Quantum information processing with indefinite input-output direction

Abstract

Quantum theory has revolutionized our understanding of physics and opened up new possibilities for information processing. This dissertation explores a fascinating extension of quantum theory by relaxing the traditional notion of information flow direction in quantum devices. We introduce the concept of bidirectional quantum devices and develop a rigorous mathematical framework to analyze input-output inversions and quantum operations on these devices. Remarkably, this framework allows for the existence of quantum operations with indefinite input-output direction.

In this dissertation, we delve into the advantages and applications of these operations in various information processing tasks. We start by examining an intuitive quantum game where we find that operations with indefinite input-output direction provide a clear advantage over strategies limited to a fixed input-output direction. Next, we study the quantum correlations generated by multipartite operations. We establish Tsirelson bounds of violation of a class of inequalities known as causal inequalities and show that the bounds can be violated by correlations generated by multipartite operations on bidirectional devices. In fact, we find out that, surprisingly, these operations have the remarkable capability to generate any correlation. Subsequently, we establish input-output indefiniteness as a novel resource and present a systematic method for quantifying and experimentally detecting it.

Finally, we explore the potential application of indefinite input-output direction in the transmission of both classical and quantum information through noisy channels. We demonstrate its superiority over standard communication protocols.