Entanglement cost in non-local quantum computation

TL;DR

This paper provides a comprehensive review of non-local quantum computation, focusing on entanglement cost bounds and its implications across quantum cryptography, complexity, and physics.

Contribution

It offers a detailed analysis of entanglement cost bounds in NLQC and explores its applications and connections to various quantum information fields.

Findings

Reviewed upper and lower bounds on entanglement cost

Connected NLQC to quantum cryptography and complexity

Discussed applications in quantum gravity and communication

Abstract

This is a book-length treatment of the subject of non-local quantum computation (NLQC). NLQC is a method for implementing quantum operations that interact two systems without directly bringing the systems together. Instead, a single round of communication and shared entanglement is used. NLQC has appeared in the context of quantum cryptography, computational complexity, communication complexity, quantum gravity, and other applications. The understanding of entanglement cost in NLQC is closely tied to questions in all of these areas. We review upper and lower bounds on entanglement cost, as well as some of the applications of NLQC and its connections to other subjects.