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We present an exact rate analysis for a secret key that can be shared amongtwo parties employing a linear quantum repeater chain. One of our mainmotivations is to address the question whether simply placing quantum memoriesalong a quantum communication channel can be beneficial in a realistic setting.The underlying model assumes deterministic entanglement swapping of single-spinquantum memories and it excludes probabilistic entanglement distillation, andthus two-way classical communication, on higher nesting levels. Within thisframework, we identify the essential properties of any optimal repeater scheme:entanglement distribution in parallel, entanglement swapping as soon andparallel quantum storage as little as possible. While these features areobvious or trivial for the simplest repeater with one middle station, for morestations they cannot always be combined. We propose an optimal scheme includingchannel loss and memory dephasing, proving its optimality for the case of twostations and conjecturing it for the general case. In an even more realisticsetting, we consider additional tools and parameters such as memory cut-offs,multiplexing, initial state and swapping gate fidelities, and finite linkcoupling efficiencies in order to identify potential regimes in memory-assistedquantum key distribution beyond one middle station that exceed the rates of thesmallest quantum repeaters as well as those obtainable in all-optical schemesunassisted by stationary memory qubits and two-way classical communication.

Exact rate analysis for quantum repeaters with imperfect memories and entanglement swapping as soon as possible