Device-Independent Quantum Key Distribution Using Random Quantum States

TL;DR

This paper investigates the performance of randomly generated two-qubit states in device-independent quantum key distribution, analyzing how entanglement and Bell-nonlocality vary with state rank and impact secure key rates.

Contribution

It provides a comprehensive analysis of the distribution of entanglement and Bell-nonlocality in random states and establishes bounds on secure key rates for mixed states.

Findings

Entanglement and Bell-nonlocality decrease with increasing state rank.

Pure states maximize, Werner states minimize secure key rates among states with same entanglement.

Secure key rate declines more sharply than quantum resources as rank increases.

Abstract

We Haar uniformly generate random states of various ranks and study their performance in an entanglement-based quantum key distribution (QKD) task. In particular, we analyze the efficacy of random two-qubit states in realizing device-independent (DI) QKD. We first find the normalized distribution of entanglement and Bell-nonlocality which are the key resource for DI-QKD for random states ranging from rank-1 to rank-4. The number of entangled as well as Bell-nonlocal states decreases as rank increases. We observe that decrease of the secure key rate is more pronounced in comparison to that of the quantum resource with increase in rank. We find that the pure state and Werner state provide the upper and lower bound, respectively, on the minimum secure key rate of all mixed two-qubit states possessing the same magnitude of entanglement under general as well as optimal collective attack strategies.