Bloch sphere representation of a qubit.

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

Mixed states can be represented by points inside the Bloch sphere.

Unitary transformations correspond to rotations of the qubit vector in the Bloch sphere.

The 2-dimensional case of such a transformation would consist of mapping pure states on the surface of the Bloch sphere to mixed states within the Bloch sphere.

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

Bloch sphere showing eigenvectors for Pauli Spin matrices.

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

* Bloch sphere

Bloch sphere

In quantum mechanics, the Bloch sphere is a geometrical representation of the pure state space of a two-level quantum mechanical system ( qubit ), named after the physicist Felix Bloch.

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

The north and south poles of the Bloch sphere are typically chosen to correspond to the standard basis vectors and, respectively,

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

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

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

It is based on researches on stylistic modeling carried out by Gerard Assayag and Shlomo Dubnov and on researches on improvisation with the computer by G. Assayag, M. Chemillier and G. Bloch ( aka the OMax Brothers ) in the Ircam Music Representations group.

* 2007 – The painting Portrait of Suzanne Bloch ( 1904 ), by the Spanish artist Pablo Picasso, is stolen from the São Paulo Museum of Art, along with O Lavrador de Café by the major Brazilian modernist painter Candido Portinari.

There is also a broader definition, as described by Marc Bloch ( 1939 ), that includes not only warrior nobility but all three estates of the realm: the nobility, the clerics, and the peasantry bonds of manorialism ; this is sometimes referred to as a " feudal society ".

The most widely held theory is put forth by Marc Bloch.

Bloch said it is related to the Frankish term * fehu-ôd, in which * fehu means " cattle " and-ôd means " goods ", implying " a moveable object of value.

It is this radical notion that peasants were part of feudal relationship that sets Bloch apart from his peers.

While humanizing and questioning him, Stirling gives credit to Bloch for helping to break through the monotonous methodological alternance between positivism and narrative history, creating a new, synthetic version of the historical practice that has since become so ingrained in the discipline that it is typically overlooked.

The classic multivibrator circuit ( also called a plate-coupled multivibrator ) is first described by H. Abraham and E. Bloch in Publication 27 of the French Ministère de la Guerre, and in Annales de Physique 12, 252 ( 1919 ).

The Bates Motel is an important part of Psycho, a 1959 novel by Robert Bloch, and Alfred Hitchcock's 1960 film, Psycho.

The researches of Langevin and those of Eugene Bloch have shown that the greater part of the Lenard effect is certainly due to this ' Hertz effect '.

Puns and other forms of word play have been used by many famous writers, such as Alexander Pope, James Joyce, Vladimir Nabokov, Robert Bloch, Lewis Carroll, John Donne, and William Shakespeare, who is estimated to have used over 3, 000 puns in his plays.

To this end, he compares George Orwell's Coming Up for Air with Frederik Pohl and C. M. Kornbluth's The Space Merchants and concludes that the basic building block and distinguishing feature of a science fiction novel is the presence of the novum, a term Darko Suvin adapts from Ernst Bloch and defines as " a discrete piece of information recognizable as not-true, but also as not-unlike-true, not-flatly-( and in the current state of knowledge ) impossible ".

Bloch diagnosed the disease as due to ' congestion of blood in the brain ' ( a meaningless diagnosis in modern medical practice as such congestion is anatomically impossible ), and after some controversy this diagnosis was also accepted by the famous Hanoverian court physician, Johann Georg Ritter von Zimmermann, an admirer of Mendelssohn.

Beaumont was much admired by the well-known colleagues who outlived him ( Ray Bradbury, Harlan Ellison, Richard Matheson, Robert Bloch, Roger Corman ), and his work is currently in the process of being rediscovered.

where k is a real or complex number ( the Bloch wavevector or Floquet exponent ).

Ludwigshafen is the birthplace of the former German chancellor Helmut Kohl and the philosopher Ernst Bloch.

Similarly R. Bloch supposed it might be an adjectival form in-no from * nuptu -, meaning " he who is moist ".

In June, the operative called Bloch and said that he could not see Bloch anymore, specifically saying, " A contagious disease is suspected ".

Amory Bloch Lovins ( born November 13, 1947 ) is an American physicist, environmental scientist, writer, and Chairman / Chief Scientist of the Rocky Mountain Institute.

The list of composers who benefited from Coolidge's support is impressive, including also Ernest Bloch, Frank Bridge, Alfredo Casella, George Enescu, Howard Hanson, Gian Francesco Malipiero, Paul Hindemith, Bohuslav Martinů, Darius Milhaud, Rebecca Helferich Clarke, and Albert Roussel.

* The Ernest Bloch Music Festival, an annual composers ' symposium and showcase for progressive and contemporary music, is held in Newport.

As a theory of phonological representation, autosegmental phonology developed a formal account of ideas that had been sketched in earlier work by several linguists, notably Bernard Bloch ( 1948 ), Charles Hockett ( 1955 ) and J. R. Firth ( 1948 ).

Graphical representation of Bloch Function

* Bloch sphere, geometrical representation of the pure state space of a two-level quantum mechanical system

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

The representation on the Bloch sphere for a state vector will simply be the vector of expectation values.

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