Generation of One‐Way Gaussian Steering by Gaussian Channel and Converting One‐Way Gaussian Steering by Beamsplitters

Abstract

Gaussian steering is used to characterize the intrinsic quantum correlation of Gaussian states under Gaussian measurement. Here we study the generation of one‐way Gaussian steering and the conversion of one‐way Gaussian steering. It is found that one‐way Gaussian steering could be generated by using Gaussian channels, either the Gaussian lossy channel or the Gaussian amplification channel. Exploiting the one‐way Gaussian steering in a two‐partite quantum system consists of two subsystems marked with A and B, one‐way Gaussian steering (steering from A to B) can be converted to the other one‐way Gaussian steering (steering from B to A) using linear optics, and vice versa.

Unidirectional Gaussian One‐Way Steering

“…Although one-way steering is observed from both  →  and  →  in various TMGSs ρ , [31,[33][34][35][36][37][38] we demonstrated that the state ρ can, in general , exhibit one-way steering solely from  → . Such unidirectionality restriction is shown to emerge as a consequence of the fact that the intensity difference of the modes  and  is verified to remain always positive, regardless of the physical and environmental parameters of ρ .…”

“…where   = 𝛽 − 𝛿 T 𝛼 −1 𝛿 represents the Schur complement of the mode  in the covariance matrix 𝜎  defined by Equation (35).…”

“…]. Experimentally, the three independent elements, 𝜎 11 , 𝜎 22 , and 𝜎 12 , of the covariance matrix (35), can be measured via the standard homodyne detection method, [51] which allows experimental values of the Gaussian steerabilities  → and  → to be obtained.…”

“…( 37), i.e., G B→A = max 0, 1 2 ln det β det σ AB . Experimentally, the three independent elements, σ 11 , σ 22 , and σ 12 , of the covariance matrix (35), can be measured via the standard homodyne detection method [51], which allows experimental values of the Gaussian steerabilities G A→B and G B→A to be obtained. AB versus the population inversion η for two different values of the linear gain coefficient A: (a) A = 200 kHz and (b) A = 1000 kHz corresponding to atomic injection rates r 0 = 22 kHz and r 0 = 108 kHz, respectively.…”

“…Unlike various TMGS ρ systems [31,[33][34][35][36][37][38] in which one-way steering is bidirectional, that is, it can emerge from  →  and  → , herein, we mainly demonstrate that the state at hand ρ can solely exhibit one-way steering from  → . Furthermore, we show that this unidirectionality restriction emerges as a consequence of the fact that the intensity difference of the modes  and  is verified to always remain positive, regardless of the physical and environmental parameters of ρ .…”