We introduce multipartite entanglement distribution protocols that use a quantum switch to deliver stabilizer states to a number of remote end users. As in existing schemes, the first step in our protocols involves Bell pair generation between the switch and each end user. However, unlike existing schemes that wait for all Bell pairs to be established before distributing the desired state -- for example, via a projective measurement -- our approach stores only a minimal subset of Bell pairs while processing every subsequent Bell pair immediately. In doing so, our protocols reduce the average Bell pair storage time compared to existing schemes, resulting in less cumulative noise as a direct consequence. On the theoretical side, our protocol design is grounded in the structure of vertex covers in graph states up to local complementation. Through a comprehensive numerical evaluation, we compare the fidelities of delivered states with those of a baseline scheme, for state sizes up to n = 50 qubits. Simulations also show that our protocols can achieve the critical fidelity threshold of 1/2 for multipartite entanglement in a wider range of depolarization rates and success probabilities of Bell-pair generation. Overall, our protocols always achieve an equal or higher fidelity of the distributed state, and can reduce infidelity by up to 45%.

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.

Stabilizer states are a prime resource for a number of applications in quantum information science, such as secret-sharing and measurement-based quantum computation. This motivates us to study the entanglement of noisy stabilizer states across a bipartition. We show that the spectra of the corresponding reduced states can be expressed in terms of properties of an associated stabilizer code. In particular, this allows us to show that the coherent information is related to the so-called syndrome entropy of the underlying code. We use this viewpoint to find stabilizer states that are resilient against noise, allowing for more robust entanglement distribution in near-term quantum networks. We specialize our results to the case of graph states, where the found connections with stabilizer codes reduces back to classical linear codes for dephasing noise. On our way we provide an alternative proof of the fact that every qubit stabilizer code is equivalent up to single-qubit Clifford gates to a graph code.

Noisy hardware forms one of the main hurdles to the realization of a near-term quantum internet. Distillation protocols allows one to overcome this noise at the cost of an increased overhead. We consider here an experimentally relevant class of distillation protocols, which distillntokend-to-end entangled pairs using bilocal Clifford operations, a single round of communication and a possible final local operation depending on the observed measurement outcomes. In the case of permutationally invariant depolarizing noise on the input states, we find a correspondence between these distillation protocols and graph codes. We leverage this correspondence to find provably optimal distillation protocols in this class for several tasks important for the quantum internet. This correspondence allows us to investigate use cases for so-called non-trivial measurement syndromes. Furthermore, we detail a recipe to construct the circuit used for the distillation protocol given a graph code. We use this to find circuits of short depth and small number of two-qubit gates. Additionally, we develop a black-box circuit optimization algorithm, and find that both approaches yield comparable circuits. Finally, we investigate the teleportation of encoded states and find protocols which jointly improve the rate and fidelities with respect to prior art.