Data compression for ensembles of identically prepared quantum systems

Abstract

One of the consequences of the No Cloning Theorem is that many copies of the same quantum statecontain more information than just one copy. But what kind of information? And how much? Anatural way to approach these questions is provided by the task of quantum data compression, whereinformation is defined as the minimum amount of of memory needed to store the quantum state.Knowing the ultimate compression limit is important for the design of quantum machines with finitememory, and also for the design of communication networks where quantum data collected at differentnodes are transmitted to a central location for joint processing. In this talk I will present recent re-sults on the optimal compression of identically prepared particles, highlighting the interplay betweenphysical and information-theoretic aspects, suggesting applications, and discussing open problems.