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Projective measurements certify the full 2 log(d) bits of device-independent randomness from any dimension d in bipartite systems.

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2026-06-26 14:01 UTC pith:TZOCKSAX

load-bearing objection Projective MUB protocols hit the full 2 log(d) DI randomness bound in every dimension, with explicit constructions and numerical noise checks.

arxiv 2606.21369 v2 pith:TZOCKSAX submitted 2026-06-19 quant-ph

Maximal global device-independent randomness from projective measurements in every dimension

M\'at\'e Farkas , Piotr Mironowicz , Remigiusz Augusiak This is my paper
classification quant-ph
keywords device-independent randomnessquantum random number generationprojective measurementsmutually unbiased basesbipartite quantum systemsrandomness certificationDIQRNG
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper shows that projective measurements, the type easiest to realize in the lab, can certify the maximum possible amount of device-independent randomness: exactly 2 log(d) bits from a d-dimensional bipartite quantum system, for every d at least 2. This rate is achieved by explicit protocols constructed from mutually unbiased bases. The authors further supply numerical bounds indicating that the certified rate remains positive under realistic experimental noise. A sympathetic reader would care because the result removes the need for more complex measurements while still saturating the theoretical upper limit on secure randomness extraction.

Core claim

Using projective measurements one can certify 2 log(d) bits of device-independent randomness from a bipartite system of local dimension d for every d ≥ 2, thus reaching the theoretically maximum possible rate of DIQRNG. Explicit protocols reaching this bound are constructed from mutually unbiased bases, and numerical analysis shows the protocols remain robust under imperfect implementations.

What carries the argument

Explicit protocols based on mutually unbiased bases that saturate the 2 log(d) randomness bound when only projective measurements are used on a bipartite system of local dimension d.

Load-bearing premise

The protocols built from mutually unbiased bases actually reach the full 2 log(d) certified randomness rate and the numerical noise analysis correctly bounds what is achievable in imperfect experiments.

What would settle it

Running the mutually unbiased bases protocol in dimension d=3 or higher and obtaining a certified randomness rate below 2 log(d) in an experiment with projective measurements would falsify the saturation claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • The maximum DIQRNG rate becomes achievable with the simplest class of measurements for every dimension.
  • Explicit constructions exist that work uniformly for all d ≥ 2.
  • Numerical evidence indicates positive certified rates survive moderate experimental noise.
  • No higher-dimensional or non-projective measurements are required to reach the information-theoretic limit.

Where Pith is reading between the lines

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

  • Practical DIQRNG setups could adopt these MUB-based protocols without changing their measurement hardware.
  • The same constructions might extend to other device-independent tasks such as randomness expansion or key distribution.
  • If the numerical noise bounds hold under real-device imperfections, the protocols offer a concrete route to high-rate secure randomness generators.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

0 major / 2 minor

Summary. The paper claims that projective measurements suffice to achieve the maximal rate of 2 log(d) bits of device-independent randomness from a bipartite system of local dimension d, for every d ≥ 2. Explicit protocols are constructed from mutually unbiased bases (MUBs) that saturate this bound, and numerical analysis is provided to bound the achievable rate under imperfect (noisy) implementations.

Significance. If the explicit constructions and saturation proofs hold, the result is significant: it shows that the information-theoretic maximum DI randomness rate is attainable with the simplest class of measurements (projective ones) that are already standard in experiments, removing the need for more complex POVMs or higher-dimensional resources in the asymptotic regime.

minor comments (2)
  1. The abstract states that the MUB-based protocols 'saturate the 2 log(d) bound'; a brief remark in the introduction or §2 on why the MUB choice is optimal (or at least sufficient) for all d would help readers unfamiliar with the dimension-dependent MUB existence results.
  2. In the numerical noise analysis, the method used to obtain the bounds (e.g., SDP formulation, relaxation order, or solver) is not mentioned in the provided abstract; adding one sentence on the computational technique would improve reproducibility.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive summary, significance assessment, and recommendation to accept the manuscript.

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper constructs explicit protocols from mutually unbiased bases that achieve the stated 2 log(d) bound using projective measurements, with separate numerical computation of noise robustness. No step reduces by construction to a fitted input, self-definition, or load-bearing self-citation chain; the maximum rate is treated as an external theoretical benchmark saturated by the constructions. The argument is self-contained against the provided claims and does not rely on renaming or smuggling ansatzes.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum mechanics for DI certification and the assumption that mutually unbiased bases exist and suffice for the protocols in every dimension d ≥ 2.

axioms (2)
  • standard math Quantum mechanics governs device-independent randomness certification from observed statistics
    The entire DIQRNG security proof framework relies on this background theory.
  • domain assumption Mutually unbiased bases exist and can be used to construct the protocols for every integer d ≥ 2
    The explicit protocols are stated to be based on MUBs; existence for all d is not proven in mathematics but is invoked here.

pith-pipeline@v0.9.1-grok · 5721 in / 1244 out tokens · 17628 ms · 2026-06-26T14:01:09.031717+00:00 · methodology

0 comments
read the original abstract

Device-independent random number generation (DIQRNG) is the most secure form of generating private randomness using quantum physical processes. Its strength lies in producing numbers that are impossible to predict by any eavesdropper restricted by the laws of quantum theory. Moreover, security is proven solely from observed measurement statistics, without the need to characterise or trust the devices used in random number generation. Implementing DIQRNG is, however, costly, as it requires high-quality entangled systems. It is therefore important to make the best use of available resources. In this work, we show that using projective measurements -- which are most readily implementable experimentally -- one can certify $2\log(d)$ bits of device-independent randomness from a bipartite system of local dimension $d$ for every $d \ge 2$, thus reaching the theoretically maximum possible rate of DIQRNG. We provide explicit protocols reaching $2\log(d)$ bits based on mutually unbiased bases. Furthermore, we compute numerical bounds on the rate for the case of imperfect implementations, showing that our protocols are robust to experimental noise.

Figures

Figures reproduced from arXiv: 2606.21369 by M\'at\'e Farkas, Piotr Mironowicz, Remigiusz Augusiak.

Figure 1
Figure 1. Figure 1: Certified randomness (min-entropy) as a function of [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗

discussion (0)

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Forward citations

Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Bell inequalities tailored to optimal global randomness certification

    quant-ph 2026-06 unverdicted novelty 7.0

    Two families of Bell inequalities are constructed whose maximal quantum violations certify 2 log d random bits for arbitrary d using d x d maximally entangled states.

  2. Bell inequalities tailored to optimal global randomness certification

    quant-ph 2026-06 conditional novelty 6.0

    New d-outcome Bell inequalities certify 2 log d bits of global randomness at maximal violation; analytic self-testing of the optimal strategy is proven for d=3.

Reference graph

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