Practical figures of merit and thresholds for entanglement distribution in quantum networks

Abstract

Before global-scale quantum networks become operational, it is important to consider how to evaluate their performance so that they can be suitably built to achieve the desired performance. In this work, we consider three figures of merit for the performance of a quantum network: the average global connection time, the average point-to-point connection time, and the average largest entanglement cluster size. These three quantities are based on the generation of elementary links in a quantum network, which is a crucial initial requirement that must be met before any long-range entanglement distribution can be achieved. We evaluate these figures of merit for a particular class of quantum repeater protocols consisting of repeat-until-success elementary link generation along with entanglement swapping at intermediate nodes in order to achieve long-range entanglement. We obtain lower and upper bounds on these three quantities, which lead to requirements on quantum memory coherence times and other aspects of quantum network implementations. Our bounds are based solely on the inherently probabilistic nature of elementary link generation in quantum networks, and they apply to networks with arbitrary topology. CONTENTS

Efficient Computation of the Waiting Time and Fidelity in Quantum Repeater Chains

“…We rewrite eqs. (42) and (43) as function of the Werner parameters w A and w B of the input states rather than their fidelities F A and F B using eq. (2), which yields eqs.…”

“…Existing analytical work is mostly aimed at estimating the mean waiting time or fidelity (see also [22], [42], [43] for other figures of merit). Some of this work builds on an approximation of the mean waiting time under the small-probability assumption [17], [23], [31], [44], while for a small number of segments or for some protocols it is possible to compute the waiting time probability distribution exactly [13], [30], [43], [45], [46]. However, depending on the application different statistics become relevant.…”

“…When the first pair in one of the segments is ready, it has to wait until the second segment finalizes, and it decoheres while waiting. In this context, one may need to discard the entanglement after some maximum amount of time [43], [47], [48]. Entanglement is also used as a resource for implementing non-local gates in distributed quantum computers [49].…”

Designing a quantum network protocol

“…Work in this field has been slowly emerging over the last few years (see e.g. [13,49,57,58,76,86]). Recently, a proposal for a quantum network stack inspired by TCP/IP has been put forward ( Fig.…”

Routing space exploration for scalable routing in the quantum Internet

“…Quantum information and quantum computations [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] will not only reformulate our view of the nature of computation and communication, but will also open new possibilities for realizing high-performance computer architectures and telecommunication networks [10][11][12][13][14][15][16][17][28][29][30][31][33][34][35][36][37][38][39][40][41][42][43][44][45][62][63][64][65][66][67]…”