Error Correcting Codes in Quantum Theory

A new type of uncertainty relation is presented, concerning the information-bearing properties of a discrete quantum system. A natural link is then revealed between basic quantum theory and the linear error correcting codes of classical information theory. A subset of the known codes is described, having properties which are important for error correction in quantum communication. It is shown that a pair of states which are, in a certain sense, open-quote open-quote macroscopically different,close-quote close-quote can form a superposition in which the interference phase between the two parts is measurable. This provides a highly stabilized open-quote open-quote Schroedinger cat close-quote close-quote state. copyright 1996 The American Physical Society