Information Gain vs. State Disturbance in Quantum Theory

Abstract

The engine that powers quantum cryptography is the principle that there are no physical means for gathering information about the identity of a quantum system's state (when it is known to be prepared in one of a set of nonorthogonal states) without disturbing the system in a statistically detectable way. This situation is often mistakenly described as a consequence of the ``Heisenberg uncertainty principle.'' A more accurate account is that it is a unique feature of quantum phenomena that rests ultimately on the Hilbert space structure of the theory along with the fact that time evolutions for isolated systems are unitary. In this paper we shall explore several aspects of the information--disturbance principle in an attempt to make it firmly quantitative and flesh out its significance for quantum theory as a whole.