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Rigorous phase-error-estimation security framework for QKD with correlated sources

Guillermo Currás-Lorenzo, Margarida Pereira, Kiyoshi Tamaki, Marcos Curty

TL;DR

A simple yet powerful mathematical framework is introduced to directly extend phase-error-estimation-based security proofs for imperfect but uncorrelated sources to also incorporate encoding correlations, significantly narrowing the gap between theoretical security guarantees and real-world QKD implementations.

Abstract

Practical QKD modulators introduce correlations between consecutively emitted pulses due to bandwidth limitations, violating key assumptions underlying many security proof techniques. Here, we address this problem by introducing a simple yet powerful mathematical framework to directly extend phase-error-estimation-based security proofs for imperfect but uncorrelated sources to also incorporate encoding correlations. Our framework overcomes important limitations of previous approaches in terms of generality and rigor, significantly narrowing the gap between theoretical security guarantees and real-world QKD implementations.

Rigorous phase-error-estimation security framework for QKD with correlated sources

TL;DR

A simple yet powerful mathematical framework is introduced to directly extend phase-error-estimation-based security proofs for imperfect but uncorrelated sources to also incorporate encoding correlations, significantly narrowing the gap between theoretical security guarantees and real-world QKD implementations.

Abstract

Practical QKD modulators introduce correlations between consecutively emitted pulses due to bandwidth limitations, violating key assumptions underlying many security proof techniques. Here, we address this problem by introducing a simple yet powerful mathematical framework to directly extend phase-error-estimation-based security proofs for imperfect but uncorrelated sources to also incorporate encoding correlations. Our framework overcomes important limitations of previous approaches in terms of generality and rigor, significantly narrowing the gap between theoretical security guarantees and real-world QKD implementations.
Paper Structure (2 sections, 8 theorems, 86 equations, 1 figure)

This paper contains 2 sections, 8 theorems, 86 equations, 1 figure.

Table of Contents

  1. Security framework based on phase-error estimation
  2. Extending existing phase-error bounds to incorporate encoding correlations

Key Result

Corollary 1

Consider a prepare-and-measure QKD protocol with an uncorrelated source. In each round $k$, the source is characterized by a family of states $\{\ket*{\psi_{j_k}^{(k)}}_{T_k}\}_{j_k \in \mathcal{J}}$ indexed by the setting $j_k \in \mathcal{J}$. Suppose there exists an admissibility set $\mathcal{S} Now consider the analogous protocol with a source exhibiting correlations up to length $l_c$, where

Figures (1)

  • Figure 1: Secret-key rate versus channel attenuation for a BB84 protocol with a source suffering from LTI correlations, assuming the exponential decay model in \ref{['eq:delta_bound']}. The secret-key rates are obtained by combining \ref{['cor:fidelity bound']} with the uncorrelated security analysis of Ref. curras-lorenzoSecurityFramework2025. The solid lines correspond to $\xi_1 = 10^{-6}$ and the dashed lines correspond to $\xi_1 = 10^{-3}$. The lines labelled by $l_c=1$ and $l_c=5$ consider correlations truncated artificially at length $l_c$ (i.e. $\xi_l = 0$ for $l > l_c$), while $l_c = \infty$ corresponds to unbounded correlations handled via \ref{['lem:trace_distance_bound']}. The dashed dotted line corresponds to the ideal case of no correlations.

Theorems & Definitions (16)

  • Corollary 1
  • Corollary 2: Fidelity bound to reference states
  • Lemma 1
  • Theorem 1: Variable-length security of QKD protocols from EUR+LHL
  • proof
  • Remark 1
  • Theorem 2
  • proof
  • Corollary 1: Per-round admissibility conditions
  • Remark 2
  • ...and 6 more