Distributing quantum states with finite lifetime

This paper considers a quantum node tasked with the teleportation of multiple information-carrying qubit (ICQ) streams, each to a different receiver, by means of entanglements, local operations, and classical communi-cation. Our vision is that the node establishes entangled qubit pairs (EQPs) with the receivers before the arrival of ICQs, rather than waiting for their arrival. In this vein, the paper focuses on the class of protocols referred to as class I that instantaneously teleport arriving ICQs using preestablished EQPs, preventing arriving ICQs from decohering. The excess ratio epsilon r is introduced as a quantifier of the system resources per arriving ICQ, and epsilon r =1 is shown to be a critical threshold. With epsilon r > 1: for arrival streams characterized by interarrivals stochastically larger than exponential random variables, any member of class I teleports all arriving ICQs after a finite transient. With epsilon r < 1: for stationary ergodic arrival streams, there exists no protocol that teleports all arriving ICQs after a finite transient. This work thus establishes the ultimate limit for distributing quantum states with finite lifetime. Within class I, a protocol referred to as fresh information delivery (FID) is introduced and its optimality is proven. The operational characteristic of FID is provided in terms of the tradeoff between the waiting time of the EQP before it is utilized for teleportation and the excess ratio. Numerical experiments, comparing the proposed FID protocol with alternatives, corroborate the theoretical results. The results in this paper can be used for designing quantum nodes, paving the way for the implementation of the future quantum internet.