Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Finite Key Rates for QKD Protocols with Data Filtering

Walter O. Krawec

TL;DR

The paper addresses finite-key security for QKD protocols that employ data filtering and discarding. It develops a general security proof framework that combines Bouman–Fehr quantum sampling with entropic uncertainty to bound the min-entropy of the non-discarded data and to derive a finite-key key length expressed as $\ell = \min_{c_0\ge n_0}[c_0\cdot c - \log_2\gamma(\Psi,\mathcal{S},c_0)] - \lambda_{EC} - 2\log_2\frac{1}{\sqrt{\epsilon_\delta^{cl}}}$. The main contributions include a four-step proof strategy (ideal-state construction, propagation through filtering, final entropy bound, and a robust reduction to the real protocol) and the application to Extended B92, yielding the first finite-key security proof against general coherent attacks for the full protocol. The results provide a concrete finite-key rate bound under depolarizing noise and demonstrate consistency with asymptotic limits while offering improvements over previous finite-key analyses at low signal counts, highlighting practical relevance for secure QKD with data filtering.

Abstract

In this paper, we derive a new proof of security for a general class of quantum cryptographic protocol involving filtering and discarded data. We derive a novel bound on the quantum min entropy of such a system, based in large part on properties of a certain classical sampling strategy. Finally, we show how our methods can be used to readily prove security of the Extended B92 protocol, providing the first finite key proof of security for this protocol against general, coherent, attacks.

Finite Key Rates for QKD Protocols with Data Filtering

TL;DR

The paper addresses finite-key security for QKD protocols that employ data filtering and discarding. It develops a general security proof framework that combines Bouman–Fehr quantum sampling with entropic uncertainty to bound the min-entropy of the non-discarded data and to derive a finite-key key length expressed as . The main contributions include a four-step proof strategy (ideal-state construction, propagation through filtering, final entropy bound, and a robust reduction to the real protocol) and the application to Extended B92, yielding the first finite-key security proof against general coherent attacks for the full protocol. The results provide a concrete finite-key rate bound under depolarizing noise and demonstrate consistency with asymptotic limits while offering improvements over previous finite-key analyses at low signal counts, highlighting practical relevance for secure QKD with data filtering.

Abstract

In this paper, we derive a new proof of security for a general class of quantum cryptographic protocol involving filtering and discarded data. We derive a novel bound on the quantum min entropy of such a system, based in large part on properties of a certain classical sampling strategy. Finally, we show how our methods can be used to readily prove security of the Extended B92 protocol, providing the first finite key proof of security for this protocol against general, coherent, attacks.

Paper Structure

This paper contains 4 sections, 4 theorems, 34 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Main Result
  4. Application: Extended B92

Key Result

Lemma 1

Let $\ket{\psi}_{AE} = \sum_{a\in J}\ket{a}^M\ket{E_a}$ be a quantum state, with $J\subset\{0,1\}^n$. Assume a measurement of the $A$ system is made in some other orthonormal basis $N$, resulting in quantum state $\rho_{NE}$. Then: where $c = \max_{i,j}|\braket{n_i|m_j}|^2$.

Figures (2)

  • Figure 1: Evaluating our finite key-rate result $\ell/N$ (Solid), where $N$ is the total number of signals sent, and comparing to asymptotic results from lucamarini2009robust (Dashed). Left: Ideal devices ($x=1$ in the POVM); Right: practical devices ($x=\cos^2\frac{\theta}{2}$ for the measurement POVMs). Here, we test $\theta = \pi/3$ for various noise levels, $Q$. Note the change in $y$-axis scale between the two figures. Similar results are found for other $\theta$, with decreasing key-rates as $\theta$ decreases (which is a property of this protocol lucamarini2009robust).
  • Figure 2: Comparing our new result (Solid) from finite key results in amer2020finite (Dashed) for $\theta = \pi/2$ and $\theta = \pi/3$ with ideal measurement devices. Here, the noise parameter is $Q=1\%$. We note our result gives better key-rates in lower signal counts; similar trends were found in the practical device setting and other noise levels. See text for additional discussion on how to compare.

Theorems & Definitions (5)

  • Lemma 1
  • Theorem 1
  • Lemma 2
  • Theorem 2
  • proof