From Stochastic Optics to theWigner Formalism: The Role of the Vacuum Field in Optical Quantum Communication Experiments

Abstract

TheWigner formalism in the Heisenberg picture constitutes a bridge that connects QuantumOptics to Stochastic Optics. The vacuum field appears explicitly in the formalism, and the wavelikeaspects of light are emphasised. In addition, the zeropoint intensity as a threshold for detection is acommon denominator in both theories. In this paper, after summarising the basic rules of the Wignerapproach and its application to parametric down-conversion, some new results are presented thatdelve into the physical meaning of the zeropoint field in optical quantum communication. Specifically,the relationship between Bell-state distinguishability and the number of sets of zeropoint modesthat take part in the experiment is analysed in terms of the coupling between the phases of thedifferent fields involved and the subtraction of the zeropoint intensity at the detectors. Additionally,the connection between the compatibility theorem in quantum cryptography and zeropoint fieldis stressed.

Innsbruck Teleportation Experiment in the Wigner Formalism: A Realistic Description Based on the Role of the Zero-Point Field

“…The role of the ZPF inputs in Bell state analysis has been investigated in previous works [31,33,34] by focusing on Bell state distinguishability of two photons, entangled in n dichotomic degrees of freedom, which are not mixed at the analyzer, and BSM of the one-photon polarization-momentum Bell states. The common denominator is the relationship between distinguishability of Bell states and an adequate balance between the number of amplified sets of ZPF modes entering the analyzer and the number of the sets of ZPF modes entering the idle channels located inside the analyzer.…”

“…The role of the zero-point intensity as a threshold for detection has been applied elsewhere to Bell state analysis [31,33,34]. In this article, new advances have been made in this area.…”

“…The combination of the possibility of transmitting and storing quantum information via the ZPF has revealed that the WRHP formalism is a very useful tool in analyzing the influence of the vacuum field in experiments on optical quantum communication [29][30][31][32][33][34]. Specifically, this approach has been applied to the analysis of teleportation experiments, such as entanglement swapping [32] and the Rome teleportation experiment [33].…”

“…The study of the Rome experiment showed the great importance of the zero-point inputs in BSM [31], in such a way that the distinguishability of the four polarizationmomentum Bell states of a single photon can be understood from a sufficient balance between the zero-point inputs at the source of entanglement and those that intervening in the Bell state analyzer. More recently, the role of the zero-point amplitudes as hidden variables on Bell state distinguishability and their application to teleportation [16] have been investigated [34].…”

Parallel Algorithm for Calculating the Wigner Function for a Quantum System With a Polynomial Potential

“…Решение современных задач квантовой информатики [1][2][3], квантовой связи и криптографии [4,5], задач обработки сигнала [6][7][8] содержит аппарат квантовой механики в фазовом пространстве. Функция Вигнера [9] играет важную роль при нахождении средних по фазовому пространству квантовых характеристик системы [10][11][12][13][14][15][16][17][18][19][20]…”