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arxiv: 2606.01262 · v1 · pith:FXWJL4R6new · submitted 2026-05-31 · 🪐 quant-ph

Large Alphabet Set Time-bin Encoded Measurement-Device-Independent Quantum Key Distribution

Gokul Agasthilingam , Harinee Natarajan , Varun Raghunathan This is my paper

Pith reviewed 2026-06-28 16:53 UTC · model grok-4.3

classification 🪐 quant-ph
keywords time-bin encodingMDI-QKDlarge alphabet setsecret key ratequantum key distributionsingle-photon detectorsfiber spools
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The pith

Expanding time-bin encoding to eight states boosts MDI-QKD secret key rates by factors of three and 2.63 at 2 km and 50 km.

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

The paper demonstrates an experimental implementation of time-bin encoded MDI-QKD using an expanded set of eight states instead of the usual two. By encoding information across more time bins, each successful coincidence measurement at the central node carries more bits of information, raising the overall secret key rate without requiring new hardware. Measurements with real fiber spools show rates of 401 bits per second at 2 km and 28 bits per second at 50 km for the eight-state version, compared to lower rates with standard encoding. This approach is also compared favorably to a similar scheme in the coherent-one-way protocol. The results suggest that alphabet expansion offers a direct path to higher performance in existing MDI-QKD setups.

Core claim

Using eight time-bin states rather than two in a standard MDI-QKD setup with single-photon detectors and fiber spools yields secret key rates of 401 bps at 2 km and 28 bps at 50 km, which are 3 times and 2.63 times higher than the conventional two-state rates of 133.6 bps and 10.7 bps respectively.

What carries the argument

The large alphabet set time-bin encoding, which increases the number of possible coincidence events and maps each successful alphabet exchange to multiple bits.

If this is right

  • Secret key rates improve by a factor of three at short distances and 2.63 at longer distances compared to two-state encoding.
  • The method requires no additional hardware modifications to the standard MDI-QKD setup.
  • Larger alphabet sets provide a clear advantage in MDI-QKD over similar encodings in the coherent-one-way protocol due to increased Z-basis coincidences.
  • This scaling approach supports higher key rates in quantum key distribution networks.

Where Pith is reading between the lines

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

  • The security model may need explicit verification for alphabets larger than eight if error rates deviate from predictions.
  • Further increases in alphabet size could yield additional rate gains if detector timing resolution allows.
  • Integration with other MDI-QKD variants might extend the benefit beyond time-bin encoding.

Load-bearing premise

The security proof and error-rate model for two-state time-bin MDI-QKD remain valid without change when the number of time bins increases to eight.

What would settle it

A measured secret key rate with eight states that falls below the two-state rate after accounting for the increased coincidence probability would indicate the model does not extend directly.

Figures

Figures reproduced from arXiv: 2606.01262 by Gokul Agasthilingam, Harinee Natarajan, Varun Raghunathan.

Figure 1
Figure 1. Figure 1: The Z [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Illustration of MDI-QKD transmission for four state encoding at Alice and Bob, with coincidence measurements performed at Charlie. The level-d coincidence measurement outcomes correspond to detection events of the form: 7|𝑑%*⟩0𝑑!+18, with clicks at i-th and j-th time-bins for detectors D1 and D2, respectively. pairs are analyzed to distinguish whether Alice and Bob transmitted different states among {|𝑓(⟩,… view at source ↗
Figure 4
Figure 4. Figure 4: (a) Schematic of the MDI-QKD experimental setup. Continuous wave lasers at Alice and Bob are modulated using intensity modulator (IM) and phase modulator (PM). A 90:10 beam splitter directs 10% of the optical power to an optical spectral analyzer (OSA) for wavelength monitoring. The modulated pulses are then sent to variable optical attenuators (VOAs) to set the mean photon number. An optical delay line (O… view at source ↗
Figure 7
Figure 7. Figure 7: (a) Comparison of the normalized SKR as a function of d considering ideal case for MDI-QKD (purple curve), and COW-QKD (green curve), simulated non-ideal case for MDI￾QKD (blue curve), and COW-QKD (red curve) and experimental results for MDI-QKD in (blue data points) and COW-QKD (red data points). (b) Table summarizing the normalized SKR for the ideal, non-ideal simulations, and experiments. and COW experi… view at source ↗
read the original abstract

We report on the experimental demonstration of an expanded basis set (called here as alphabet set) time-bin encoded measurement-device-independent quantum key distribution (MDI-QKD). While MDI-QKD is known to prevent detector-side attacks, it inherently suffers from reduced secret key rate (SKR) due to coincidence measurements performed at the central measurement node. To address this limitation, we encode states across multiple time-bins thereby increasing possible coincidence events and mapping each successful alphabet exchange to multiple bits, thereby increasing the information capacity per alphabet transmitted. Using a standard MDI-QKD set-up with real fiber spools and single-photon avalanche photodetectors, we achieve SKRs of 401 (133.6) bps and 28 (10.7) bps for 8 (2) encoded states for distances of 2 and 50 km, respectively, resulting in 3- and 2.63-times improvement, respectively when compared to the conventional two-state encoding. Furthemore, the large alphabet set MDIQKD results are compared with a similar encoding scheme implemented for coherent-one-way (COW) protocol. This comparison reveals a clear advantage of using a larger alphabet set for MDI-QKD, where increased Z-basis coincidence events yields increased SKR. These results provide important insights into the scalability of MDI-QKD key-rates without requiring additional hardware modifications, paving the way for next-generation, quantum key distribution networks.

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 reports an experimental demonstration of time-bin encoded MDI-QKD using an expanded 8-state alphabet set (versus the conventional 2-state encoding) over real fiber spools with SPAD detectors. It claims SKRs of 401 bps (133.6 bps) at 2 km and 28 bps (10.7 bps) at 50 km, corresponding to 3 imes and 2.63 imes improvements, respectively, and compares the results favorably to a similar large-alphabet COW implementation.

Significance. If the security analysis is shown to hold, the work provides a concrete experimental route to raising MDI-QKD key rates by increasing the number of time bins per symbol without new hardware, together with a direct head-to-head comparison against COW that isolates the benefit of higher Z-basis coincidence probability.

major comments (2)
  1. [Abstract / Security Analysis] Abstract and § on security analysis: the text states that the existing two-state time-bin MDI-QKD security proof and error-rate model are applied without modification to the 8-state case. Because both the Z-basis coincidence probability and the X-basis phase-error bound scale with the number of time bins, the phase-error upper bound and decoy-state inequalities must be re-derived or explicitly verified for eight bins; no such derivation or verification is supplied, rendering the numerical SKR values dependent on an unexamined extrapolation.
  2. [Results] Results section: the headline SKR figures (401 bps at 2 km, 28 bps at 50 km) are given without accompanying raw coincidence counts, measured error-rate tables, or explicit finite-key security-parameter bounds, preventing independent assessment of whether post-selection or finite-size corrections materially affect the reported improvement factors.
minor comments (2)
  1. [Abstract] Abstract: “Furthemore” is a typographical error.
  2. [Abstract] Notation: the parenthetical values (133.6 bps, 10.7 bps) are not defined in the abstract; clarify whether they represent 2-state rates or statistical uncertainties.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment point by point below.

read point-by-point responses

  1. Referee: [Abstract / Security Analysis] Abstract and § on security analysis: the text states that the existing two-state time-bin MDI-QKD security proof and error-rate model are applied without modification to the 8-state case. Because both the Z-basis coincidence probability and the X-basis phase-error bound scale with the number of time bins, the phase-error upper bound and decoy-state inequalities must be re-derived or explicitly verified for eight bins; no such derivation or verification is supplied, rendering the numerical SKR values dependent on an unexamined extrapolation.

    Authors: The time-bin MDI-QKD security framework is formulated for an arbitrary number of time bins; the Z-basis coincidence probability enters the key-rate formula directly as the sifting gain, while the X-basis phase-error bound is obtained from the same visibility measurement and decoy-state estimation procedure used in the two-state case. Because the state preparation in the X basis and the measurement outcomes remain structurally unchanged, the existing inequalities apply without modification. To satisfy the referee’s request for explicit verification, we will add a short appendix in the revised manuscript that substitutes N=8 into the decoy-state bounds and confirms that the phase-error upper bound remains valid under the same assumptions. revision: partial

  2. Referee: [Results] Results section: the headline SKR figures (401 bps at 2 km, 28 bps at 50 km) are given without accompanying raw coincidence counts, measured error-rate tables, or explicit finite-key security-parameter bounds, preventing independent assessment of whether post-selection or finite-size corrections materially affect the reported improvement factors.

    Authors: We agree that the raw data and finite-key parameters should be provided for full transparency. In the revised manuscript we will insert tables listing the measured Z- and X-basis coincidence counts, the observed error rates, the total number of pulses sent, and the concrete finite-key parameters (ε, ε_EC, n, etc.) used to obtain the reported secret-key rates. This addition will allow readers to reproduce the improvement factors of 3× and 2.63×. revision: yes

Circularity Check

0 steps flagged

No circularity; experimental rates reported directly from measurements

full rationale

The paper is an experimental demonstration reporting measured SKRs (401 bps at 2 km, 28 bps at 50 km) using real fiber spools and SPADs. No equations, derivations, or parameter-fitting steps are described that reduce by construction to inputs. The assumption that two-state security bounds apply unchanged to eight states is an unverified extrapolation, but it is not a self-referential derivation or fitted prediction within the paper's own chain. Central claims rest on direct experimental data, which are externally falsifiable and independent of any internal loop.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the experimental realization and on the unstated premise that the standard MDI-QKD security model applies unchanged to the eight-state alphabet; no new entities are postulated and no parameters are fitted to produce the reported rates.

axioms (1)
  • domain assumption Security proofs and error models for two-state time-bin MDI-QKD extend without modification to an eight-state alphabet
    The abstract invokes the conventional MDI-QKD framework and reports key rates without presenting a revised security analysis.

pith-pipeline@v0.9.1-grok · 5799 in / 1385 out tokens · 23529 ms · 2026-06-28T16:53:51.919695+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

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    Nature Photonics4, 686–689 (2010) https://doi.org/10.1038/nphoton.2010.214

    Lydersen L, et al. Hacking commercial quantum cryptography systems by tailored bright illumination. Nat. Photonics 2010;4:686–9. https://doi.org/10.1038/nphoton.2010.214 23. Lo HK, Curty M, Qi B. Measurement-device-independent quantum key distribution. Phys. Rev. Lett. 2012;108:130503. https://doi.org/10.1103/PhysRevLett.108.130503 24. Rubenok A, Slater J...

    work page doi:10.1038/nphoton.2010.214 2010

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    Modelling a measurement-device-independent quantum key distribution system

    Chan P, Slater JA, Lucio-Martinez I, Rubenok A, Tittel W. Modelling a measurement-device-independent quantum key distribution system. Opt. Express 2014;22:12716–36. https://doi.org/10.1364/OE.22.012716 40. Brádler K, Mirhosseini M, Fickler R, Broadbent A, Boyd RW. Finite-key security analysis for multilevel quantum key distribution. New J. Phys. 2016;18:0...

    work page doi:10.1364/oe.22.012716 2014