo-research-exec 0.30.1-codeagent). Language models were tools in that process; they are not authors. The named author is accountable for the content.
- Models: drafting by openai/gpt-oss-120b, zai-org/glm-5.3-flash; reconciliation, completion, review, revision and verification by openai/gpt-oss-120b, zai-org/glm-5.3-flash, moonshotai/kimi-k2.6, with the QNFO model router as a fallback.
- Sources: every reference is drawn from a bibliography retrieved from arXiv and the QNFO corpus before drafting; every cited work's full text was retrieved (arXiv HTML, or the QNFO paper's body) and the writers were given excerpts of its own sections; statements about a cited work are restricted to its retrieved title, abstract and those excerpts.
- Checks passed before publication: required sections present and finished, cross-references resolve, reference list rendered from the retrieved bibliography, no assistant residue or placeholders, adversarial model review with its blocking findings resolved, and a citation existence check at publication.
- Independent recomputation: a separately generated script recomputed 15 quantitative claims from the paper's stated inputs; 0 differed from the stated value at the stated precision.
- Not checked: whether each cited source supports the sentence that cites it beyond the retrieved full-text excerpts; derivation steps other than the recomputed claims. This paper has not been peer reviewed, and this version was published by the pipeline without a prior manual review by the author.

## References

[1] Problems and solutions of the Fourth International Students' Olympiad in Cryptography NSUCRYPTO. arXiv:1806.02059. https://arxiv.org/abs/1806.02059
[2] A combinatorial one-cocycle in a moduli space of knots from the Vassiliev invariant of order 3. arXiv:2212.03778. https://arxiv.org/abs/2212.03778
[3] Towards a classification of unitary elements of C*-algebras. arXiv:2304.01761. https://arxiv.org/abs/2304.01761
[4] Conformal Structure of Quantum Wave Mechanics. arXiv:2208.10969. https://arxiv.org/abs/2208.10969
[5] The structure of weak shocks in quantum plasmas. arXiv:0801.1295. https://arxiv.org/abs/0801.1295
[6] One-loop corrections to the photon propagator in the curved-space QED. arXiv:0906.3837. https://arxiv.org/abs/0906.3837
[7] Toward a topological description of Legendrian contact homology of unit conormal bundles. arXiv:2212.13705. https://arxiv.org/abs/2212.13705
[8] Families of superintegrable Hamiltonians constructed from exceptional polynomials. arXiv:1206.0480. https://arxiv.org/abs/1206.0480
[12] https://papers.qnfo.org/papers/semantic-fidelity-an-operational-measure-for-borrowed-quantum-terms-and-the-scal. QNFO: Semantic Fidelity: An Operational Measure for Borrowed Quantum Terms and the Scale at Which They Fail.
[13] https://papers.qnfo.org/papers/paper-beyond-the-qubit. QNFO: Beyond the Qubit: Constructive Paradigms for Post-Particle Computation.