Data compression for quantum population coding

Abstract

Quantum states provide information about multiple,mutually complementary observables. Such information is not accessible from asingle system, but becomes accessible when a population of many identicallyprepared systems is available. In this context, an important question is howmuch information is contained into n copies of the same state. A rigorous wayto quantify such information is through the task of quantum data compression,where the goal is to store the quantum state into the smallest number ofquantum bits. The problem of compressing identically prepared systems isrelevant in several areas, including the design of quantum sensors thatcollect data and transfer them to a central location, and the design ofquantum learning machines that store patterns in their internal memory. Inthis talk I will characterize the minimum amount of memory needed tofaithfully store sequences of identically prepared quantum states, showinghow the size of the memory grows with the number of particles in thesequence. In addition, I will discuss how much quantum memory can be tradedwith classical memory. Finally, I will conclude by showing an application ofquantum compression to high precision measurements of time and frequency.