On the Capacity Region of Bipartite and Tripartite Entanglement Switching

Abstract

We study a quantum switch serving a set of users in a star topology. The function of the switch is to create bipartite or tripartite entangled state among users at the highest possible rates at a fixed ratio. We model a set of randomized switching policies. Discovering that some are better than others, we present analytical results for the case where the switch stores one qubit per user, and find that the best policies outperform a time division multiplexing (TDM) policy for sharing the switch between bipartite and tripartite state generation. This performance improvement decreases as the number of users grows. The model is easily augmented to study the capacity region in the presence of qubit decoherence, obtaining similar results. Moreover, decoherence appears to have little effect on capacity. We also study a smaller class of policies when the switch stores two qubits per user.

Policies for elementary links in a quantum network

“…Such an extension would involve multiple cooperating agents, in contrast to the independent agents considered in this work, and can in principle be formulated for an arbitrary network topology. A simple, but relevant example of a network topology, which has also been considered recently, is the starshaped network used for the so-called "quantum entanglement switch" [80][81][82][83]. As we might expect, these extra elements of entanglement distillation and swapping will make analytic analysis (as done in this work) intractable.…”

“…One of the goals of this work is to explicitly formalize the approaches taken in the aforementioned works within the context of decision processes, because this allows us to systematically study different policies and calculate quantities that are relevant for quantum networks, such as entanglement distribution rates and fidelities of the quantum states of the links. This work is complementary to prior work that uses Markov chains to analyze waiting times and entanglement distribution rates for a chain of quantum repeaters [65,[130][131][132]; we also refer to the work on entanglement switches in [80][81][82][83], which use both discrete-time and continuous-time Markov chains. This work is also complementary to prior work that analyzes the quantum state in a quantum repeater chain with noisy quantum memories [133][134][135][136][137].…”

Request Scheduling in Quantum Networks

“…In addition to the future work already mentioned, we foresee the following open research directions in the context of this study: extension to multipartite entanglement (e.g., along the lines of [42]); integration with communication protocols (e.g., [26]) and link layer stacks (e.g., [12]); analysis of the relation between distributed quantum applications and underlying interconnection network ( [14]); study of the fairness vs. efficiency trade-off in local link state routing protocols (e.g., [9]); extension to multiple local entanglement per node pair (such as in [29]); definition of a SLAs for distributed quantum applications ( [11]) and service differentiation [19]); further simulations with more general topologies and application request models.…”

“…For completeness, we mention that in the literature there is a growing number of studies dealing with sparse aspects of quantum routing, which are however only marginally relevant to the specific problem that we address and, thus, are not analyzed in details. They include, among the others: the definition of protocol stacks [32], [12], [26], the identification of capacity regions [42], studies on tools for performance evaluation of quantum networks [3], multi-partite entanglement distribution [27], and the design of networked quantum applications [13].…”

On the Quantum Performance Evaluation of Two Distributed Quantum Architectures

“…For a string of quantum repeaters with the goal of producing entanglement over long distances, some analytical studies exist that characterize the quality of very specific quantum states, and study their distribution to guarantee a minimum threshold quality see, e.g., [7,20,33,52]. Some analytical studies also exist for the so-called quantum switch, [56][57][58], wherein the authors study the maximum possible rate of entanglement switching and the expected number of entangled qubits in storage. These works are very different in spirit since they focus on the creation of quantum entanglement over long distances, and not on tradeoffs between network and computation operations as we do here.…”