On the path to entanglement

Peter Mark Ainsworth

Alena Chang, Guoliang Xue

In this paper, we study the properties of path metrics of an entanglement path for a given entanglement swapping order of the path. We show how to efficiently compute the path metrics of an entanglement path for any given swapping order. We show that different entanglement swapping orders for the same path can lead to different expected throughputs. A key finding is that the binary operator corresponding to entanglement swapping along a path is not associative. We further show that the problem of computing an s-t path with maximum expected throughput under any entanglement swapping order does not have the subpath optimality property, which is a key property most path finding algorithms such as Dijkstra’s algorithm rely on. We use extensive simulations to validate our theoretical findings.

Anoosha Fayyaz, Prashant V. Krishnamurthy, Kaushik Parasuram Seshadreesan +2 more

Optimal routing is a fundamental challenge in quantum networking, with several approaches proposed to identify the most efficient path for end-to-end (e2e) entanglement generation between pairs of nodes. In this paper, we show that prior entanglements - entanglements generated in a previous network cycle but not yet utilized - are an important consideration in optimal path selection due to the dynamic nature of quantum networks. Specifically, we investigate whether a longer path with pre-existing entanglements can outperform a shorter path that starts from scratch. We account for key quantum constraints, including noisy entanglement generation and swapping, fidelity decay, probabilistic operations, and link discarding upon swap failure. Simulations reveal that longer paths with prior entanglements can establish e2e entanglement faster than shorter paths under certain conditions. We further introduce the notion of entanglement diversity, where multiple paths can be used to improve performance - either by selecting the first successful path to minimize time or using both paths to enhance fidelity through distillation. These findings highlight the importance of incorporating prior entanglements into path selection strategies for optimizing quantum communication networks.

Yan Wang, Yichang Shou, Jiawei Liu +5 more

Quantum entanglement, a fundamental concept in quantum mechanics, lies at the heart of many current and future quantum technologies. A pivotal task is the generation and control of diverse quantum entangled states in a more compact and flexible manner. Here, we introduce an approach to achieve diverse path entanglement by exploiting the interaction between noncommutative metasurfaces and entangled photons. Different from other path entanglements, our quantum path entanglement is evolution path entanglement of photons on Poincaré sphere. Due to quantum entanglement between idler photons and structured signal photons, evolution path of idler photons on the fundamental Poincaré sphere can be nonlocally mirrored by structured signal photons on any higher-order Poincaré sphere, resulting in quantum path entanglement. Benefiting from noncommutative metasurfaces, diverse quantum path entanglement can be switched across different higher-order Poincaré spheres using distinct combination sequences of metasurfaces. Our method allows for the tuning of diverse quantum path entanglement across a broad spectrum of quantum states, offering a significant advancement in the manipulation of quantum entanglement.