Quantum Information Theory with Spatially Separated Parties

Portland State University, Portland OR

Investigators

Abstract

Many of the most important phenomena in the field of quantum information involve spatially separated quantum subsystems. These subsystems may be entangled, correlated in a way that cannot be explained within classical physics. All subsystems can communicate classical information with each other (LOCC, for local operations and classical communication). Important examples of such protocols include entanglement generation and manipulation, quantum teleportation, quantum key distribution and cryptography, and certain proposed implementations of quantum computing. A formal mathematical description applicable in general to these situations is known to be rather complex and difficult. Therefore, it is an important open problem to fully understand the LOCC class of measurements, but progress along these lines has been limited up to the present time. One important step will be to understand how LOCC differs from the larger class of separable measurements. The Principal Investigator (PI) has recently devised a novel method of determining whether or not a separable quantum measurement can be implemented by LOCC. If it can, the approach devises an LOCC protocol which does so. If successful, the proposed work will extend this result to further understand how LOCC differs from separable measurements, and will also address important questions about LOCC itself, such as whether it is possible to bound the amount of communication needed at each round. The aim will also be to extend the PI's recent results on LOCC measurements to what is known as quantum operations, where the concern is only about the overall statistics that emerge from all the outcomes taken together. The proposed work will also contribute to our understanding about the creation of entanglement between two spatially separated systems, in part as an extension of the PI's recent results on the capacity of a bipartite unitary operation to create entanglement. Broader impact: The PI has long been involved in undergraduate and graduate education, and his involvement in research has improved the quality of his teaching and deepened his interactions with students, contributing to education at both undergraduate and graduate levels through the PI's supervision of undergraduates in research projects and collaboration with graduate students. The PI is a frequent seminar speaker to a quantum information seminar series at a local university. The PI has also published several pedagogical papers and is presently working on a new one on the topic of quantum teleportation.