Mechanism of interaction of discrete and continuous variable states for efficient generation of hybrid entangled states

TL;DR

This paper presents a theoretical framework for generating hybrid entangled states by interacting discrete-variable and continuous-variable states using a highly transmissive beam splitter, involving displacement operations and photon detection.

Contribution

It introduces a novel mechanism for hybrid entanglement generation based on simultaneous displacements and photon registration, extending previous experimental work.

Findings

Conditions for balanced hybrid entangled states are identified.

The proposed method aligns with previous experimental demonstrations.

Theoretical insights facilitate efficient hybrid entanglement generation.

Abstract

We develop theory of realization of hybrid entanglement between discrete-variable (single photon) and continuous-variable states (coherent states). A highly transmissive beam splitter (HTBS) is used for interaction of the ingredients. Mechanism for generating the hybrid entangled states is based on the simultaneous displacement of the discrete-variable state on equal in absolute value but opposite in sign displacement amplitudes by coherent components, in such a way that all the information about the displacement amplitudes is lost with subsequent registration of photons in the auxiliary mode. Conditions for the balanced hybrid entangled states generation are found. Our approach follows along lines experimentally demonstrated in Nat. Photonics 8, 570-574 (2014).