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A BRIEF INTRODUCTION TOINFORMATION THEORY

In this chapter we will give some basic background that is useful in the study of quantum information theory. Our primary focus will be on learning how to quantify information. This will be done using a concept known as entropy, a quantity that can be said to be a measure of disorder in physics. Information is certainly the opposite of disorder, so we will see how entropy can be used to characterize the information content in a signal and how to determine how many bits we need to reliably transmit a signal. Later these ideas will be tied in with quantum information processing. In this chapter we will also briefly look at problems in computer science and see why we might find quantum computers useful. This chapter won’t turn you into a computer engineer, we are simply going to give you the basic fundamentals.

CLASSICAL INFORMATION

Quantum computation is an entirely new way of information processing. For this reason traditional methods of computing and information processing you are familiar with are referred to as classical information. For those new to the subject, we begin with a simple and brief review of how information is stored and used in computers. The most basic piece of information is called a bit, and this basically represents a yes–no answer to a question. To represent this mathematically, we use the fact that we’re dealing with a two-state system and choose to represent information using base 2 or binary numbers. A binary ...

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