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.
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.
Quantum correlations play a fundamental role in quantum information science. Within bipartite mixed states, they can arise in different incarnations, i.e. Bell nonlocality, steering, and entanglement. Besides being of fundamental interest, they can all be exploited to attain enhancements in quantum information processing tasks over classical methods. Here, in a two-mode Gaussian state [Formula: see text], where the mode [Formula: see text]([Formula: see text]) is generated during the first(second) transition of a correlated-emission laser, we perform a comparative study between the three forms of quantum correlations in the presence of dissipation and thermal noise. We use the master equation of the state [Formula: see text] to obtain the first and second moments of the laser modes variables in the steady state regime. Under realistic experimental conditions, we show that Bell nonlocality could be exhibited by the state [Formula: see text] only when the two laser modes [Formula: see text] and [Formula: see text] are weakly entangled, in contrast, it disappears when they are strongly entangled. Especially, we find that Bell nonlocality is strongly sensitive to thermal noise. Also, we show that the state [Formula: see text] can display one-way and two-way steering in a wide range of operating parameters. In particular, we demonstrate that one-way steering can be detected solely in the direction [Formula: see text]. Against thermal noise, entanglement is found to be more robust than steering, which is in turn found to be more robust than Bell nonlocality. The obtained results are helpful in understanding the behavior of quantum nonlocality in dissipative-noisy environments, and may find potential applications for quantum information tasks.
Abstract Steering is a type of quantum nonlocality that exhibits an inherent asymmetry between two observers. In a nondegenerate three‐level laser coupled to a two‐mode squeezed vacuum reservoir, under realistic experimental conditions, the Gaussian steering of two laser modes, and , generated within the cascade transitions, respectively are examined. It is found that the steerability is always higher than that from ; in addition, the steering asymmetry cannot exceed ln 2, which implies that the state never diverges to an extremal asymmetry state. It is shown how squeezed noise can play a constructive role in realizing one‐way steering. As the main result, it is demonstrated that the state can exhibit one‐way steering solely from , which is shown to emerge as a consequence of the fact that the intensity difference of the modes and is verified to remain always positive, irrespective of the physical and environmental parameters of . The generated unidirectional one‐way steering may provide a useful resource for the distribution of the trust in future asymmetric quantum information tasks.
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.
In this paper, we analyze, under realistic experimental conditions, entanglement and quantum discord in a two-mode Gaussian state [Formula: see text] coupled to a thermal reservoir. The mode [Formula: see text]([Formula: see text]) is generated during the first(second) transition of a nondegenerate three-level laser. The gain medium of the laser is a set of three-level atoms in a cascade configuration. The atoms are prepared initially in a superposition of the upper and lower levels. In the good cavity-limit, applying the master equation we obtain the covariance matrix of the state [Formula: see text] at steady-state. We use the entanglement of formation and the Gaussian quantum discord to quantify entanglement and quantum correlations beyond entanglement, respectively. The two indicators of nonclassicality are defined by means of the von Neumann entropy, and obtained as functions of the parameters characterizing the physical and environmental parameters of the state [Formula: see text], i.e. atomic coherence, dissipation and thermal photon number. As results, we find that maximum entanglement and discord could be achieved by adjusting the degree of atomic coherence. In contrary to the expectation based on the assumption that entanglement is a part of quantum discord, it is found that the latter can be less than the former. Under thermal noise effect, we find that quantum discord measured when the state [Formula: see text] exhibits entanglement diminishes drastically, while that measured when the [Formula: see text] is separable displays a relatively robust behavior seeming to be captured over a wide range of temperature. Our results assert that nondegenerate three-level lasers may play a crucial role in the implementation of quantum processing tasks, particularly those who do not need entangled states.
Quantum steering refers to the apparent possibility of exploiting nonseparable quantum correlations to remotely influence the quantum state of an observer via local measurements. Different from entanglement and Bell nonlocality, quantum steering exhibits an inherent asymmetric property, which makes it relevant for many asymmetric quantum information processing tasks. Here, we study Gaussian quantum steering between two mechanical modes in an optomechanical ring cavity. Using experimentally feasible parameters, we show that the state of the two considered modes can exhibit two-way steering and even one-way steering. Instead of using unbalanced losses or noises, we propose a simple practical way to control the direction of one-way steering. A comparative study between the steering and entanglement of the studied modes shows that both steering and entanglement undergo a sudden death-like behavior. In particular, steering is found more fragile against thermal noise remaining constantly upper-bounded by entanglement. The proposed scheme may be meaningful for one-sided device-independent quantum key distribution, where the security of such protocol depends fundamentally on the direction of steering.
Quantum steering is a kind of quantum correlations stronger than entanglement but weaker than Bell nonlocality. In an optomechanical system pumped by squeezed light and driven in the red sideband, we study---under thermal effects---stationary Gaussian steering and its asymmetry of two mechanical modes. In the resolved sideband regime using experimentally feasible parameters, we show that Gaussian steering can be created by quantum fluctuations transfer from the squeezed light to the two mechanical modes. Moreover, one-way steering can be observed by controlling the squeezing degree or the environmental temperature. A comparative study between Gaussian steering and Gaussian R\'enyi-2 entanglement of the two considered modes shows on one hand that both steering and entanglement suffer from a sudden death-like phenomenon with early vanishing of steering in various circumstances. On the other hand, steering is found stronger than entanglement, however, remains constantly upper bounded by Gaussian R\'enyi-2 entanglement, and decays rapidly to zero under thermal noise.