Tools for the Analysis of Quantum Protocols Requiring State Generation Within a Time Window

Abstract

Quantum protocols commonly require a certain number of quantum resource states to be available simultaneously. An important class of examples is quantum network protocols that require a certain number of entangled pairs. Here, we consider a setting in which a process generates a quantum resource state with some probability p in each time step, and stores it in a quantum memory that is subject to timedependent noise. To maintain sufficient quality for an application, each resource state is discarded from the memory after w time steps. Let s be the number of desired resource states required by a protocol. We characterise the probability distribution X (w,s) of the ages of the quantum resource states, once s states have been generated in a window w. Combined with a time-dependent noise model, knowledge of this distribution allows for the calculation of fidelity statistics of the s quantum resources. We also give exact solutions for the first and second moments of the waiting time τ (w,s) until s resources are produced within a window w, which provides information about the rate of the protocol. Since it is difficult to obtain general closed-form expressions for statistical quantities describing the expected waiting time E(τ (w,s) ) and the distribution X (w,s) , we present two novel results that aid their computation in certain parameter regimes. The methods presented in this work can be used to analyse and optimise the execution of quantum protocols. Specifically, with an example of a Blind Quantum Computing (BQC) protocol, we illustrate how they may be used to infer w and p to optimise the rate of successful protocol execution. INDEX TERMS Quantum networks, performance analysis, scan statisticsThis article has been accepted for publication in IEEE Transactions on Quantum Engineering.

Frontiers of Computing - Evolutionary Trends and Cutting-Edge Technologies in Computer Science and Next Generation Application

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