Efficient computation of the waiting time and fidelity in quantum repeater chains

Abstract

We provide two algorithms for computing the probability distribution of waiting time and fidelity in quantum repeater chains constructed from probabilistic components. Their polynomial runtimes improve upon existing algorithms’ exponential scaling.

Efficient Optimization of Cutoffs in Quantum Repeater Chains

“…A quantum repeater chain connects two endpoints via several repeaters and aims to generate entanglement between the endpoints. In this section, we elaborate on the class of quantum repeater chain protocols we study in this work, which is an extension of the class studied in [18] with the addition of cut-offs. While doing so, we refer to both the endpoints and the repeater stations as nodes and to an entangled state between two nodes as a link.…”

“…We here describe how we model each of the four PROTOCOL-UNITs described in section II-A, which is identical to the modelling in [18], except for the newly introduced CUT-OFF unit. For each PROTOCOL-UNIT, we describe the success condition as well as the quantum state that it outputs.…”

“…We sidestep the challenge of analytical characterization by computing the probability distribution of the waiting time and fidelity of the first generated entangled pair between the repeater's end nodes. For this, we improve the closedform expressions by Brand et al [18] to get faster algorithm runtimes and extend the expressions to repeater schemes which involve distillation and cut-offs. The runtime of the algorithm which evaluates these expressions is polynomial in the pre-specified size of the computed probability distribution's support.…”

“…The latter operation does not change the output state's fidelity with the target state |Φ + ⟩. The success probability p dist of distillation is a function of the input states' Werner parameters (see [18] for details). The cut-off (CUT-OFF) success condition depends deterministically on the waiting time or the fidelity of the input links.…”

“…The states that any PROTOCOL-UNIT outputs are Werner states at any time of the execution of the protocol. Indeed, a successful entanglement swap or distillation attempt maps Werner states to Werner states (see [18] for a brief explanation). Also, the CUT-OFF leaves the input states untouched in case of success, thereby outputting Werner states if it got those as input.…”