Finite Heisenberg group and its application in quantum computing and information

The Heisenberg group has been instrumental in the development of a wide range of mathematical topics. Techniques involving its representation theory often yield interesting results or straightforward proofs of existing theorems. It is well known that the Heisenberg group appears in various areas, such as quantum theory, signal theory, theory of theta functions, and number theory. This paper contains some new results on harmonic analysis on finite Heisenberg groups. We also describe finite Heisenberg groups and their algebraic structure. The aim of this paper is investigation of finite Heisenberg group; also specify a complete set of inequivalent irreducible representations. We also recall the use of finite Heisenberg group in various areas of Quantum Information & Computing. For example we study the properties of the discrete Wigner function. In particular we analyze the entanglement properties by using discrete Wigner function.