Coherent representation of fields and deformation quantization

Motivated by some well-known results in the phase space description of quantum optics and quantum information theory, we aim to describe the formalism of quantum field theory by explicitly considering the holomorphic representation for a scalar field within the deformation quantization program. Notably, the symbol of a symmetric ordered operator in terms of holomorphic variables may be straightforwardly obtained by the quantum field analogue of the Husimi distribution associated with a normal ordered operator. This relation also allows to establish a [Formula: see text]-equivalence between the Moyal and the normal star-products. In addition, by writing the density operator in terms of coherent states we are able to directly introduce a series representation of the Wigner functional distribution, which may be convenient in order to calculate probability distributions of quantum field observables without performing formal phase space integrals at all.

Quantum Teleportation and Holomorphic Representation of CCR

For the treatment of teleportation of continuous quantum variables, often the Wigner functions are used. In this paper, we will show that by using the holomorphic representation of the canonical commutation relations (CCR), the teleportation of continuous quantum variables is treated in a parallel way as the teleportation of qubits.