by Xauri'El Zwaan

Created on: March 11, 2009

We live in an 'information age'. Information technology is all around us - computers, cell phones, bar codes, GPS satellites - and it's constantly ramifying. All of this is a consequence of a specialized branch of mathematics known as 'information theory', which is concerned with quantifying, communicating, and manipulating the information encoded into physical systems or 'states'. In information theory, information is seen as a pattern which distinguishes one physical state from another; the fundamental unit of information is a 'bit'. A bit can be thought of as a question which is answered either 'yes' or 'no', that is, 'one' or 'zero'.

Quantum mechanics is the science which describes the behaviour of the extremely small particles that make up reality at the most basic level - protons, neutrons, electrons, quarks. At the quantum scale, reality is not easily understandable by humans used to things being in only one place at once and being able to simultaneously know the speed and position of things. And when information theory gets entangled with quantum theory, things start to get a bit wierd.
The fundamental unit of quantum information is not the bit but the 'qubit'. If a bit is a question that is answered 'yes' or 'no', a qubit is a question that could also be answered 'well, yes and no....' This is because of the Heisenberg Uncertainty Principle, which states that it is impossible to accurately simultaneously measure the position and the velocity of a subatomic particle without changing them. This means that particles which have not been measured exist not in any discrete state, but as a quantum probability wave called a 'superposition of states' which describes merely how likely it is that they are in any given state. Measuring the state of the particle 'collapses' the probability wave into a specific physical state, but before it is measured the particle is literally in all possible states at once. This is not just an abstract bit of mathematics; it governs the real behaviour of quantum particles, and is the operating principle behind technology like bar code scanners and digital cameras.
Therefore, a qubit which describes a 'simple' quantum system like the spin of an electron in a magnetic field can be in the measured states of one or zero; or it can be in an unmeasured superposition describing the probability that, if measured, it would turn out to be in either of these states. A series of three bits can encode any binary number from 000 (zero) to 111

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