Symmetric extendibility for qudits and tolerable error rates in quantum cryptography

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.

4 pages, no figures

References in corpus (6)

• Security bound of two-bases quantum key-distribution protocols using qudits
• Symmetric extension in two-way quantum key distribution
• Spectrum conditions for symmetric extendible states
• Asymptotic correctability of Bell-diagonal quantum states and maximum tolerable bit error rates
• Asymptotic correctability of Bell-diagonal qudit states and lower bounds on tolerable error probabilities in quantum cryptography
• Robustness of the BB84 quantum key distribution protocol against general coherent attacks