In this study, we quantify quantum steering, quantum entanglement, and quantum discord and their interconnection using the technique of parametric down-conversion. Initially, two single-mode Gaussian states together with a non-linear crystal in a cavity are considered. The behavior of the three kinds of quantum correlations depend on the phase of the coherent pump field, purity, and non-classicality of the input states, and the damping rates of the cavity. The amount and time evolution of the quantum correlations enhances with the difference between the non-classicality of the initial states. In presence of the damping rates, the quantum steering and quantum entanglement (quantum discord) increase (decreases) with the purity of the input cavity field. We note that the amount and survival time of the quantum correlations can be controlled by varying the relative phase associated to the coherent pump field. The boundaries of the three kinds of quantum correlations are defined and explained with respect to each other, which form a hierarchy.
In this study, we quantify quantum steering, quantum entanglement, and quantum discord and their interconnection using the technique of parametric down-conversion. Initially, two single-mode Gaussian states together with a non-linear crystal in a cavity are considered. The behavior of the three kinds of quantum correlations depend on the phase of the coherent pump field, purity, and non-classicality of the input states, and the damping rates of the cavity. The amount and time evolution of the quantum correlations enhances with the difference between the non-classicality of the initial states. In presence of the damping rates, the quantum steering and quantum entanglement (quantum discord) increase (decreases) with the purity of the input cavity field. We note that the amount and survival time of the quantum correlations can be controlled by varying the relative phase associated to the coherent pump field. The boundaries of the three kinds of quantum correlations are defined and explained with respect to each other, which form a hierarchy.
Abstract Quantum discord, an appropriate measure of quantum correlation, is analyzed in a two-mode Gaussian state of the cavity field evolved by a system of quantum beat laser. In the laser system, two arbitrary single-mode Gaussian states of the cavity fields and an external classical field couple to the atomic lasing medium. We calculate the time-dependent expression for the quantum discord both analytically and numerically, by following the reduced density matrix equation of the resulting cavity field. In this framework, we investigate the generation and control of Gaussian quantum discord in the two-mode Gaussian state of the cavity field at the output in terms of the purity and non-classicality of the two input cavity modes, the Rabi frequency of the classical driving field, the relative phase of the coupling parameters, and the damping rates of the cavity modes. The behaviour of quantum discord appears oscillatory due to the quantum beats in the output cavity field developed by the classical driving field in the medium as time passes. Moreover, we find that quantum discord switches on and off while adjusting the relative phase of the coupling parameters. Analysis of the analytical results agrees well with our numerical simulations.
As an active quantum system, the correlated spontaneous emission laser has many valuable applications in quantum information processing. Here, we report on temporal evolution of the quantum correlations such as quantum discord, entanglement, steering, and Bell non-locality for the field retrieved in the form of two-mode Gaussian state using a system of correlated spontaneous emission laser. We consider the initial modes of the cavity field as two independent arbitrary single-mode Gaussian states inside the cavity. The density matrix for the resulting cavity field is evaluated both analytically and numerically with respect to the time evolution of the laser system. The influences of the non-classicality and purity of the initial cavity modes, the Rabi frequency of the classical coupling field, and the cavity damping rates are studied thoroughly. We show explicitly that the boundaries for the four kinds of the temporal quantum correlations of the cavity field retrieved satisfy a strict hierarchy.
Abstract Generating and controlling continuous-variable entanglement is a central requirement for quantum information processing protocols. In the present contribution, we investigate the bipartite Gaussian entanglement of the two-mode Gaussian state produced by a parametric converter, with the two cavity modes initially prepared as arbitrary, non-classical single-mode Gaussian states of tunable purity and non-classicality. The entanglement is witnessed using the Simon's separability criterion, which is necessary and sufficient for Gaussian states, along with the Duan's inseparability criterion. We solve its dynamics as functions of the coherent pump-field phase, the cavity decay rates, and the non-classicality and purity of the initial modes. The entanglement evolves as a damped oscillation and emerges only once there is a difference between the non-classicalities of the two input states, becoming stronger as this difference grows. Likewise, the phase of the pump-field controls both the strength and time duration of entanglement. Higher input purity moderately strengthens and prolongs the correlations, whereas the cavity decay rates are the main source of decoherence. Finally, we compare the two criteria and find that the Simon's condition shows nearly continuous entanglement, whereas Duan's criterion responds only where the correlations are strong, leaving transient windows in which the state is separable under Duan yet still inseparable under Simon. These theoretical results suggest that, the non-classicality of the input field and the phase of the pump field can serve as effective control parameters for achieving tunable bipartite Gaussian entanglement, offering guidance for future practical realizations in cavity-based systems.
Beam splitters are important components in numerous tasks of quantum information protocols used either in simple or in an interferometric arrangement or together with other quantum systems. This report shows interesting aspects of the quantum correlations of two-mode Gaussian state (TMGS) for the photons retrieved via a linear beam splitter when they are initially employed at the input of either pure or mixed two single-mode Gaussian states (TSMGSs). The quantum correlations obey the boundaries of quantum non-locality, steering, entanglement and discord for pure input states. Though Bell inequality does not violate, quantum steering, entanglement and discord exist in the quantum state evolved by the beam splitter when input states become mixed. Specifically, the quantum steering, entanglement and discord persist to some degrees against the thermal photon number, the Bell inequality is, nonetheless, obeyed by the quantum state except in a very sharp regime.
Abstract In this paper, we investigate the creation of quantum correlations such as entanglement, the Gaussian quantum discord and quantum steering in a quantum system under consideration via the linear beam splitter with squeezed thermal and a single-mode Gaussian states at the inputs. This quantum system generates bright entangled output two-mode light. Specifically, the quantum entanglement can be enhanced through increasing the purity of the Gaussian state and the squeezing parameter at the input states. The quantum correlations reveal similar characteristics for each case. That means when we increase the non-classicality, purity and squeezing parameter, the quantum correlations show enhanced profile. On the other hand, upon increasing the mean thermal photon number at the input, the quantum correlations indicate inverse relation.
Quantum states can be correlated in ways beyond what is possible for classical states. These correlations are considered as the main resource for quantum computation and communication tasks. In this thesis, I present my studies on the different forms of Quantum Correlations known as "Quantum Discord", "Einstein-Podolsky-Rosen(EPR) Steering" and "Bel-type correlations" in the continuous-variable quantum states and investigate their practical applications for the secure quantum communication. While previously quantum entanglement was considered as the only form of quantum correlation, in the recent years a notion known as quantum discord which captures extra quantum correlations beyond entanglement was introduced by Ollivier and Zurek. This sort of non-classicality that can exist even in separable states, has raised so much aspiration for the potential applications, as they are less fragile than the entangled states. Therefore, of especial interest is to know if a bipartite quantum state is discordant or not. In this thesis I will describe the simple and efficient experimental technique that we have introduced and experimentally implemented to verify quantum discord in unknown Gaussian states and a certain class of non-Gaussian states. According to our method, the peak separation between the marginal distributions of one subsystem conditioned on two different outcomes of homodyne measurement conducted on the other subsystem is an indication of nonzero quantum discord. We implemented this method experimentally by preparing bipartite Gaussian and non-Gaussian states and proved nonzero quantum discord in all the prepared states. Though quantum key distribution has become a mature technology, the possibility of hacking the devices used in the quantum communications has motivated the scientists to develop the schemes where one or non of the devices used by the communicating parties need to be trusted. Quantum correlations are the key to develop these schemes. Particularly, EPR steering is connected to the one-sided-deviceindependent quantum key distribution in which devices of one party are solely trusted and Bell-type correlations to the fully device-independent quantum key distribution where non of the apparatuses of the communicating parties is trusted. Here, I will present the result of our theoretical and experimental research to develop one-sided-device-independent quantum key distribution in continuous variables. We identify all Gaussian protocols that can in principle be one-sided-device independent. This consists of 6 protocols out of 16 possible Gaussian protocols, which surprisingly includes the protocol that applies only coherent states. We experimentally implemented both the entanglement-based and coherent state protocols and manifested their loss tolerance. Our results open the door for the practical secure quantum communications, asserting the link between the EPR-steering andone-sided-device-independence. Due to the maturity of quantum information using continuous variables, it is important to develop a Bell-type inequality in this regime. Despite its fundamental importance, Bell-type correlation is linked to the device-independent quantum key distribution. I developed a computer modelling based on the proposal of ref [1, 2] to demonstrate continuous-variable Bell-type correlation. The results of my computer simulations that are presented in this thesis show the feasibility of these proposals, which makes the real-life implementation of continuous-variable device-independent quantum key distribution possible.