The quantum switch is a vital component for the development of the quantum internet. In an entanglement distribution network, the function of a quantum switch is to generate elementary entanglement with its clients followed by entanglement swapping to distribute end-to-end entanglement of sufficiently high fidelity between clients. The threshold on entanglement fidelity is any quality of service requirement specified by the clients as dictated by the application they run on the network. We consider a discrete time model for a quantum switch that attempts generation of fresh elementary entanglement with clients in each time step in the form of maximally entangled qubit pairs, or Bell pairs, which succeed probabilistically; the successfully generated Bell pairs are stored in noisy quantum memories until they can be swapped. We focus on establishing the value of entanglement distillation of the stored Bell pairs prior to entanglement swapping in presence of their inevitable aging, i.e., decoherence: For a simple instance of a switch with two clients, an exponential decay of entanglement fidelity, and a wellknown probabilistic but heralded two-to-one distillation protocol, given a threshold end-to-end entanglement fidelity, we use the Markov Decision Processes framework to identify the optimal action policy - to wait, to distill, or to swap that maximizes throughput. We compare the switch's performance under the optimal distillation-enabled policy with that excluding distillation. Simulations of the two policies demonstrate the improvements that are possible in principle via optimal use of distillation with respect to average throughput, average fidelity and jitter of end-to-end entanglement, as functions of fidelity threshold. Our model thus helps capture the role of entanglement distillation in mitigating the effects of decoherence in a quantum switch in an entanglement distribution network, adding to the growing literature on quantum switches.
Entanglement distillation is a fundamental operation in quantum information processing used to obtain higher-fidelity entangled pairs from a supply of less entangled quantum states using local operations aided by classical communication (LOCC). In a physically relevant setting, where states with an initial fidelity of
f0, probabilistically generated over multiple,
m, memory pairs distributed between two parties, Alice and Bob, are pairwise distilled, the optimal policy identifies the system-configuration dependent sequence of entanglement generation and distillation operations that need to be performed in order to minimize the expected time to reach some target fidelity
fT>f0. Here, we formulate and systematically analyze this task as a Markov decision problem and using a value iteration algorithm, obtain optimal deterministic policies that minimize the expected waiting time required to reach a target fidelity. Our results show that the expected waiting time under the optimal policy decreases with increasing generation probability
p and number of quantum memories
m - as expected. In contrast, it exhibits non-monotonic behavior with respect to
f0 for a fixed fidelity gap,
(Δf=fT−f0). While the optimal policy consistently outperforms baseline policies such as the greedy, nested and entanglement pumping policies, its relative advantage is regime-dependent, being determined by the system parameters (
p,f0,fT,m), and exhibits a nontrivial dependence on the fidelity gap
Δf. Our results highlight the value of formulating entanglement distillation as a Markov decision problem, enabling the systematic design of policies that achieve target fidelity thresholds for quantum information tasks in realistic resource-constrained settings.
A quantum switch is one of the most fundamental network elements for connecting different quantum devices. In this paper, we explore the “optimal entanglement policy” of a quantum switch under a scenario where the stored and entangled qubits in the quantum switch may undergo a decoherence process. Finding an optimal entanglement policy is important as it enables a quantum switch to make a judicious basis measurement based on the number of existing link-level entanglements to maximize the “weighted throughput”. We use a Markov decision process framework to model the dynamics of the quantum switch, and theoretically reveal a threshold-based relationship between bipartite and tripartite policies under a very general class of weight functions with a weight parameter β. We further extend our analysis to uncover athreshold-based structure of optimal policies. In particular, the optimal policy for the quantum switch is a bipartite or tripartite policy when β is below a threshold β∗Bor above a threshold β∗T, respectively. When β∗B∗T, the optimal policy becomes a “threshold-based and state-dependent entanglement policy”. We also extend the work to allow a mixture of bipartite and tripartite policies by introducing a state-dependent mixed action. We theoretically show threshold-related relationships between mixed and bipartite/tripartite policies. Moreover, we extend this analysis to study optimal policies and characterize the threshold-based structure when the mixed action is considered. We carry out extensive numerical experiments to confirm that the optimal entanglement policy has such structural property when the mixed action is considered or not.
Entanglement distillation and entanglement swapping have been extensively studied assuming perfect quantum memories. However, near-term quantum networks will be fundamentally limited by quantum memories with a finite coherence time, resulting in complex choices for the timing and ordering of these operations. In this work, we study entanglement distillation and entanglement swapping at the level of the elementary building blocks of noisy quantum repeater networks, with the goal of elucidating the fundamental tradeoffs induced by memory decoherence. First, we focus on a minimal one-hop setting, where we analytically compare ``distill-as-soon-as-possible'' and ``distill-as-late-as-possible'' strategies against a baseline strategy that simply discards the older entangled state. We find that in the low memory coherence time regime, discarding the older entangled state achieves higher expected output fidelity, while in the high coherence time regime, delaying distillation until the end achieves the highest expected output fidelity and, over most of the deadline range, the highest weighted coherent information, at the expense of a lower success probability. We then extend our analysis to two-hop repeater chains using Monte Carlo simulation. In this setting, we find that the highest weighted coherent information is achieved by strategies that defer distillation to the end of the time window, with \textsf{Distill-ALAP-then-Swap-ALAP} and \textsf{Swap-ASAP-then-Distill-ALAP} leading at different operating points, while \textsf{Discard-Oldest-then-Swap} never reaches positive weighted coherent information in any regime tested. Together, these results clarify how decoherence reshapes the optimal operation timing in quantum networks and provide instructive insights into the link-level principles that govern larger-scale architectures.
Quantum switches are envisioned to be an integral component of future entanglement distribution networks. They can provide high quality entanglement distribution service to end-users by performing quantum operations such as entanglement swapping and entanglement purification. In this work, we characterize the capacity region of such a quantum switch under noisy channel transmissions and imperfect quantum operations. We express the capacity region as a function of the channel and network parameters (link and entanglement swap success probability), entanglement purification yield and application level parameters (target fidelity threshold). In particular, we provide necessary conditions to verify if a set of request rates belong to the capacity region of the switch. We use these conditions to find the maximum achievable end-to-end user entanglement generation throughput by solving a set of linear optimization problems. We develop a max-weight scheduling policy and prove that the policy stabilizes the switch for all feasible request arrival rates. As we develop scheduling policies, we also generate new results for computing the conditional yield distribution of different classes of purification protocols. The conclusions obtained in this work can yield useful guidelines for subsequent quantum switch designs.
Quantum networks (QNs) enable secure distributed quantum computing and sensing over next-generation optical communication networks by distributing entangled states over optical channels. However, quantum switches (QSs) in such QNs, which perform entanglement distribution, have limited resources, e.g., single-photon sources (SPSs) and quantum memories, which are sensitive to noise and losses. Efficient QS resource allocation is needed to minimize entanglement distribution delay. This paper proposes a QS resource allocation framework that jointly optimizes the average entanglement distribution delay and entanglement distillation operations to improve end-to-end (e2e) fidelity and meet user-specific rate and fidelity requirements. The proposed framework accounts for realistic QN noise and imperfections, deriving analytical expressions for quantum memory decoherence noise and resulting e2e fidelity after distillation. It also considers practical deployment factors, allowing QSs to control 1) nitrogen-vacancy (NV) center SPS types based on their isotopic decomposition, and 2) nuclear spin regions based on coupling strength and distance from NV center’s electron spin. The QS resource allocation optimization problem is solved using a simulated annealing algorithm. Simulation results show that the proposed framework manages to satisfy all users rate and fidelity requirements, unlike existing distillation-agnostic, minimal distillation, and physics-agnostic frameworks which do not perform distillation, perform minimal distillation, and do not control the physics-based NV center characteristics, respectively. Furthermore, the proposed framework results in significant reductions in the average e2e entanglement distribution delay, along with enhancements in the average e2e fidelity compared to the aforementioned existing frameworks.
We study a quantum switch serving a set of users. The function of the switch is to convert bipartite entanglement generated over individual links connecting each user to the switch, into bipartite or tripartite entangled states among (pairs or groups of) users at the highest possible rates at a fixed ratio. Such entanglement can then be converted to quantum-secure shared secret bits among pairs or triples of users using E91-like Quantum Key Distribution (QKD) protocols. The switch can store a certain number of qubits in a quantum memory for a certain length of time, and can make two-qubit Bell-basis measurements or three-qubit GHZ-basis projective measurements on qubits held in the memory. 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 at a given time step, and find that the best policies outperform a time division multiplexing (TDM) policy for sharing the switch between bipartite and tripartite entanglement 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 can store two qubits per user. The full manuscript can be found at https://arxiv.org/abs/1901.06786.