title: Local quantum transformations requiring infinite rounds of classical communication.
abstract: In this Letter, we investigate the number of measurement and communication rounds needed to implement certain tasks by local quantum operations and classical communication (LOCC), a relatively unexplored topic. To demonstrate the possible strong dependence on the round number, we consider the problem of converting three-qubit entanglement into two-qubit form, specifically in the random distillation setting of [Phys. Rev. Lett. 98, 260501 (2007)]. We find that the number of LOCC rounds needed for a transformation can depend on the amount of entanglement distilled. In fact, for a wide range of transformations, the required number of rounds is infinite (unbounded). This represents the first concrete example of a task needing an infinite number of rounds to implement.
authors.affiliation: Center for Quantum Information and Quantum Control, Department of Physics, University of Toronto, Toronto, Ontario M5S 3G4, Canada.
authors.forename: Eric
authors.initials: E
authors.lastname: Chitambar