Statistical analysis of quantum entangled network generation

TL;DR

This paper introduces analytical techniques to evaluate the statistical properties of quantum entanglement network generation, improving the understanding of performance metrics like secret key rate and quantum memory requirements.

Contribution

It develops a novel analytical framework using Markov chains and complex analysis to precisely analyze entanglement generation times and error distributions, enhancing prior computational methods.

Findings

Exact probability distributions for errors and entanglement times obtained.

Statistical fluctuation analysis tightens secret key rate bounds by 1000x.

Tighter bounds on quantum memory lifetimes derived.

Abstract

We develop techniques to analyse the statistics of completion times of non-deterministic elements in quantum entanglement generation, and how they affect the overall performance as measured by the secret key rate. By considering such processes as Markov chains, we show how to obtain exact expressions for the probability distributions over the number of errors that a network acquires, as well as the distribution of entanglement establishment times. We show how results from complex analysis can be used to analyse Markov matrices to extract information with a lower computational complexity than previous methods. We apply these techniques to the Innsbruck quantum repeater protocol, and find that consideration of the effect of statistical fluctuations tightens bounds on the secret key rate by 3 orders of magnitude. We also use the theory of order statistics to derive tighter bounds on the minimum quantum memory lifetimes that are required in order to communicate securely.