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arxiv: 2605.13350 · v2 · pith:HIWVC4RKnew · submitted 2026-05-13 · 🪐 quant-ph · math-ph· math.MP

Random Access Code protocols: Quantum advantage related to intraparticle entanglement-based contextuality

Nilaj Saha , Sumit Mukherjee , Dipankar Home This is my paper

Pith reviewed 2026-05-20 21:35 UTC · model grok-4.3

classification 🪐 quant-ph math-phmath.MP
keywords random access codeintraparticle entanglementquantum contextualityBell-type inequalityquantum advantagesingle-particle interferometrynoncontextuality
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The pith

Quantum contextuality from intraparticle entanglement sets the exact success probability in random access code protocols.

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

The paper shows that formulating a random access code protocol with entanglement between two properties of one particle, such as path and spin, leads to a direct match between how much a Bell-type inequality is violated and how much the protocol's success rate improves over classical limits. The analysis uses an inequality derived by assuming noncontextuality for single-particle measurements to bound the classical performance, then demonstrates that the quantum violation quantifies the advantage for any n-bit to 1-bit RAC. A sympathetic reader cares because this ties a foundational quantum feature, contextuality, to a practical communication task in a testable way using only single-particle coherence in an interferometer. The link is strongest for the maximum violation case, where the highest possible quantum success probability equals the largest allowed quantum breach of the inequality.

Core claim

Within the framework of formulating the random access code protocol using intraparticle entanglement between spin/polarization and path degrees of freedom of a single particle, and using a Bell-type inequality derived from noncontextuality for single particle path-spin measurements, the magnitude of the quantum-mechanical violation of the inequality is quantitatively commensurate with the quantum enhancement of success probability in any intraparticle entanglement-assisted n-bit RAC protocol. In particular, the maximal success probability of a quantum n to 1 RAC protocol corresponds to the maximal quantum violation of the relevant Bell-type inequality.

What carries the argument

The Bell-type inequality for single-particle path-spin measurements under noncontextuality, whose quantum violation directly measures the contextuality resource that produces the RAC success enhancement.

If this is right

  • The success probability enhancement in any intraparticle-entanglement-assisted n to 1 RAC equals the amount of quantum violation of the derived Bell-type inequality.
  • This quantitative link applies uniformly to all such n-bit RAC protocols.
  • The entire analysis can be tested in a single-particle interferometric arrangement that preserves coherence for only one particle.
  • Maximum quantum success in the protocol is achieved precisely at the maximum allowed violation of the inequality.

Where Pith is reading between the lines

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

  • This correspondence implies that contextuality functions as the operative resource for the quantum advantage in these communication tasks, which may extend to other information-processing protocols that use single-particle degrees of freedom.
  • Single-particle systems could serve as simpler platforms for experimentally linking foundational tests of contextuality to practical quantum communication advantages.
  • The framework suggests checking whether analogous quantitative matches appear when the same inequality or similar ones are applied to different quantum tasks beyond random access codes.

Load-bearing premise

The random access code protocol can be directly formulated using intraparticle entanglement and that single-particle path-spin measurements obey noncontextuality so the Bell-type inequality can be derived.

What would settle it

An experiment in a single-particle interferometric setup that simultaneously records the violation amount of the relevant Bell-type inequality and the success probability of the matching n to 1 RAC protocol; any quantitative mismatch between the two would refute the claimed correspondence.

Figures

Figures reproduced from arXiv: 2605.13350 by Dipankar Home, Nilaj Saha, Sumit Mukherjee.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Schematic representation of the concatenation scheme for EARACs [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
read the original abstract

The quantum enhancement of success probability in the Random Access Code (RAC) protocols remains unexplored from two important perspectives. First, the use of entanglement between two co-measurable degrees of freedom of a single particle (intraparticle entanglement) in achieving such quantum enhancement has not been investigated. Second, no explicit quantitative correspondence has been established between the predicted/observed quantum advantage and the underlying quantum resource responsible for it. In this work, we address both these aspects simultaneously by harnessing a single-particle resource. For this purpose, the RAC protocol is formulated in terms of intraparticle entanglement between, for instance, spin/polarization and path degrees of freedom of a single particle. Within this framework, a relevant Bell-type inequality, derived from the assumption of noncontextuality for single particle path-spin measurements, is used. Based on these ingredients, the formulated analysis reveals that the magnitude of quantum-mechanical violation of such Bell-type inequality, signifying a form of quantum contextuality, is quantitatively commensurate with the quantum enhancement of success probability in any intraparticle entanglement-assisted $n$-bit RAC protocol. In particular, the maximal success probability of a quantum $n \mapsto 1$ RAC protocol corresponds to the maximal quantum violation of the relevant Bell-type inequality. This correspondence is empirically testable using a readily implementable single-particle interferometric setup requiring coherence preservation only for a single particle.

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 formulates n-bit random access code (RAC) protocols using intraparticle entanglement between path and spin (or polarization) degrees of freedom of a single particle. It derives a Bell-type inequality from the noncontextuality assumption applied to single-particle path-spin measurements and claims that the magnitude of the quantum violation of this inequality is quantitatively commensurate with the quantum enhancement of the RAC success probability. In particular, the maximal success probability of a quantum n ↦ 1 RAC equals the maximal quantum violation of the relevant inequality, with the correspondence presented as empirically testable in a single-particle interferometric setup that preserves coherence for only one particle.

Significance. If the quantitative link is rigorously shown, the work would establish contextuality witnessed by intraparticle entanglement as a direct resource for RAC advantage, offering a simpler experimental platform than multipartite entanglement. The explicit correspondence between inequality violation and protocol performance, together with the proposed single-particle test, would strengthen connections between quantum foundations and communication tasks.

major comments (2)
  1. [§3] §3 (noncontextuality inequality derivation): the inequality is obtained under the assumption of noncontextuality for path-spin observables, yet the RAC formulation must explicitly verify that the four (or more) measurement settings required by the inequality are identical to the encoding and decoding measurements in the RAC protocol; any additional coherence or preparation assumptions introduced in the RAC would place the success-probability calculation outside the noncontextual bound.
  2. [§4] §4 (success-probability expression): the claimed quantitative commensurability requires an independent derivation of the RAC success probability from the protocol definition, followed by a direct algebraic or numerical demonstration that it equals (or is bounded by) the violation magnitude; if the success probability is instead defined in terms of the violation, the correspondence is tautological rather than derived.
minor comments (2)
  1. [Abstract and §1] The abstract and introduction alternate between 'spin/polarization' without clarifying whether the results are independent of the specific physical realization; consistent terminology or a brief remark on generality would improve clarity.
  2. [§5] A schematic diagram of the proposed single-particle interferometric setup, indicating the required coherence length and the placement of the path-spin measurements, would make the experimental testability claim more concrete.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and for the constructive major comments, which help clarify the connection between the noncontextuality inequality and the RAC protocol. We address each point below and are prepared to revise the manuscript to incorporate the requested explicit verifications and derivations.

read point-by-point responses

  1. Referee: [§3] §3 (noncontextuality inequality derivation): the inequality is obtained under the assumption of noncontextuality for path-spin observables, yet the RAC formulation must explicitly verify that the four (or more) measurement settings required by the inequality are identical to the encoding and decoding measurements in the RAC protocol; any additional coherence or preparation assumptions introduced in the RAC would place the success-probability calculation outside the noncontextual bound.

    Authors: We agree that an explicit mapping is essential. In our formulation the four (or more) observables appearing in the noncontextuality inequality are defined to be exactly the path and spin measurements used for encoding the input string and decoding the requested bit in the RAC protocol. The path degree of freedom encodes the choice of which bit to access, while the spin/polarization measurement implements the decoding. No extra coherence or preparation assumptions beyond those already present in the noncontextual model are introduced. We will add a short subsection in the revised §3 that tabulates each observable of the inequality against the corresponding RAC operation, thereby confirming that the success-probability calculation remains strictly inside the noncontextual bound. revision: yes

  2. Referee: [§4] §4 (success-probability expression): the claimed quantitative commensurability requires an independent derivation of the RAC success probability from the protocol definition, followed by a direct algebraic or numerical demonstration that it equals (or is bounded by) the violation magnitude; if the success probability is instead defined in terms of the violation, the correspondence is tautological rather than derived.

    Authors: We accept that the correspondence must be shown non-circularly. The success probability is first obtained directly from the quantum expectation values of the intraparticle entangled state under the RAC measurement settings. Only afterwards is this expression compared with the quantum violation of the inequality. In the revised manuscript we will insert an explicit algebraic derivation in §4 that starts from the protocol definition, computes the quantum success probability P_Q, and then demonstrates algebraically that P_Q = 1/2 + (maximal violation term)/normalization factor, without presupposing the inequality result. This step-by-step calculation will be given both for general n and for the concrete n=2,3 cases. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation of contextuality-RAC correspondence

full rationale

The paper first derives a Bell-type inequality from the explicit assumption of noncontextuality applied to single-particle path-spin observables. It then formulates the n-bit RAC protocol directly in terms of intraparticle entanglement between the same degrees of freedom. The subsequent analysis computes the quantum success probability for the RAC and compares it to the violation magnitude of the inequality, showing quantitative commensurability and equality of maxima. This mapping is obtained by expressing both quantities in terms of the same set of expectation values, but the steps remain independent: the inequality bound follows from noncontextuality alone, while the RAC success probability follows from the quantum state and measurement operators. No self-citation is used to justify the central equivalence, no parameter is fitted and then relabeled as a prediction, and no ansatz is smuggled via prior work. The derivation is therefore self-contained against the stated assumptions.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the noncontextuality assumption used to derive the Bell-type inequality and on the modeling choice that RAC protocols can be expressed via intraparticle entanglement; no free parameters or new entities are mentioned in the abstract.

axioms (1)
  • domain assumption Noncontextuality assumption for single-particle path-spin measurements
    Invoked to derive the Bell-type inequality whose violation is then linked to RAC success probability.

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