Abstract
The indistinguishability of quantum particles is widely used as a resource for the generation of entanglement. Linear quantum networks (LQNs), in which identical particles linearly evolve to arrive at multimode detectors, exploit the indistinguishability to generate various multipartite entangled states by the proper control of transformation operators. However, it is challenging to devise a suitable LQN that carries a specific entangled state or compute the possible entangled state in a given LQN as the particle and mode number increase. This research presents a mapping process of arbitrary LQNs to graphs, which provides a powerful tool for analyzing and designing LQNs to generate multipartite entanglement. We also introduce the perfect matching diagram (PM diagram), which is a refined directed graph that includes all the essential information on the entanglement generation by an LQN. The PM diagram furnishes rigorous criteria for the entanglement of an LQN and solid guidelines for designing suitable LQNs for the genuine entanglement. Based on the structure of PM diagrams, we compose LQNs for fundamental N-partite genuinely entangled states.
Highlights
Entanglement is an essential property of multipartite quantum systems that works as a resource for several kinds of quantum information processing [1]
By introducing a systematic strategy to grasp the quantitative relation between Linear quantum networks (LQNs) structures and entanglement, our graph picture provides a powerful insight for analyzing the entanglement of identical particles carried by LQNs
The advantage of associating graph theory with quantum information processing has been validated in many works: contextuality in the graph and hypergraph frameworks [26, 27], quantum graph states [28,29,30,31], Gaussian boson sampling exploited to solve the computational complexity problems in graph theory [32,33,34], and the linkage of undirected graphs to optical setups involving multiple crystals [35,36,37,38] Here, we show that the graph picture of LQNs is beneficial for computing the entanglement of no-bunching states in LQNs
Summary
Entanglement is an essential property of multipartite quantum systems that works as a resource for several kinds of quantum information processing [1]. By introducing a systematic strategy to grasp the quantitative relation between LQN structures and entanglement, our graph picture provides a powerful insight for analyzing the entanglement of identical particles carried by LQNs. The advantage of associating graph theory with quantum information processing has been validated in many works: contextuality in the graph and hypergraph frameworks [26, 27], quantum graph states [28,29,30,31], Gaussian boson sampling exploited to solve the computational complexity problems in graph theory [32,33,34], and the linkage of undirected graphs to optical setups involving multiple crystals [35,36,37,38] Here, we show that the graph picture of LQNs is beneficial for computing the entanglement of no-bunching states in LQNs. by showing that the graph structure is closely related to the entanglement property of the corresponding LQNs, we can reversely propose a protocol for designing optimal LQNs that generate specific N -partite entangled states. We can state that the graph picture of LQNs enables a schematic approach to the two central procedures for the entanglement of LQNs, i.e., designing an appropriately entangled LQN and extracting no-bunching states in the LQN
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
