Nowadays, it is widely acknowledged that information can serve as a thermodynamic fuel capable of powering the extraction of useful work through measurements and feedback control. Moreover, it has been demonstrated that the work extractable from a correlated bipartite state can effectively distinguish entangled states from separable ones. In this context, we introduce an operational criterion denoted as [Formula: see text] to witness the presence of entanglement in a two-mode Gaussian state [Formula: see text], based on the amount of work that can be extracted from a thermal bath using a Szilard-like engine. In this setup, the state [Formula: see text] acts as the working medium of the engine, where modes [Formula: see text] and [Formula: see text] are generated during the first and second transitions of a nondegenerate three-level laser, and are coupled to a shared two-mode thermal bath. Our results reveal that the proposed criterion [Formula: see text] vanishes when [Formula: see text] is a product state. Furthermore, [Formula: see text] reaches its maximum value when [Formula: see text] is coupled to a vacuum bath, but it diminishes under the influence of thermal noise. Notably, the degree of entanglement detected by [Formula: see text] can be tuned via the atomic coherence of the laser. Finally, a comparison of [Formula: see text] with a reliable measure of entanglement such as logarithmic negativity, demonstrates perfect agreement in identifying the presence of entanglement in [Formula: see text].
Nowadays, it is widely acknowledged that information can serve as a thermodynamic fuel capable of powering the extraction of useful work through measurements and feedback control. Moreover, it has been demonstrated that the work extractable from a correlated bipartite state can effectively distinguish entangled states from separable ones. In this context, we introduce an operational criterion denoted as [Formula: see text] to witness the presence of entanglement in a two-mode Gaussian state [Formula: see text], based on the amount of work that can be extracted from a thermal bath using a Szilard-like engine. In this setup, the state [Formula: see text] acts as the working medium of the engine, where modes [Formula: see text] and [Formula: see text] are generated during the first and second transitions of a nondegenerate three-level laser, and are coupled to a shared two-mode thermal bath. Our results reveal that the proposed criterion [Formula: see text] vanishes when [Formula: see text] is a product state. Furthermore, [Formula: see text] reaches its maximum value when [Formula: see text] is coupled to a vacuum bath, but it diminishes under the influence of thermal noise. Notably, the degree of entanglement detected by [Formula: see text] can be tuned via the atomic coherence of the laser. Finally, a comparison of [Formula: see text] with a reliable measure of entanglement such as logarithmic negativity, demonstrates perfect agreement in identifying the presence of entanglement in [Formula: see text].
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.
We show how the presence of entanglement in a bipartite Gaussian state can be detected by the amount of work extracted by a continuous-variable Szilard-like device, where the bipartite state serves as the working medium of the engine. We provide an expression for the work extracted in such a process and specialize it to the case of Gaussian states. The extractable work provides a sufficient condition to witness entanglement in generic two-mode states, becoming also necessary for squeezed thermal states. We extend the protocol to tripartite Gaussian states and show that the full structure of inseparability classes cannot be discriminated based on the extractable work. This suggests that bipartite entanglement is the fundamental resource underpinning work extraction.
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.
The connections between thermodynamics and quantum information processing are of paramount importance. Here, we address a bipartite entanglement via extracted work in a cavity magnomechanical system contained inside an yttrium iron garnet (YIG) sphere. The photons and magnons interact through an interaction between magnetic dipoles. A magnetostrictive interaction, analogous to radiation pressure, couple's phonons and magnons. The extracted work was obtained through a device similar to the Szilárd engine. This engine operates by manipulating the photon-magnon as a bipartite quantum state. We employ logarithmic negativity to measure the amount of entanglement between photon and magnon modes in steady and dynamical states. We explore the extracted work, separable work, and maximum work for squeezed thermal states. We investigate the amount of work extracted from a bipartite quantum state, which can potentially determine the degree of entanglement present in that state. Numerical studies show that entanglement, as detected by the extracted work and quantified by logarithmic negativity, is in good agreement. We show the reduction of extracted work by a second measurement compared to a single measurement. Also, the efficiency of the Szilard engine in steady and dynamical states is investigated. We hope this work is of paramount importance in quantum information processing.
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.
We study a Szilard engine based on a Gaussian state of a system consisting of two bosonic modes placed in a noisy channel. As the initial state of the system is taken an entangled squeezed thermal state, and the quantum work is extracted by performing a measurement on one of the two modes. We use the Markovian Kossakowski-Lindblad master equation for describing the time evolution of the open system and the quantum work definition based on the second order Rényi entropy to simulate the engine. We also study the information-work efficiency of the Szilard engine as a function of the system parameters. The efficiency is defined as the ratio of the extractable work averaged over the measurement angle and the erasure work, which is proportional to the information stored in the system. We show that the extractable quantum work increases with the temperature of the reservoir and the squeezing between the modes, average numbers of thermal photons and frequencies of the modes. The work increases also with the strength of the measurement, attaining the maximal values in the case of a heterodyne detection. The extractable work is decreasing by increasing the squeezing parameter of the noisy channel and it oscillates with the phase of the squeezed thermal reservoir. The efficiency mostly has a similar behavior with the extractable quantum work evolution. However information-work efficiency decreases with temperature, while the quantity of the extractable work increases.