Qubit

A '''quantum bit''', or '''qubit''' (sometimes ''qbit'') is a unit of [[quantum information]]. That information is described by a state in a 2-level [[quantum mechanics|quantum mechanical]] system which is formally equivalent to a two-dimentional [[Wikipedia:vector space| vector space]] over the [[Wikipedia:complex number| complex numbers]]. The two basis states (or [[Wikipedia:vector| vectors]]) are conventionally written as $|0\; \backslash rangle$ and $|1\; \backslash rangle$ (pronounced: 'ket 0' and 'ket 1') as this follows the usual [[bra-ket notation]] of writing [[pure states|quantum states]]. Hence a qubit can be thought of as a [[quantum mechanics|quantum mechanical]] version of a classical data [[Wikipedia:bit| bit]]. A [[pure qubit state]] is a linear [[quantum superposition]] of those two states. This means that each [[qubit]] can be represented as a linear combination of $|0\; \backslash rangle$ and $|1\; \backslash rangle$: : $|\; \backslash psi\; \backslash rangle\; =\; \backslash alpha\; |0\; \backslash rangle\; +\; \backslash beta\; |1\; \backslash rangle,$ where α and β are [[Wikipedia:Complex number|complex]] [[probability amplitude]]s. α and β are constrained by the equation : $|\; \backslash alpha\; |^2\; +\; |\; \backslash beta\; |^2\; =\; 1.$ The probability that the qubit will be measured in the state $|0\; \backslash rangle$ is $|\; \backslash alpha\; |^2$ and the probability that it will be measured in the state $|1\; \backslash rangle$ is $|\; \backslash beta\; |^2$. Hence the total probability of the system being observed in either state $|0\; \backslash rangle$ or $|1\; \backslash rangle$ is 1. This is significantly different from the state of a classical [[Wikipedia:bit|bit]], which can only take the value 0 or 1. A qubit's most important distinction from a classical bit, however, is not the continuous nature of the state (which can be replicated by any [[Wikipedia:analog signal|analog]] quantity), but the fact that multiple qubits can exhibit [[quantum entanglement]]. Entanglement is a [[nonlocal]] property that allows a set of qubits to express [[superposition]]s of different binary strings (01010 and 11111, for example) simultaneously. Such "quantum parallelism" is one of the keys to the potential power of quantum computation. In essence, each independent state of the quantum particle used in the computer can follow its own independent computation path to conclusion while its other states are observed and changed. A number of [[qubit]]s taken together is a [[quantum register]]. [[What is Quantum Computation?|Quantum computer]]s perform calculations by manipulating qubits. Similarly, a unit of quantum information in a 3-level quantum system is called a [[qutrit]], by analogy with the unit of classical information [[Wikipedia:trit| trit]]. The term "'''Qudit'''" is used to denote a unit of quantum information in a ''d''-level quantum system. [[Wikipedia:Benjamin Schumacher| Benjamin Schumacher]] discovered a way of interpreting quantum states as information. He came up with a way of compressing the information in a state, and storing the information on a smaller number of states. This is now known as Schumacher compression. Schumacher is also credited with inventing the term qubit (See, for example, Phys. Rev. A 51 2738 (1995)). The [[state space]] of a single qubit register can be represented geometrically by the [[Bloch sphere]]. This is a two dimensional space which has an underlying geometry of the surface of a sphere. This essentially means that the single [[qubit]] register space has two local degrees of freedom. An ''n''-qubit register space has 2''n''+1 − 2 degrees of freedom. This is much larger than 2''n'', which is what one would expect classically with no [[entanglement]]. {{FromWikipedia}} [[Category:Handbook of Quantum Information]]