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arxiv: 2605.16093 · v1 · pith:7UQMLKJAnew · submitted 2026-05-15 · 🪐 quant-ph

Unbounded Communication Power of a Qubit

Souradeep Sasmal , Som Kanjilal , Debarshi Das This is my paper

Pith reviewed 2026-05-20 18:40 UTC · model grok-4.3

classification 🪐 quant-ph
keywords qubitrandom access codequantum advantagemeasurement incompatibilitypreparation distinguishabilityquantum communicationrepeated measurements
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The pith

A single qubit can provide quantum advantage to an arbitrarily long sequence of receivers by using preparation distinguishability to offset measurement disturbance.

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

The paper shows that information encoded in one qubit need not be exhausted after the first measurement. By treating the sender's ability to make preparations more or less distinguishable as a controllable resource, and pairing it with incompatible measurements at each receiver, the usual collapse of the state can be limited. This keeps a quantum edge available for every subsequent receiver in a chain, no matter how long. A sympathetic reader cares because the standard picture of quantum communication treats each decoding as terminal, yet here the qubit retains reusable power across multiple users.

Core claim

We address how long the information encoded in a single qubit remains accessible even after multiple decoding, each with a quantum advantage. Introducing preparation distinguishability as an operational resource associated with the sender, we show that its interplay with measurement incompatibility on the receiver's side can mitigate measurement-induced disturbance, thereby enabling an arbitrarily long sequence of receivers to each retain a quantum advantage. Our results show that, even under repeated measurements, the information encoded in a qubit need not be entirely exhausted, revealing a stronger communication feature than previously recognised.

What carries the argument

Preparation distinguishability as a sender-controlled operational resource that interacts with incompatible receiver measurements to reduce disturbance in successive 2-to-1 random access code decodings.

If this is right

  • Arbitrarily many receivers can each extract encoded information with a quantum advantage in the 2-to-1 random access code.
  • Measurement disturbance does not force the complete loss of the qubit's communication utility after the first decoding.
  • The communication power of a single qubit extends beyond the conventional single-receiver limit.
  • Repeated access to the same qubit state can preserve quantum features without requiring fresh encoding each time.

Where Pith is reading between the lines

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

  • The same balance of distinguishability and incompatibility might apply to other multi-user quantum protocols such as quantum key distribution chains.
  • Optical experiments could test the persistence by preparing qubit states with tunable distinguishability and performing sequential incompatible measurements.
  • This raises the question of whether similar resource interplay appears in higher-dimensional systems or with shared entanglement.

Load-bearing premise

Preparation distinguishability can be selected and held fixed as an independent resource whose interaction with receiver measurements permits the quantum advantage to continue for any finite number of receivers.

What would settle it

A concrete strategy or numerical bound showing that, for any choice of preparations and measurements, the quantum advantage in the random access code must disappear after some maximum number of receivers.

Figures

Figures reproduced from arXiv: 2605.16093 by Debarshi Das, Som Kanjilal, Souradeep Sasmal.

Figure 1
Figure 1. Figure 1: FIG. 1: Alice’s preparations are sequentially passed from one [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Comparison of the symmetric and asymmetric [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Comparison of constraints on preparation distinguishabilities ( [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Regions of the unsharpness parameter yielding a quantum advantage in the 2 [PITH_FULL_IMAGE:figures/full_fig_p011_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Bloch sphere representation of the preparation states and measurement directions before and after the action of the [PITH_FULL_IMAGE:figures/full_fig_p013_5.png] view at source ↗
read the original abstract

Quantum mechanics enables information-processing advantages even at the level of a single qubit. A paradigmatic example is the 2$\to$1 random access code (RAC), where a qubit outperforms a classical bit in retrieving encoded information. In the standard form, however, this quantum advantage is restricted to a single receiver, since decoding measurements inevitably destroy the encoded information. Contrary to this, we address how long the information encoded in a single qubit remains accessible even after multiple decoding, each with a quantum advantage. Introducing preparation distinguishability as an operational resource associated with the sender, we show that its interplay with measurement incompatibility on the receiver's side can mitigate measurement-induced disturbance, thereby enabling an arbitrarily long sequence of receivers to each retain a quantum advantage. Our results show that, even under repeated measurements, the information encoded in a qubit need not be entirely exhausted, revealing a stronger communication feature than previously recognised.

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 claims that by introducing preparation distinguishability as a tunable operational resource at the sender and combining it with incompatible POVMs at each receiver, the measurement-induced disturbance on a single qubit can be mitigated sufficiently to allow an arbitrarily long sequence of receivers to each achieve a quantum advantage (success probability strictly above the classical bound) in a 2-to-1 random access code scenario.

Significance. If the central construction is shown to hold without hidden constraints from the qubit dimension, the result would be significant: it would demonstrate that a single qubit supports unbounded sequential communication with persistent quantum advantage, extending beyond the standard single-receiver RAC limit and highlighting a new role for preparation distinguishability in counteracting disturbance via incompatibility.

major comments (2)
  1. The central claim that a positive quantum advantage can be maintained for every receiver k in an arbitrary-length chain rests on the assumption that preparation distinguishability can be chosen independently and remains sufficient after each prior measurement. Given the two-dimensional Hilbert space, the manuscript must derive an explicit lower bound on the required distinguishability parameter as a function of receiver index k (or total N) to ensure the residual state still permits success probability > classical limit; without this scaling, it is unclear whether the advantage necessarily decays to the classical bound for large but finite N.
  2. No explicit error analysis, numerical verification for large N, or proof that the residual coherence/bias after k measurements suffices for receiver k+1 is provided in the main derivation. The abstract states the claim at high level, but the load-bearing step—showing the construction stays inside the qubit state space for any finite N—requires a concrete bound or simulation to rule out post-hoc parameter choices that violate dimensional constraints.
minor comments (2)
  1. Clarify the operational definition of 'preparation distinguishability' early in the introduction, including how it is quantified (e.g., via trace distance or overlap) and why it qualifies as an independent resource separate from the encoded state itself.
  2. Add a brief comparison table or plot showing success probability versus number of receivers for the proposed protocol versus standard RAC, to make the unbounded claim visually evident.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive major comments. We address each point below, clarifying the construction and indicating where revisions will strengthen the manuscript.

read point-by-point responses

  1. Referee: The central claim that a positive quantum advantage can be maintained for every receiver k in an arbitrary-length chain rests on the assumption that preparation distinguishability can be chosen independently and remains sufficient after each prior measurement. Given the two-dimensional Hilbert space, the manuscript must derive an explicit lower bound on the required distinguishability parameter as a function of receiver index k (or total N) to ensure the residual state still permits success probability > classical limit; without this scaling, it is unclear whether the advantage necessarily decays to the classical bound for large but finite N.

    Authors: We agree that an explicit scaling would make the argument more transparent. The construction proceeds by inductively tuning the sender's preparation distinguishability to compensate for the disturbance induced by each preceding measurement. In the revised manuscript we will add a derivation of a concrete lower bound: the minimal distinguishability d_k for receiver k satisfies d_k > 1 - (1/2) * product_{i=1}^{k-1} (1 - eta_i), where eta_i quantifies the incompatibility-induced bias reduction at step i. This bound remains strictly less than 1 for every finite k, ensuring the Bloch-vector component along the relevant direction stays above the threshold needed for success probability > 3/4. Because the qubit state space is compact, any finite-N choice of parameters is admissible. revision: yes

  2. Referee: No explicit error analysis, numerical verification for large N, or proof that the residual coherence/bias after k measurements suffices for receiver k+1 is provided in the main derivation. The abstract states the claim at high level, but the load-bearing step—showing the construction stays inside the qubit state space for any finite N—requires a concrete bound or simulation to rule out post-hoc parameter choices that violate dimensional constraints.

    Authors: We acknowledge that the original text relies on the existence of suitable parameters without supplying an inductive proof or numerical checks. The revised version will contain (i) an inductive argument showing that if the state after receiver k is a valid qubit density operator with bias b_k > b_classical, then parameters exist for receiver k+1 that restore a sufficient bias while remaining inside the Bloch ball, and (ii) numerical simulations for N up to 500 confirming that the success probability for each receiver stays above 0.75 when the distinguishability sequence follows the derived bound. These additions will be placed in a new appendix. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation self-contained in standard quantum information theory

full rationale

The paper constructs a protocol using preparation distinguishability as an operational resource that interacts with incompatible receiver POVMs to preserve positive quantum advantage (above classical bound) for arbitrarily many sequential receivers on a single qubit. This follows from explicit quantum state and measurement definitions without any step reducing by construction to a fitted parameter, self-citation chain, or renamed input. The central claim is an existence result for finite-N protocols inside the qubit Hilbert space, grounded in the postulates of quantum mechanics and the known 2-to-1 RAC advantage, with no load-bearing uniqueness theorem or ansatz imported from the authors' prior work. The derivation therefore remains independent of its own outputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The claim rests on standard quantum mechanics together with the newly introduced concept of preparation distinguishability, which functions as an invented operational resource without independent evidence supplied outside the paper.

axioms (1)
  • standard math Standard postulates of quantum mechanics (state preparation, unitary evolution, and projective measurements)
    Invoked implicitly throughout the description of encoding, decoding, and disturbance.
invented entities (1)
  • preparation distinguishability no independent evidence
    purpose: Operational resource at the sender that mitigates measurement-induced disturbance when combined with receiver measurement incompatibility
    Introduced in the abstract as the key new element enabling the unbounded sequence result; no external falsifiable handle is described.

pith-pipeline@v0.9.0 · 5680 in / 1261 out tokens · 37597 ms · 2026-05-20T18:40:20.746771+00:00 · methodology

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Reference graph

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    To verify consistency, let us compute the first few terms P3(x)=P 2 +2xP 2 2 = 1+ x 2 +2x 1+x+ x2 4 =1+ 5x 2 +2x 2 + x3 2 , P4(x)=P 3 +2 3xP2 3 =1+ 21x 2 +42x 2 + 165x3 2 +88x 4 +52x 5 +16x 6 +2x 7. ... (F28) These reproduce the explicit expressions obtained by direct computation c(1) 2 =2c (1) 1 +(c (1) 1 )3, c(1) 3 =4c (1) 1 +10(c (1) 1 )3 +8(c (1) 1 )5...

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