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Secure Communication with Unreliable Entanglement Assistance

Meir Lederman, Uzi Pereg

TL;DR

An achievable secrecy rate region is derived for general quantum wiretap channels, and a multi-letter secrecy capacity formula for the special class of degraded channels, and an achievable secrecy rate region is derived for general quantum wiretap channels.

Abstract

Secure communication is considered with unreliable entanglement assistance, where the adversary may intercept the legitimate receiver's entanglement resource before communication takes place. The communication setting of unreliable assistance, without security aspects, was originally motivated by the extreme photon loss in practical communication systems. The operational principle is to adapt the transmission rate to the availability of entanglement assistance, without resorting to feedback and repetition. Here, we require secrecy as well. An achievable secrecy rate region is derived for general quantum wiretap channels, and a multi-letter secrecy capacity formula for the special class of degraded channels.

Secure Communication with Unreliable Entanglement Assistance

TL;DR

An achievable secrecy rate region is derived for general quantum wiretap channels, and a multi-letter secrecy capacity formula for the special class of degraded channels, and an achievable secrecy rate region is derived for general quantum wiretap channels.

Abstract

Secure communication is considered with unreliable entanglement assistance, where the adversary may intercept the legitimate receiver's entanglement resource before communication takes place. The communication setting of unreliable assistance, without security aspects, was originally motivated by the extreme photon loss in practical communication systems. The operational principle is to adapt the transmission rate to the availability of entanglement assistance, without resorting to feedback and repetition. Here, we require secrecy as well. An achievable secrecy rate region is derived for general quantum wiretap channels, and a multi-letter secrecy capacity formula for the special class of degraded channels.
Paper Structure (42 sections, 8 theorems, 99 equations, 3 figures)

This paper contains 42 sections, 8 theorems, 99 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Definitions
  3. Basic Definitions
  4. Wiretap Channel
  5. Coding with Unreliable Assistance
  6. Correct Decoding
  7. Secrecy
  8. Achievable rate pairs
  9. Previous Work
  10. Unsecure Communication
  11. No Assistance
  12. Reliable Assistance
  13. Unreliable Assistance
  14. Secure Communication
  15. No Assistance
  16. ...and 27 more sections

Key Result

Theorem 1

The capacity of a quantum channel $\mathcal{L}_{A\to B}$ without secrecy and without assistance satisfies

Figures (3)

  • Figure 1: Illustration of secure communication with unreliable entanglement assistance in the presence of an eavesdropper that may steal the entanglement resource. The figures show an imaginary switch that decides whether Eve will intercept the entanglement assistance or not. There are two scenarios: (a) "left mode": Bob receives the entanglement resource and performs a measurement to decode both the guaranteed information and the excess information. (b) "right mode": Eve has intercepted the entanglement resource. Bob decodes the guaranteed information alone. The information needs to be secret in both scenarios.
  • Figure 2: Notation of channel capacities with and without secrecy, and with different levels of entanglement assistance. The first column corresponds to communication without a secrecy requirement, and the second column comprises secrecy capacities.
  • Figure 3: Quantum superposition coding

Theorems & Definitions (16)

  • Definition 1
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Theorem 1: see Holevo:98pSchumacherWestmoreland:97p
  • Theorem 2: see BennettShorSmolin:99p
  • Theorem 3: see pereg2023communication
  • Theorem 4: see cai2004quantumdevetak2005private
  • Theorem 5: see QiSharmaWilde:18p
  • ...and 6 more