In the treatment of quantum theory we’ve used so far we have been looking at closed systems. These are quantum systems that do not interact with the outside world. That is, an idealized model. In reality, quantum systems interact with the outside environment. The problem if that interactions with the environment can introduce noise and cause errors. To deal with this and construct, for example, real quantum computers and communications systems, we are going to need some kind of error correction.

Before we get there, we are going to have to develop a mathematical formalism to describe quantum systems that interact with the environment. We refer to systems of this type as open systems. Open quantum systems are important for the following reason: in an open quantum system, a pure state can evolve into a mixed state. The downside of this is that we need pure states to do quantum computation, and hence this type of evolution into mixed states is undesirable. In this chapter we will describe some of the formalism used to describe open quantum systems and then discuss error correction techniques.


At the most basic level, it can be said that the power of quantum information processing comes from the fact that quantum states can exists in superpositions. To review, this means that while a qubit could be in the state |0〉 or the state |1〉, it can also be found in the state

where α, β are complex constants that satisfy |α|2 + |β|2

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