Adventures in Phase Space: From Non-Commuting Coordinates to Quantum Error Correction

Yan Jiang-feng

In this paper,Moyal-Weyl multiplcation sign and Bopp shift are introduced.By considering the relation of non-commutative in coordinate-coordinate and momentum-momentum,the Wigner function of charged harmonic oscillator in non-commutative phase spaces are discussed.By using algebraic relation of quantum mechanics in non-commutative phase space,it has been found that the Wigner function depends on the addition item of non-commutative parameters,compared with the commutative space.

James A. Brooke, Franklin E. Schroeck

Grigori Gennadievich Amosov, Мокеев Александр Сергеевич

Abstract In the present paper we continue our study of non-commutative operator graphs in infinite-dimensional spaces. We consider examples of the non-commutative operator graphs generated by resolutions of identity corresponding to the Heisenberg–Weyl group of operators acting on the Fock space over one-particle state space. The problem of quantum error correction for such graphs is discussed.

Lorenza Viola

Nicolas Fabre, Arne Keller, P. Milman

We introduce a quasiprobability phase space distribution with two pairs of azimuthal-angular coordinates. This representation is well adapted to describe quantum systems with discrete symmetry. Quantum error correction of states encoded in continuous variables using translationally invariant states is studied as an example of application. We also propose an experimental scheme for measuring such distribution.

Walter J. Deal