Symmetric extendibility for qudits and tolerable error rates in quantum cryptography

TL;DR

This paper investigates the symmetric extendibility of two-qudit states to determine upper bounds on error rates in quantum cryptography, demonstrating that these bounds are tight in finite-dimensional systems.

Contribution

It provides new upper bounds on tolerable error rates for qudit-based quantum cryptographic protocols using two-way error correction, confirming their sharpness.

Findings

Upper bounds on error rates match known lower bounds in key cases

Symmetric extendibility analysis applies to two-qudit states in quantum cryptography

Results establish the limits of error correction protocols in finite dimensions

Abstract

Symmetric extendibility of quantum states has recently drawn attention in the context of quantum cryptography to judge whether quantum states shared between two distant parties can be purified by means of one-way error correction protocols. In this letter we study the symmetric extendibility in a specific class of two-qudit states, i. e. states composed of two d-level systems, in order to find upper bounds on tolerable error rates for a wide class of qudit-based quantum cryptographic protocols using two-way error correction. In important cases these bounds coincide with previously known lower bounds, thereby proving sharpness of these bounds in arbitrary finite-dimensional systems.