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.
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.
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.
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 the context of bipartite bosonic systems, two notions of classicality of correlations can be defined: P classicality, based on the properties of the Glauber-Sudarshan P function; and C classicality, based on the entropic quantum discord. It has been shown that these two notions are maximally inequivalent in a static (metric) sense, as they coincide only on a set of states of zero measure. We extend and reinforce quantitatively this inequivalence by addressing the dynamical relation between these types of nonclassicality in a paradigmatic quantum-optical setting: the linear mixing at a beam splitter of a single-mode Gaussian state with a thermal reference state. Specifically, we show that almost all P-classical input states generate outputs that are not C classical. Indeed, for the case of zero thermal reference photons, the more P-classical resources at the input the less C classicality at the output. In addition, we show that the P classicality at the input---as quantified by the nonclassical depth---does instead determine quantitatively the potential of generating output entanglement. This endows the nonclassical depth with a new operational interpretation: it gives the maximum number of thermal reference photons that can be mixed at a beam splitter without destroying the output entanglement.
A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is suitably squeezed. We demonstrate, experimentally, that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to, but not entangled with, a third mode. Specifically, we show that a beam splitter can create three-mode entanglement by acting on two modes of a three-mode fully separable Gaussian state without entangling the two modes themselves. This beam splitter property is a key mechanism behind the performance of the protocol for entanglement distribution by separable states. Moreover, the property also finds application in collaborative quantum dense coding in which decoding of transmitted information is assisted by interference with a mode of the collaborating party.
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.