A complexity theory for non-local quantum computation

Authors:
Open Access
Publisher website
Google Scholar
Abstract
Non-local quantum computation (NLQC) replaces a local interaction between two systems with a single round of communication and shared entanglement. Despite many partial results, it is known that a characterization of entanglement cost in at least certain NLQC tasks would imply significant breakthroughs in complexity theory. Here, we avoid these obstructions and take an indirect approach to understanding resource requirements in NLQC, which mimics the approach used by complexity theorists: we study the relative hardness of different NLQC tasks by identifying resource efficient reductions between them. Most significantly, we prove that f -measure and f -route, the two best studied NLQC tasks, are in fact equivalent under O ( 1 ) overhead reductions. This result simplifies many existing proofs in the literature and extends several new properties to f -measure. For instance, we obtain sub-exponential upper bounds on f -measure for all functions, and efficient protocols for functions in the complexity class M o d k L . Beyond this, we study a number of other examples of NLQC tasks and their relationships.
Funding Information
  • National Science and Engineering Research Council of Canada (RGPIN-2025-03966)
  • National Science and Engineering Research Council of Canada (ALLRP 597823-24)
  • Agence Nationale de la Recherche (ANR-22-PETQ-0007)
  • Air Force Research Laboratory (FA9550-23-1-0363)
  • National Science Foundation (CCF-2144219)
  • Marie Skłodowska-Curie Actions (01081458)

This publication has 33 references indexed in Scilit: