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Cryptographic Fragility of Standard Quantum Repeater Protocols

Abhishek Sadhu, Sharu Theresa Jose

TL;DR

A Cryptographic Network Stack centered on a trapdoor verification protocol that exploits private randomness to restore operational stability without requiring channel characterization and shows that the standard BBPSSW distillation protocol recursively purifies error syndromes rather than entanglement.

Abstract

The security of the proposed quantum Internet relies on repeater protocols designed under the assumption of stochastic, characterizable noise. We demonstrate that in adversarial environments this assumption induces performance vulnerabilities for computationally bounded repeater nodes. We show that the standard BBPSSW distillation protocol recursively purifies error syndromes rather than entanglement. This leads to a state of low fidelity despite diagnostic metrics indicating perfect convergence. Moreover, we show that the verifier cannot check the adversarial influence via the maximum likelihood estimation algorithm since it is blind to computationally bounded observers. To address these vulnerabilities, we propose a Cryptographic Network Stack centered on a trapdoor verification protocol. The protocol exploits private randomness to restore operational stability without requiring channel characterization.

Cryptographic Fragility of Standard Quantum Repeater Protocols

TL;DR

A Cryptographic Network Stack centered on a trapdoor verification protocol that exploits private randomness to restore operational stability without requiring channel characterization and shows that the standard BBPSSW distillation protocol recursively purifies error syndromes rather than entanglement.

Abstract

The security of the proposed quantum Internet relies on repeater protocols designed under the assumption of stochastic, characterizable noise. We demonstrate that in adversarial environments this assumption induces performance vulnerabilities for computationally bounded repeater nodes. We show that the standard BBPSSW distillation protocol recursively purifies error syndromes rather than entanglement. This leads to a state of low fidelity despite diagnostic metrics indicating perfect convergence. Moreover, we show that the verifier cannot check the adversarial influence via the maximum likelihood estimation algorithm since it is blind to computationally bounded observers. To address these vulnerabilities, we propose a Cryptographic Network Stack centered on a trapdoor verification protocol. The protocol exploits private randomness to restore operational stability without requiring channel characterization.
Paper Structure (10 sections, 3 theorems, 16 equations)

This paper contains 10 sections, 3 theorems, 16 equations.

Table of Contents

  1. Introduction
  2. The adversarial strategy
  3. Cryptographic Network Stack
  4. Discussion
  5. Acknowledgements
  6. Analysis of the BBPSSW Map Under Adversarial Perturbation
  7. Analysis of entanglement filtering Under Adversarial Perturbation
  8. Measure-Theoretic Analysis of Tomographic Blindness
  9. Security Reduction for Trapdoor Verification
  10. Security Reduction for Blind Schur-Sampling

Key Result

Theorem 1

Let $\rho^{(m)}_{\text{jam}}$ denote the state after $m$ rounds of the recursive BBPSSW protocol when applied to the adversarial state eq:jammingstate. For any polynomial repeater runtime $m \cdot t_{BBPSSW} \ll \tau$ and noise parameter $\eta \in (0, 1]$, the protocol admits a unique and locally st

Theorems & Definitions (3)

  • Theorem 1: Purification Divergence
  • Proposition 1: Tomographic Blindness
  • Theorem 2: Trapdoor Security