Quantum Information, 2 Volume Set, 2nd Edition

3 Discrete Quantum States versus Continuous Variables

Jens Eisert

Freie Universität Berlin, Department of Physics, Arnimallee 14, 14195 Berlin, Germany

3.1 Introduction

Much of the theory of quantum information science has originally been developed in the realm of quantum bits and trits, so for finite‐dimensional quantum systems. The closest analogue of the classical bit is the state of the two‐level quantum system, and, indeed, quite a lot of intuition of classical information theory carries over to the quantum domain (1,2). Yet, needless to say, many quantum systems do not fall under this category of being finite dimensional, and the familiar simple quantum mechanical harmonic oscillator is an example. Such an oscillator may be ...