Operator symbols in the description of observable-state systems

Vladimir N. Chernega, S. N. Belolipetskiy, Olga V. Man’ko +1 more

Abstract This paper presents a review of star-product formalism. This formalism provides a description for quantum states and observables by means of the functions called’ symbols of operators’. Those functions are obtained via bijective maps of the operators acting in Hilbert space. Examples of the Wigner-Weyl symbols (Wigner quasi-distributions) and tomographic probability distributions (symplectic, optical and photon-number tomograms) identified for the states of the quantum systems are discussed. Properties of quantizer-dequantizer operators required for construction of bijective maps of two operators (quantum observables) onto the symbols of the operators are studied. The relationship between structure constants of associative star-product of operator symbols and quantizer-dequantizer operators is reviewed.

K. Tamvakis

T.T. TAYLOR

Grigori Gennadievich Amosov, Ya. A. Korennoy, Vladimir I. Man’ko

Explicit expressions for most interesting quantum observable operators in optical tomography representation are found. A general formalism of the symbols of the operators is presented in the optical tomography representation. The symbols of the operators in the form of singular and regular generalized functions are found, and suggestions for their use in experimental data processing in quantum tomography are given.

David J. Ross

Alexandre de A. Barbosa, Bernardo Lula, Aércio Ferreira de Lima

Simulation fulfills an important mechanism for the study and the development of many areas. Quantum computation simulation tools have become essential, because no effective quantum hardware has been implemented yet. However, the currently available simulators have serious deficiencies, which makes the description of this new computational paradigm incomplete. This article presents a universal quantum circuit simulator, called Zeno, and the symbolic extension that is being developed to it. The extension will allow a symbolic description of the system's state allied to the graphical representation of the circuit to be visualized together. Users will be able to work in a faster and more efficient way than making this calculations by hand. The extension will make possible a faithful description of the system computation like the descriptions observed in related literature.