Role of memory errors in quantum repeaters

We investigate the influence of memory errors in the quantum repeater scheme for long-range quantum communication. We show that the communication distance is limited in standard operation mode due to memory errors resulting from unavoidable waiting times for classical signals. We show how to overcome these limitations by (i) improving local memory and (ii) introducing two operational modes of the quantum repeater. In both operational modes, the repeater is run blindly, i.e., without waiting for classical signals to arrive. In the first scheme, entanglement purification protocols based on one-way classical communication are used allowing to communicate over arbitrary distances. However, the error thresholds for noise in local control operations are very stringent. The second scheme makes use of entanglement purification protocols with two-way classical communication and inherits the favorable error thresholds of the repeater run in standard mode. One can increase the possible communication distance by an order of magnitude with reasonable overhead in physical resources. We outline the architecture of a quantum repeater that can possibly ensure intercontinental quantum communication.

Figure 1

(Color online) Maximal repeater level and fidelity $F$ as function of the operational and measurement errors $(1-p=1-\eta )$. The distance on repeater level 1 is $10\mathrm{km}$; every level ($L2$ to $L12$) doubles this distance. Dark lines have decoherence time ${\kappa }^{-1}=1\mathrm{s}$, light lines have ${\kappa }^{-1}=0.1\mathrm{s}$. Solid lines are a lower bound on the maximal distance for a repeater run with the Innsbruck protocol and with initial Werner states of fidelity 0.8 on level 1. Dashed lines show the limits of the purification map, which are an upper bound on any repeater run in error detection mode (with the exception of blind mode, Sec. 5). For a more detailed discussion see text.

Figure 2

(Color online) Maximal repeater level and fidelity $F$ as function of the operational and measurement errors $(1-p=1-\eta )$. The distance on repeater level $1$ is $10\mathrm{km}$; every level ($L2$ to $L10$) doubles this distance. The decoherence time is ${\kappa }^{-1}=1\mathrm{s}$, the curve is a lower bound on the maximal distance for a repeater run with the Innsbruck protocol and with initial Werner states of fidelity 0.9 on level 1, showing a weak dependence on the initial fidelity as compared to Fig. 1. Additionally the fidelity was required to finally be above 0.9 on every level and all its lower levels in the repeater.