Search

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.

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 $% \hat{\varrho}_{c_{1}c_{2}}$ coupled to a two-mode vacuum reservoir. The mode $c_{1}$($c_{2}$) is emitted during the first(second) transition of a nondegenerate three-level cascade laser. By means of the master equation of the state $\hat{\varrho}_{c_{1}c_{2}}$, we derive analytical expression of the steady-state covariance matrix of the modes $c_{1}$ and $c_{2}$. Using realistic experimental parameters, we show that the state $\hat{\varrho}% _{c_{1}c_{2}}$ can exhibit asymmetric steering. Furthermore, by an appropriate choice of the physical parameters of the state $\hat{\varrho}% _{c_{1}c_{2}}$, we show that one-way steering can be achieved. Essentially, we demonstrate that one-way steering can, in general, occur only from $% c_{1}\rightarrow c_{2}$. Besides, we perform a comparative study between the steering of the two laser modes and their Gaussian R\'{e}nyi-2 entanglement. As results, 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 $\hat{\varrho}_{c_{1}c_{2}}$% . In particular, we found that the steering remains always less than the Gaussian R\'{e}nyi-2 entanglement.

Quantum steering displays an inherent asymmetric property that differs from entanglement and Bell nonlocality. Besides being of fundamental interest, steering is relevant to many asymmetric quantum information tasks. Here, we propose a scheme to generate and manipulate Gaussian quantum steering between two spatially distant mechanical modes of two optomechanical cavities coupled via an optical fiber, and driven by blue detuned lasers. In the unresolved sideband regime, we show, under realistic experimental conditions, that strong asymmetric steering can be generated between the two considered modes. Also, we show that one-way steering can be achieved and practically manipulated through the lasers drive powers and the temperatures of the cavities. Further, we reveal that the direction of one-way steering depends on the sign of the difference between the energies of the mechanical modes. Finally, we discuss how to access the generated steering. This work opens up new perspectives for the distribution of long-distance trust which is of great interest in secure quantum communication.

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, we examine, under realistic experimental conditions, the Gaussian steering of two laser modes, $\mathcal{A}$ and $\mathcal{B}$, generated within the cascade transitions, respectively. We find that the $\mathcal{A}\rightarrow \mathcal{B}$ steerability is always higher than that from $\mathcal{B}\rightarrow \mathcal{A}$; in addition, the steering asymmetry cannot exceed $\ln 2$, which implies that the state $\hat{\varrho}_{\mathcal{AB}}$ never diverges to an extremal asymmetry state. We show how squeezed noise can play a constructive role in realizing one-way steering. As the main result, we demonstrate that the state $\hat{\varrho}_{\mathcal{AB}}$ can exhibit one-way steering solely from $\mathcal{A}\rightarrow \mathcal{B}$, which we show to emerge as a consequence of the fact that the intensity difference of the modes $\mathcal{A}$ and $\mathcal{B}$ is verified to remain always positive, irrespective of the physical and environmental parameters of $\hat{\varrho}_{\mathcal{AB}}$. The generated unidirectional one-way steering may provide a useful resource for the distribution of the trust in future asymmetric quantum information tasks.

Coherence arises from the superposition principle, where it plays a central role in quantum mechanics. In [Phys.Rev.Lett.114,210401(2015)], it has been shown that the freezing phenomenon of quantum correlations beyond entanglement, is intimately related to the freezing of quantum coherence (QC). In this paper, we compare the behaviour of entanglement and quantum discord with quantum coherence in two di erent subsystems (optical and mechanical). We use respectively the en-tanglement of formation (EoF) and the Gaussian quantum discord (GQD) to quantify entanglement and quantum discord. Under thermal noise and optomechanical coupling e ects, we show that EoF, GQD and QC behave in the same way. Remarkably, when entanglement vanishes, GQD and QC re-main almost una ected by thermal noise, keeping non zero values even for high temperature, which in concordance with [Phys.Rev.Lett.114,210401(2015)]. Also, we nd that the coherence associated with the optical subsystem are more robustagainst thermal noisethan those of the mechanical subsystem. Our results con rm that optomechanical cavities constitute a powerful resource of QC., Comment: 9 figures, 15 pages

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.

Einstein-Podolski-Rosen steering is a form of quantum correlation exhibiting an intrinsic asymmetry between two entangled systems. In this paper, we propose a scheme for examining dynamical Gaussian quantum steering of two mixed mechanical modes. For this, we use two spatially separated optomechanical cavities fed by squeezed light. We work in the resolved sideband regime. Limiting to the adiabatic regime, we show that it is possible to generate dynamical Gaussian steering via a quantum fluctuations transfer from squeezed light to the mechanical modes. By an appropriate choice of the environmental parameters, one-way steering can be observed in different scenarios. Finally, comparing with entanglement - quantified by the Gaussian R\'enyi-2 entropy-, we show that Gaussian steering is strongly sensitive to the thermal effects and always upper bounded by entanglement degree.

Using the Gaussian R\'enyi-2 entropy, we analyse the behaviour of two different aspects of quantum correlations (entanglement and quantum discord) in two optomechanical subsystems (optical and mechanical). We work in the resolved sideband and weak coupling regimes. In experimentally accessible parameters, we show that it is possible to create entanglement and quantum discord in the considered subsystems by quantum fluctuations transfer from either light to light or light to matter. We find that both mechanical and optical entanglement are strongly sensitive to thermal noises. In particular, we find that the mechanical one is more affected by thermal effects than that optical. Finally, we reveal that under thermal noises, the discord associated with the entangled state decays aggressively, whereas the discord of the separable state (quantumness of correlations) exhibits a freezing behaviour, seeming to be captured over a wide range of temperature.