Some Quantum Gate Operators for Continuum Variables in q-Deformed Coordinate Representation

Abstract

By virtue of deformation quantization methods we introduce the q-deformed coordinate representation. A new set of completeness and orthogonality relations composed of the ket and bra which are not mutually Hermitian conjugates are derived. Further, using the eigenket and eigenbra for q-deformed coordinate some important quantum gate operators for continuum variables are realized and their properties are discussed.

Transformation of coherent state in Hadamard gate via multi-photon catalysis

“…Form equation (11), it is clear to see that the output quantum state of the TCHG depends on the number of input photons in the Fock state and the amplitude of the coherent state when the scale length σ is fixed.…”

“…Therefore, quantum gates play a crucial role * Author to whom any correspondence should be addressed. in quantum optics, quantum computation, quantum measurement and quantum state preparation [11,12]. Quantum logic gates are represented by unitary matrices or unitary operator, such as Toffoli gate, controlled-NOT gate and Hadamard gate [13][14][15].…”

Photon-Subtracted Two-Mode Squeezed Thermal State and Its Photon-Number Distribution

“…Using the completeness relation of a coherent state and ρ 2s 's normal ordering form in (8), as well as the overlap of two-mode coherent state…”

“…as well as the normal ordering form of ρ 2s in (8), the probability of finding m 1 , m 2 photons in the field is given by …”

“…Distribution functions in phase space have been a major topics in studying quantum optics and quantum statistics [1][2][3][4][5][6][7][8]. It is well known the photons of a radiation field are distributed among various states of the field.…”