Steering is a type of nonseparable quantum correlation, where its inherent asymmetric feature makes it distinct from Bell nonlocality and entanglement. In this paper, we investigate quantum steering in a two-mode Gaussian state [Formula: see text] coupled to a two-mode vacuum reservoir. The mode [Formula: see text] ([Formula: see text]) is emitted during the first (second) transition of a nondegenerate three-level cascade laser. By means of the master equation of the state [Formula: see text], we derive the analytical expression of the steady-state covariance matrix of the modes [Formula: see text] and [Formula: see text]. Using realistic experimental parameters, we show that the state [Formula: see text] can exhibit asymmetric steering. Furthermore, by an appropriate choice of the physical parameters of the state [Formula: see text], we show that one-way steering can be achieved. Essentially, we demonstrate that one-way steering can, in general, occur only from [Formula: see text]. Besides, we perform a comparative study between the steering of the two laser modes and their Gaussian Rényi-2 entanglement. As a result, we found that the entanglement and steering behave similarly in the same circumstances, i.e. both of them decay under dissipation effect; moreover, they can be well enhanced by inducing more and more quantum coherence in the state [Formula: see text]. In particular, we found that the steering remains always less than the Gaussian Rényi-2 entanglement.

arXiv:2312.04942Modern Physics Letters BJul 27, 20236 citations

One-Way Steering as a Resource for Asymmetric Quantum Communication in Three-Level Laser Systems

K. Talbi, J. El Qars, Ismail Essaoudi +3 more

Abstract We theoretically investigate the emergence and asymmetry of Gaussian quantum steering and Rényi-2 entanglement in the radiation field of a nondegenerate three-level laser system. The gain medium consists of atoms initially prepared in a coherent superposition of the upper and lower states, interacting with two quantized cavity modes coupled to a common thermal reservoir. Using the steady-state solution of the master equation and the covariance matrix formalism, we compute the Gaussian steerability in both directions and compare it to the Gaussian Rényi-2 entanglement. Our analysis reveals that, under a wide range of parameters—including gain strength, population inversion, and thermal phonon number—the system exhibits generic one-way steering from mode A to mode B , with the reverse direction being inaccessible. This asymmetry is shown to originate from the photon number imbalance between the two modes. We further demonstrate that thermal noise degrades quantum correlations, with steering being more fragile than entanglement. These results provide theoretical support for the implementation of asymmetric quantum information protocols in cavity-based platforms and could be tested with current experimental technologies.

Chinese Physics BJan 4, 20260 citations