The components of on the Bloch sphere will simply be .

In these cases, the solution then lies on the boundary of the n-dimensional Bloch sphere.

This is known as the Bloch sphere.

The set of all states in a two-level system can be mapped onto a representation known as the Bloch sphere.

The possible states for a single qubit can be visualised using a Bloch sphere (see diagram).

Specific implementations of the Bloch sphere are enumerated under the qubit article.

This can be seen as related to linear inversion giving states which lie outside the valid space (the Bloch sphere).

Microwave pulses typically 10-100 ns long are used to control the spins in the Bloch sphere.

The Bloch sphere may be generalized to an n-level quantum system but then the visualization is less useful.

The term "rotation" alludes to the Bloch sphere representation of a qubit pure state.

The Bloch sphere is a representation of a qubit, the fundamental building block of quantum computers.

The ability to carefully control the position of the state vector on the Bloch sphere is central to the realization of the qubit.

The Bloch sphere is a two-dimensional surface the points of which correspond to the state space of a spin 1/2 particle.

The superposition states of the system are described by (the surface of) a sphere called the Bloch sphere.

The Bloch sphere is a unit 2-sphere, with each pair of antipodal points corresponding to mutually orthogonal state vectors.

The natural metric on the Bloch sphere is the Fubini-Study metric.

In condensed matter physics, the Poincaré sphere is also known as the Bloch sphere.

Much of the mathematics associated with quantum theory has strong analogues inside the toy model, such as the Bloch sphere and similar forms of transformations.

Bloch sphere showing eigenvectors for Pauli Spin matrices.

In optics, the Bloch sphere is also known as the Poincaré sphere and specifically represents different types of polarizations.

Given a reasonable prior knowledge function, BME will yield a state strictly within the n-dimensional bloch sphere.

This accidental isomorphism allows to picture a geometric interpretation of the states of the two dimensional Hilbert space by using the Bloch sphere.

Hence the surface of the Bloch sphere represents all the pure states of a two-dimensional quantum system, whereas the interior corresponds to all the mixed states.

This would contract the Bloch sphere by some finite amount and the reverse process would expand the Bloch sphere, which cannot happen.

However, while the Bloch sphere parametrizes not only pure states but mixed states for 2-level systems, for states of higher dimensions there is difficulty in extending this to mixed states.