Editing Qubit (section)

==Bit versus qubit==
A [[binary digit]], characterized as 0 or 1, is used to represent information in classical computers. When averaged over both of its states (0,1), a binary digit can represent up to one bit of [[information content]], where a [[bit]] is the basic unit of [[information theory|information]]. However, in this article, the word bit is synonymous with a binary digit.

In classical computer technologies, a ''processed'' bit is implemented by one of two levels of low [[Direct Current|direct current]] [[voltage]], and whilst switching from one of these two levels to the other, a so-called "forbidden zone" between two [[logic level]]s must be passed as fast as possible, as electrical voltage cannot change from one level to another instantly.

There are two possible outcomes for the measurement of a qubit—usually taken to have the value "0" and "1", like a bit. However, whereas the state of a bit can only be binary (either 0 or 1), the general state of a qubit according to quantum mechanics can arbitrarily be a [[Quantum superposition|coherent superposition]] of ''all'' computable states simultaneously.<ref name="nielsen2010">{{cite book |last1=Nielsen |first1=Michael A. |title=Quantum Computation and Quantum Information |title-link=Quantum Computation and Quantum Information (book) |last2=Chuang |first2=Isaac L. |date=2010 |publisher=[[Cambridge University Press]] |isbn=978-1-107-00217-3 |page=[https://archive.org/details/quantumcomputati00niel_993/page/n46 13] |language=en-US}}</ref> Moreover, whereas a measurement of a classical bit would not disturb its state, a measurement of a qubit would destroy its coherence and irrevocably disturb the superposition state. It is possible to fully encode one bit in one qubit. However, a qubit can hold more information, e.g., up to two bits using [[superdense coding]].

A bit is always completely in either one of its two states, and a set of {{math|n}} bits (e.g. a [[processor register]] or some bit array) can only hold a single of its {{math|2<sup>n</sup>}} possible states at any time. A quantum state can be in a superposition state, which means that the qubit can have non-zero [[probability amplitude]] in both its states simultaneously (popularly expressed as "it can be in both states simultaneously"). A qubit requires two [[complex number]]s to describe its two probability amplitudes, and these two complex numbers can together be viewed as a 2-dimensional complex [[Vector (mathematics and physics)|vector]], which is called a ''quantum state vector'', or ''superposition state vector.'' Alternatively and equivalently, the value stored in a qubit can be described as a single point in a 2-dimensional [[complex coordinate space]].

Furthermore, a set of {{math|n}} bits can be represented by {{math|n}} binary digits, simply by concatenating the representations of each of the bits, whereas a set of {{math|n}} qubits, which is also called a [[quantum register|register]], requires {{math|2<sup>n</sup>}} complex numbers to describe its superposition state vector.<ref name="shor1996">{{cite journal |last1=Shor |first1=Peter |title=Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer∗ |journal=SIAM Journal on Computing |volume=26 |issue=5 |pages=1484–1509 |year=1997 |arxiv=quant-ph/9508027 |bibcode=1995quant.ph..8027S |doi=10.1137/S0097539795293172 |s2cid=2337707}}</ref>{{r|Williams|pages=7–17}}{{r|nielsen2010|pages=13–17}} This is because the {{math|n}} qubits are not independent from one another and therefore the register cannot be described by breaking it down and describing the individual qubits.