||CQIL - Cryptography and Quantum Information
Place: McConnell 320
Time: 14:00 - 15:00
Affiliation: Perimeter Institute
Title: LOCC Instruments
In the “distant labs” setting of quantum information processing, a multipart quantum system is distributed to various parties who are separated by some large distance. The parties are allowed to perform local measurements on their respective subsystems while coordinating their actions through classical communication. This scenario is known as LOCC (local operations and classical communication) and it plays a fundamental role in some of the most important quantum information tasks such as teleportation and quantum cryptography. However, despite this relatively simple operational description, it is quite challenging to provide a precise mathematical characterization of LOCC operations.
In this talk, I will define LOCC operations through the notion of quantum instruments, which is a useful formalism that captures both the classical and quantum outputs of a measurement. This will allow us to clearly differentiate between finite round LOCC, infinite round LOCC and asymptotic LOCC. In doing so, certain examples will be given that show these classes to be strictly different from one another. Additionally we will prove that the set of finite round, finite outcome LOCC instruments is compact, while the compactness breaks down when infinite round protocols are considered. Finally, we will discuss various open problems related to the structure of LOCC instruments.