The Eigenvector Protocol on Scalable PCM-Augmented Photonic Processors: Securing Device-Independent Quantum Key Distribution Against Post-Quantum Correlations
The convergence of advanced photonic hardware and foundational quantum information principles offers a pathway to close critical security loopholes in device-independent quantum key distribution (DI-QKD). This article examines the Eigenvector Protocol, realised on phase-change material (PCM)-augmented photonic processors such as LightPro, as a physical implementation of device-independent harmonic spectroscopy. By scaling random access code (RAC) games and computing the Information Causality (IC) sum, the protocol empirically certifies the positive semidefiniteness (PSD) of bipartite correlation kernels without assuming quantum mechanics. This capability bounds the "post-quantum" regime—encompassing almost-quantum correlations described by relaxations of the Navascués–Pironio–Acín (NPA) hierarchy—ensuring that any violation of kernel positivity inevitably breaches Information Causality. In cryptographic terms, it eliminates the finite-resource loophole that could allow supra-quantum adversaries to compromise DI-QKD. Scaling integrated photonic circuits thus becomes a cryptographic imperative, not merely an engineering goal. (Süß, 2025; Navascués et al., 2015; Pawłowski et al., 2009). Also available on Academia.edu: https://www.academia.edu/attachments/132331018/download_file?s=portfolio
The convergence of advanced photonic hardware and foundational quantum information principles offers a pathway to close critical security loopholes in device-independent quantum key distribution (DI-QKD). This article examines the Eigenvector Protocol, realised on phase-change material (PCM)-augmented photonic processors such as LightPro, as a physical implementation of device-independent harmonic spectroscopy. By scaling random access code (RAC) games and computing the Information Causality (IC) sum, the protocol empirically certifies the positive semidefiniteness (PSD) of bipartite correlation kernels without assuming quantum mechanics. This capability bounds the "post-quantum" regime—encompassing almost-quantum correlations described by relaxations of the Navascués–Pironio–Acín (NPA) hierarchy—ensuring that any violation of kernel positivity inevitably breaches Information Causality. In cryptographic terms, it eliminates the finite-resource loophole that could allow supra-quantum adversaries to compromise DI-QKD. Scaling integrated photonic circuits thus becomes a cryptographic imperative, not merely an engineering goal. (Süß, 2025; Navascués et al., 2015; Pawłowski et al., 2009). Also available on Academia.edu: https://www.academia.edu/attachments/132331018/download_file?s=portfolio
The principle of Information Causality (IC) has served as a fundamental postulate in quantum information theory, establishing critical bounds on the strength of quantum correlations and differentiating the quantum formalism from generalized non-signaling theories. While IC successfully recovers the Tsirelson bound for the first Fourier harmonic of the bipartite correlation function, its ability to enforce the full positive semi-definiteness (PSD) of the correlation kernel for all higher-order harmonics has remained a persistent axiomatic gap. Traditional Random Access Code (RAC) protocols, reliant on fixed-basis encodings, are intrinsically blind to high-frequency negative harmonics. This paper provides an exhaustive analysis of the Eigenvector Protocol—a novel -bit RAC utilizing a probabilistic mixing strategy over the eigenvector components of the correlation kernel matrix—which definitively proves that IC enforces kernel positivity for all harmonics. Furthermore, this report extensively investigates the physical implementation of the Eigenvector Protocol utilizing state-of-the-art integrated photonics. We analyze the severe scalability limitations of bulk quantum optics and traditional Mach-Zehnder Interferometer (MZI) meshes, including phase noise, temporal distributed crosstalk, and quantization errors. Also available on Academia.edu: https://www.academia.edu/attachments/132330461/download_file?s=portfolio
Süß (2026) presents a concise yet technically ambitious five-page preprint that claims to close a longstanding axiomatic gap in the information-theoretic reconstruction of bipartite quantum correlations. By introducing an explicitly constructed N-bit Random Access Code (RAC) protocol—the "Eigenvector Protocol"—the author proves analytically and verifies numerically that the principle of Information Causality (IC) alone enforces the positive semi-definiteness (PSD) of all Fourier-harmonic components of the bipartite correlation kernel for every integer k ≥ 1. This result completes the derivation chain No-Signaling + Rotational Covariance + IC ⇒ E(Δθ) = −cos(Δθ) that had previously relied on partial or numerical evidence. The work is self-contained, device-independent in spirit, and directly addresses the open Mamun, SM (2026)……………………….1 Reviewing Süß (2026), "Information Causality Implies Kernel Positivity: A Complete Proof via the Eigenvector Protocol" question left by Pawłowski et al. (2009) and subsequent numerical scans (Süß, 2025, 2026a, 2026b). This paper outlines a detailed summary, methodological critique, comparison with prior literature, assessment of strengths and limitations, and discussion of broader implications. Mamun, SM (2026)……………………….2 Reviewing Süß (2026), "Information Causality Implies Kernel Positivity: A Complete Proof via the Eigenvector Protocol" Also available on Academia.edu: https://www.academia.edu/attachments/132327893/download_file?s=portfolio
Part 6 of this record supersedes Parts 1-5. Earlier parts conjectured that Information Causality (IC) alone enforces the positive-semidefinite (PSD) structure of translation-invariant correlation kernels; the Sole-Origin and Eigenvector versions (Parts 1, 4, 5) claimed constructive proofs. This paper withdraws those proofs and replaces them with what can be proven. Two structure theorems show the withdrawal is structural, not incidental. The Barrier Lemma: any protocol whose measurement settings are independent of the encoded data satisfies S ≤ E(0)²‖u‖₂² ≤ 1, for every Bob strategy and every resource model (verified by exhaustive maximization over all Bob functions at N=4). The Pyramid Factorization Theorem: the Pawłowski concatenation satisfies S_{2ⁿ} = Π levels ≤ (sup S₂)ⁿ, so nesting can never rescue a kernel that a single level cannot detect. Two positive results take their place. A visibility dichotomy: at sub-unit visibility, explicitly non-PSD kernels are quantum-realizable via a Tsirelson factorization with sign-flipped harmonics, so no correlation principle can enforce PSD there; at unit visibility (E(0) = −1), Cauchy-Schwarz rigidity forces single-family Gram structure. The main theorem: Macroscopic Locality implies kernel positivity at unit visibility (via the Q¹ characterization of ML plus the rigidity argument). The axiomatic gap open since Pawłowski et al. (2009) is thereby closed, by Macroscopic Locality. Corollary: every unit-visibility non-PSD kernel lies outside the Almost-Quantum set, confirmed numerically by robust NPA-1+AB semidefinite programming (N = 7 settings, Clarabel, PSD control at 10⁻⁹). Whether the strictly weaker principle IC suffices remains open, and is sharpened by seven benchmark kernels, unit visibility, non-PSD, provably outside Almost Quantum, that resist every IC protocol tested: optimized N=2/3 functionals, general random-access codes up to four bits, the full concatenation pyramid with free angles, linear parity encodings, entropic and mutual-information functionals, and continuous-angle protocols. Either a fundamentally new protocol detects them (IC ⇒ PSD), or one of them satisfies IC (IC strictly weaker than ML here). Both outcomes are discoveries; the benchmark coefficients are given in full and machine-readable. An open verification suite (6 self-contained Python scripts, MIT license, ~90 s runtime) is included and reproduces every numerical claim: kernel validity, the Barrier Lemma (three exact checks), the Pyramid Factorization, the Tsirelson factorization of the dichotomy, the NPA-1+AB distances for all seven benchmarks, and the H² bound. Following the documentation practice of this series, all withdrawn claims and their precise failure modes are recorded, including one hypothesis raised and refuted during review of this work.
The concept of the Device-Independent Quantum Key Distribution (DI-QKD) constitutes the minimalist paradigm for quantum cryptography, in which the security of the distributed secret key is fully assured by the statistical properties of the data being shared between the parties that perform a quantum-based protocol. In particular, the secrecy of the distributed key is ultimately guaranteed not only thanks to the quantum nature of the underlying scheme, but also without making any assumptions about the operation of the devices being employed. Such a conservative approach is possible thanks to the non-local correlations exhibited within the shared data, i.e., the correlations of genuine quantum origin that, due to violation of a particular Bell inequality, cannot be explained by any form of common randomness pre-available to the parties. Such violation, however, must be revealed without performing any post-selection on the data, what would then open the so-called detection loophole and jeopardize the security of the protocol. In spite of the tremendous advances recently made to achieve higher detection efficiencies in Bell-violation experiments, DI-QKD remains a very experimentally difficult task due to the exponential increase of loss in the channel, e.g., implemented with optical fibres, with the distance separating the parties involved. Here, we describe a new and plausible solution to overcome the crucial problem of channel loss in the frame of DI-QKD optical implementations. In particular, we propose a novel protocol inspired by the entanglement swapping schemes, which by the usage of the state-of-the-art (e.g., quantum-dot-based or heralded) single-photon sources has potential, for the first time, to be implementable with current photonic and linear optics technologies. While allowing for any transmission losses that only decrease the rate of the key distribution without creating vulnerability, it tolerates overall detection efficiency at the 90% level even when requiring strict device-independence. We compare our scheme against protocols that involve sources based on spontaneous parametric down-conversion (SPDC), in order to explicitly show and explain why such SPDC-based proposals—even when enhanced by the entanglement swapping or qubit amplification techniques—are then largely outperformed when physical imperfections are rigorously taken into account.
This document announces the release and empirical validation of the Eigenvector Protocol Suite v4.0.4, a commercial-grade software implementation of the mathematical framework introduced in the preprint "Information Causality Implies Kernel Positivity: A Complete Proof via the Eigenvector Protocol." The software provides a real-time security layer for Quantum Key Distribution (QKD) networks by analyzing the Fourier decomposition of angular correlation functions. We report the successful validation of the software against two distinct real-world datasets: a 184,850-measurement QKD dataset and the NANOGrav 15-year pulsar timing array dataset. The software correctly distinguishes between device noise and structural anomalies, demonstrating its domain-agnostic capability to enforce Information Causality constraints. Note: The source code, architectural details, and proprietary algorithms of the Suite v4.0.4 are closed-source and not included in this publication. This document serves to establish the priority of the software's capabilities and empirical validation.
Abstract Device-independent quantum key distribution (DI-QKD) provides the gold standard for secure key exchange. Not only does it allow for information-theoretic security based on quantum mechanics, but it also relaxes the need to physically model the devices, thereby fundamentally ruling out many quantum hacking threats to which non-DI QKD systems are vulnerable. In practice though, DI-QKD is very challenging. It relies on the loophole-free violation of a Bell inequality, a task that requires high quality entanglement to be distributed between distant parties and close to perfect quantum measurements, which is hardly achievable with current technology. Notwithstanding, recent theoretical and experimental efforts have led to proof-of-principle DI-QKD implementations. In this article, we review the state-of-the-art of DI-QKD by highlighting its main theoretical and experimental achievements, discussing recent proof-of-principle demonstrations, and emphasizing the existing challenges in the field.