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# Qubit

A qubit is not to be confused with a cubit, which is an ancient measure of length.

A qubit (quantum + bit; pronounced /kyoobit/ [1] ) is a unit of quantum information. That information is described by state in a 2-level quantum mechanical system, whose two basic states are conventionally labeled $|0 \rangle$ and $|1 \rangle$ (pronounced: ket 0 and ket 1). A pure qubit state is a linear quantum superposition of those two states. This is significantly different from the state of a classical 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 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 superpositions 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.

A number of qubits taken together is a qubit register . Quantum computers 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 trit. Other names have been suggested to designate a unit of information for higher-level systems, though there is not yet general agreement on terminology. For instance qudit has been suggested both as a term to denote both a digit of quantum information (that is in a 10-level quantum system) or as a term to denote a unit of quantum information in a d-level quantum system, although the latter usage now seems to be taking hold.

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.

The state space of a single qubit register can be represented geometrically by the Bloch sphere. This is a space of dimension 2, which means essentially that the single qubit register space has two local degrees of freedom. An n-qubit register space has 2n+1 − 2 degrees of freedom which is much larger than what one would expect classically with no entanglement, that is 2n.