On the Fidelity Distribution of Link-level Entanglements under Purification

TL;DR

This paper analyzes the fidelity distribution of link-level EPR pairs in quantum networks considering decoherence and purification, proposing a new purification scheme beyond generation time and evaluating its impact on fidelity and rate.

Contribution

It introduces a novel Purification scheme Beyond the Generation time (PBG) and provides an analytical model for the fidelity distribution of stored EPR pairs under this scheme.

Findings

Analytical probability distribution of EPR pair fidelity under decoherence and purification.

PBG scheme improves fidelity at the cost of additional resource consumption.

Numerical results show the fidelity-rate trade-off of the proposed purification method.

Abstract

Quantum entanglement is the key to quantum communications over considerable distances. The first step for entanglement distribution among quantum communication nodes is to generate link-level Einstein-Podolsky-Rosen (EPR) pairs between adjacent communication nodes. EPR pairs may be continuously generated and stored in a few quantum memories to be ready for utilization by quantum applications. A major challenge is that qubits suffer from unavoidable noise due to their interaction with the environment, which is called decoherence. This decoherence results in the known exponential decay model of the fidelity of the qubits with time, thus, limiting the lifetime of a qubit in a quantum memory and the performance of quantum applications. In this paper, we evaluate the fidelity of the stored EPR pairs under two opposite dynamical and probabilistic phenomena, first, the aforementioned decoherence and second purification, i.e. an operation to improve the fidelity of an EPR pair at the expense of sacrificing another EPR pair. Instead of applying the purification as soon as two EPR pairs are generated, we introduce a Purification scheme Beyond the Generation time (PBG) of two EPR pairs. We analytically show the probability distribution of the fidelity of stored link-level EPR pairs in a system with two quantum memories at each node allowing a maximum of two stored EPR pairs. In addition, we apply a PBG scheme that purifies the two stored EPR pairs upon the generation of an additional one. We finally provide numerical evaluations of the analytical approach and show the fidelity-rate trade-off of the considered purification scheme.