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A Quantum-Memory-Free Quantum Secure Direct Communication Protocol Based on Privacy Amplification of Coded Sequences

Shang-Jen Su, Shi-Yuan Wang, Matthieu R. Bloch

TL;DR

This work addresses secure direct quantum communication without quantum memories by introducing a quantum-memory-free QSDC protocol (QMF-QSDC) that avoids wiretap coding and relies on universal privacy amplification of coded sequences. The authors develop a formal framework and theorems enabling secrecy extraction against quantum side information under collective attacks, with a focus on non-i.i.d. codewords and block-based operation. They derive both asymptotic and finite-length bounds on the extractable key length, using entropy accumulation and one-shot Renyi-based analyses, and discuss special-code simplifications and unitary-encoder properties. The results provide rigorous, practical guarantees for robust QMF-QSDC, enabling secure, memoryless quantum communications with a reusable key pool across blocks.

Abstract

We develop an information-theoretic analysis of Quantum-Memory-Free (QMF) Quantum Secure Direct Communication (QSDC) under collective attacks as an alternative to the conventional Quantum Key Distribution (QKD) protocol with one-time pads. Our main contributions are: 1) a QMF-QSDC protocol that only relies on universal hashing of coded sequences without wiretap coding; 2) a set of privacy amplification theorems for extracting secrecy from coded classical sequences against quantum side-information. These tools open the way to the design of robust QMF-QSDC protocols.

A Quantum-Memory-Free Quantum Secure Direct Communication Protocol Based on Privacy Amplification of Coded Sequences

TL;DR

This work addresses secure direct quantum communication without quantum memories by introducing a quantum-memory-free QSDC protocol (QMF-QSDC) that avoids wiretap coding and relies on universal privacy amplification of coded sequences. The authors develop a formal framework and theorems enabling secrecy extraction against quantum side information under collective attacks, with a focus on non-i.i.d. codewords and block-based operation. They derive both asymptotic and finite-length bounds on the extractable key length, using entropy accumulation and one-shot Renyi-based analyses, and discuss special-code simplifications and unitary-encoder properties. The results provide rigorous, practical guarantees for robust QMF-QSDC, enabling secure, memoryless quantum communications with a reusable key pool across blocks.

Abstract

We develop an information-theoretic analysis of Quantum-Memory-Free (QMF) Quantum Secure Direct Communication (QSDC) under collective attacks as an alternative to the conventional Quantum Key Distribution (QKD) protocol with one-time pads. Our main contributions are: 1) a QMF-QSDC protocol that only relies on universal hashing of coded sequences without wiretap coding; 2) a set of privacy amplification theorems for extracting secrecy from coded classical sequences against quantum side-information. These tools open the way to the design of robust QMF-QSDC protocols.
Paper Structure (10 sections, 7 theorems, 20 equations, 1 figure)

This paper contains 10 sections, 7 theorems, 20 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Notation
  3. System Model and Protocol
  4. System Model
  5. Proposed Protocol
  6. Protocol Analysis: Privacy Amplification on Coded Sequences
  7. Extractable Key Length In The Asymptotic Regime
  8. Extractable Key Length In The Finite-Length Regime
  9. Supporting Lemmas
  10. Proof of Lemma \ref{['lem:single_letterize_D']}

Key Result

Theorem 2

Let $B_{\textnormal{sub}}, m \in \mathbb{N}^*$ and $n = B_{\textnormal{sub}} \cdot m$. Let $R_{\textnormal{code}}$ denote the coding rate. Consider a quantum channel $\mathcal{N}_{X \rightarrow Z}$ from system $X$ to system $Z$, and a state $\rho_{XZ}^n \in \mathcal{D}_\circ(\mathcal{H}_{XZ}^{\otime

Figures (1)

  • Figure 1: The proposed QMF-QSDC protocol in block $b$.

Theorems & Definitions (15)

  • Definition 1
  • Theorem 2
  • proof
  • Theorem 3
  • proof
  • Lemma 4
  • proof
  • Corollary 5
  • proof
  • Corollary 6
  • ...and 5 more