Fidelity, purity and entanglement of two-mode spatially Gaussian-entangled light fields in Turbulence Atmosphere

TL;DR

This paper analyzes how atmospheric turbulence affects the transmission of two-mode Gaussian-entangled light, deriving formulas for quantum properties and discussing optimal conditions for long-distance quantum communication.

Contribution

It provides analytical expressions for fidelity, purity, and entanglement evolution of Gaussian-entangled states in turbulence, and explores optimal input parameters for long-distance quantum distribution.

Findings

Maximal entanglement distribution distance decreases with stronger turbulence.

Higher initial entanglement extends the distribution distance.

Optimal input parameters improve long-distance quantum entanglement transfer.

Abstract

In this paper, we investigate the propagation of two-mode spatially Gaussian-entangled quantum light fields passing through the turbulence atmosphere. From the propagation formula of the two-mode wave function in the position representation, we have derived the analytical expressions for the fidelity, purity and logarithmic negativity (entanglement) of the resulting quantum state after the long-distance atmospheric transportation. Based on the derived formulae, the effects of the atmospheric turbulences on the evolutions of quantum properties of the resulting two-mode quantum state are discussed in detail under different input parameters of the initial two-mode quantum state. The results show that the maximal distributing distance of quantum entanglement is strongly dependent on the atmospheric conditions: when the atmospheric turbulence becomes stronger and stronger, the maximal distance becomes shorter and shorter, and both the fidelity and purity decrease quicker and quicker as functions of propagating distances. Under a certain atmospheric condition, with the increasing of the input entanglement of the initial two-mode spatially Gaussian-entangled quantum state, the maximal distributing distance for preserving the entanglement gradually increases and always has a saturated (upper) limitation, and both the evolutions of the fidelity and purity are affected by the input parameters of the initial two-mode quantum state, Finally the optimal parameters of the input two-mode quantum state with the fixed input entanglement are discussed in order to obtain the optimal transfer distribution of the quantum entanglement over a long distance under a certain atmosphere. Our theoretical results are very helpful for building the distribution of the quantum entanglement via free-space atmosphere link.