Gaussian Quantum Discord Research Articles

Evolution of quantum steering in a Gaussian noisy channel

We describe the behaviour of the Gaussian quantum steering in a system of two bosonic modes evolving in a Gaussian noisy channel. The evolution based on completely positive quantum dynamical semigroups assures that the Gaussian form of the initial state of the subsystem is preserved in time. We study the quantum steering using the symplectic formalism and we find out that the steerability in the considered open system interacting with a squeezed thermal reservoir is destroyed by thermal noise and dissipation. The Gaussian quantum steerability manifests a sudden suppression, namely it decays at a finite moment of time. This behaviour is similar to the one of the quantum entanglement, compared to the Gaussian quantum discord, which is only asymptotically decreasing in time.

Qubit assisted enhancement of quantum correlations in an optomechanical system

We perform a theoretical study on quantum correlations in an optomechanical system where the mechanical mirror is perturbatively coupled to an auxiliary qubit. In our study, we consider logarithmic negativity to quantify the degree of stationary entanglement between the cavity field and mechanical mirror, and, Gaussian quantum discord as a witness of the quantumness of the correlation beyond entanglement. Utilizing experimentally feasible parameters, we show that both entanglement and quantum discord enhance significantly with increase in mirror–qubit coupling. Moreover, we find that in presence of the mirror–qubit coupling entanglement could be generated at a considerably lower optomechanical coupling strength, which is also extremely robust against the environmental temperature. Overall, our proposed scheme offers some considerable advantages for realizing the continuous-variable quantum information and communication.

Gaussian quantum discord and EPR steering in optomechanical system

We investigate the quantum correlations existing in mixed optomechanical bipartite system optic1–optic2 with radiation pressure, by using the covariance matrix of the pure tripartite system when the initial state is Gaussian. We use the negativity logarithmic to study the entanglement dynamics of bipartite system of two modes optic1–optic2. We propose a scheme for examining dynamical Gaussian quantum steering of two modes optic1–optic2. We also study the Gaussian quantum discord to measure so-called non-classical correlations which go beyond entanglement.

Enhancing quantum correlations in an optomechanical system via cross-Kerr nonlinearity

In this work, we theoretically study the quantum correlations present in an optomechanical system by invoking an additional cross-Kerr coupling between the optical and mechanical mode. Under experimentally achievable conditions, we first show that a significant enhancement of the steady-state entanglement could be achieved at a considerably lower driving power, which is also extremely robust with respect to system parameters and environmental temperature. Then, we employ Gaussian quantum discord as a witness of the genuine quantumness of the correlation present in the system and discuss its dependence on the cross-Kerr nonlinearity.

Generation of quantum discord in two-mode Gaussian systems in a thermal reservoir

In the framework of the theory of open quantum systems based on completely positive dynamical semigroups, we study the Gaussian quantum discord for a subsystem composed of two coupled bosonic modes immersed in a thermal environment. For Gaussian input states, the time evolution of discord is given in terms of the covariance matrix. For initial uni-modal squeezed states the generation of Gaussian discord takes place, for all non-zero values of the strength of interaction between the bosonic modes. After reaching some maximum value in the case of initial uni-modal squeezed states, and also for initial squeezed vacuum states with non-zero Gaussian discord, this measure of quantum correlations non-monotonically decreases in time and tends asymptotically for large times to some definite non-zero value. The asymptotic discord depends on the strength of interaction between the bosonic modes, temperature and dissipation coefficient.

Overarching framework between Gaussian quantum discord and Gaussian quantum illumination

We cast the problem of illuminating an object in a noisy environment into a communication protocol. A probe is sent into the environment, and the presence or absence of the object constitutes a signal encoded on the probe. The probe is then measured to decode the signal. We calculate the Holevo information and bounds to the accessible information between the encoded and received signal with two different Gaussian probes---an Einstein-Podolsky-Rosen (EPR) state and a coherent state. We also evaluate the Gaussian discord consumed during the encoding process with the EPR probe. We find that the Holevo quantum advantage, defined as the difference between the Holevo information obtained from the EPR and coherent state probes, is approximately equal to the discord consumed. These quantities become exact in the typical illumination regime of low object reflectivity and low probe energy. Hence we show that discord is the resource responsible for the quantum advantage in Gaussian quantum illumination.

Quantum correlation in degenerate optical parametric oscillators with mutual injections

We theoretically and numerically study the quantum dynamics of two degenerate optical parametric oscillators with mutual injections. The cavity mode in the optical coupling path between the two oscillator facets is explicitly considered. Stochastic equations for the oscillators and mutual injection path based on the positive $P$ representation are derived. The system of two gradually pumped oscillators with out-of-phase mutual injections is simulated, and its quantum state is investigated. When the incoherent loss of the oscillators other than the mutual injections is small, the squeezed quadratic amplitudes $\hat{p}$ in the oscillators are positively correlated near the oscillation threshold. It indicates finite quantum correlation, estimated via Gaussian quantum discord, and the entanglement between the intracavity subharmonic fields. When the loss in the injection path is low, each oscillator around the phase transition point forms macroscopic superposition even under a small pump noise. It suggests that the squeezed field stored in the low-loss injection path weakens the decoherence in the oscillators.

Entanglement versus Gaussian quantum discord in a double-cavity opto-mechanical system

In this paper, we investigate the robustness of the quantum correlations against the environment effects in various opto-mechanical bipartite systems. For two spatially separated opto-mechanical cavities, we give analytical formula for the global covariance matrix involving two mechanical modes and two optical modes. The logarithmic negativity as an indicator of the degree of entanglement and the Gaussian quantum discord which is a witness of quantumness of correlations are used as quantifiers to evaluate the different pairwise quantum correlations in the whole system. The evolution of the quantum correlations existing in this opto-mechanical system are analyzed in terms of the thermal bath temperature, squeezing parameter and the opto-mechanical cooperativity. We find that with desirable choice of these parameters, it is possible either to enhance or annihilate the quantum correlations in the system. Various scenarios are discussed in detail.

Decay of Gaussian correlations in local thermal reservoirs

In this paper we examine the decay of quantum correlations for the radiation field in a two-mode squeezed thermal state in contact with local thermal reservoirs. Two measures of the evolving quantum correlations between the modes are compared: the entanglement of formation and the quantum discord. We derive analytic expressions of the entanglement-death time in two special cases: when the reservoirs for each mode are identical, as well as when a single reservoir acts on the first mode only. In the latter configuration, we show that all the pure Gaussian states lose their entanglement at the same time, determined solely by the field-reservoir coupling. Also investigated is the evolution of the Gaussian quantum discord for the same choices of thermal baths. We notice that the discord can increase in time above its initial value in a special situation, namely, when the input state is mixed, and local measurements are performed on the attenuated mode. This enhancement of discord is stronger for zero-temperature reservoirs and increases with the input degree of mixing.

Quantum nature of Gaussian discord: Experimental evidence and role of system-environment correlations

We provide experimental evidence of quantum features in bi-partite states classified as entirely classical according to a conventional criterion based on the Glauber P-function but possessing non-zero Gaussian quantum discord. Their quantum nature is experimentally revealed by acting locally on one part of the discordant state. Adding an environmental system purifying the state, we unveil the flow of quantum correlations within a global pure system using the Koashi-Winter inequality. We experimentally verify and investigate the counterintuitive effect of discord increase under the action of local loss and link it to the entanglement with the environment. For a discordant state generated by splitting a state in which the initial squeezing is destroyed by random displacements, we demonstrate the recovery of entanglement highlighting the role of system-environment correlations.

Dynamic of the Gaussian quantum discord and effect of non-Markovian degree

We study the dynamic of the Gaussian quantum discord in a continuous-variable system subject to a common non-Markovian environment with zero-temperature. By considering an initial two-mode Gaussian symmetric squeezed thermal state, we show that Gaussian discord has a very different dynamic characteristic in a non-Markovian evolution versus a Markov process, and can be created by the memory effect, which features non-Markovianity. We also study the relationship between Gaussian discord and the non-Markovian degree of the environment. The results may offer us an effective experimental method to get more quantum correlations.

Nonclassical Correlation Dynamics in a System of Mesoscopic Josephson Junction Coupled to Single-mode Optical Cavity

We investigate the time evolutions of the continuous-variable entanglement and Gaussian quantum discord in a system consisting of a mesoscopic Josephson junction coupled to a single-mode optical cavity field. We can obtain the time-dependent covariance matrix using known symplectic operation and local canonical transformations. We compare the dynamics of Gaussian quantum discord with that of entanglement. It is shown that the entanglement dynamics of two-mode squeezed thermal state is richer and undergoes three different features: periodical oscillation, sudden death and revival, and no-creation of entanglement, conditioned on the average number of thermal photons in each mode, whereas the Gaussian quantum discord can only exhibit a periodical oscillation behavior during the evolution.

Non-Markovian Dynamic of Gaussian Quantum Discord in Continuous-Variable Systems

We show the special dynamic characteristic of Gaussian quantum discord, exhibited by two-mode Gaussian symmetric squeezed thermal states (STS) in continuous-variable (CV) systems with a common non-Markovian environment, is de nitely di erent from Markov processes. We demonstrate that Gaussian quantum discord can be created whenever the information ow from environment back to the system. We also show that the rate of decrease for Gaussian quantum discord is related to the coupling constant. We discover that the initial value of Gaussian quantum discord is determined by the average number of thermal photons of the system.

Remote transfer of Gaussian quantum discord.

Quantum discord quantifies quantum correlation between quantum systems, which has potential application in quantum information processing. In this paper, we propose a scheme realizing the remote transfer of Gaussian quantum discord, in which another quantum discordant state or an Einstein-Podolsky-Rosen entangled state serves as ancillary state. The calculation shows that two independent optical modes that without direct interaction become quantum correlated after the transfer. The output Gaussian quantum discord can be higher than the initial Gaussian quantum discord when optimal gain of the classical channel and the ancillary state are chosen. The physical reason for this result comes from the fact that the quantum discord of an asymmetric Gaussian quantum discordant state can be higher than that of a symmetric one. The presented scheme has potential application in quantum information network.

Rise of quantum correlations in non-Markovian environments in continuous-variable systems

We investigate the time evolution of quantum correlations, which are measured by Gaussian quantum discord in a continuous-variable bipartite system subject to common and independent non-Markovian environments. Considering an initial two-mode Gaussian symmetric squeezed thermal state, we show that quantum correlations can be created during the non-Markovian evolution, which is different from the Markovian process. Furthermore, we find that the temperature is a key factor during the evolution in non-Markovian environments. For common reservoirs, a maximum creation of quantum correlations may occur under an appropriate temperature. For independent reservoirs, the non-Markovianity of the total system corresponds to the subsystem whose temperature is higher. In both common and independent environments, the Gaussian quantum discord is influenced by the temperature and the photon number of each mode.

Applying Gaussian quantum discord to quantum key distribution

In this paper, we theoretically prove that the Gaussian quantum discord state of optical field can be used to complete continuous variable (CV) quantum key distribution (QKD). The calculation shows that secret key can be distilled with a Gaussian quantum discord state against entangling cloner attack. Secret key rate is increased with the increasing of quantum discord for CV QKD with the Gaussian quantum discord state. Although the calculated results point out that secret key rate using the Gaussian quantum discord state is lower than that using squeezed state and coherent state at the same energy level, we demonstrate that the Gaussian quantum discord, which only involving quantum correlation without the existence of entanglement, may provide a new resource for realizing CV QKD.

Quantum Discord and Classical Correlations of Two Bosonic Modes in the Two-Reservoir Model

Within the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous variable quantum discord for a system consisting of two bosonic modes embedded in two independent thermal environments. We describe the evolution of discord in terms of the covariance matrix for Gaussian input states. In the case of an entangled initial squeezed thermal state, we analyze the evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that quantum discord decays asymptotically in time under the effect of the thermal reservoirs. We describe also the evolution of classical correlations and show that they also decay asymptotically in time.

Thermal amplification of field-correlation harvesting

We study the harvesting of quantum and classical correlations from a hot scalar field in a periodic cavity by a pair of spatially separated oscillator-detectors. Specifically, we utilize non-perturbative and exact (non-numerical) techniques to solve for the evolution of the detectors-field system and then we examine how the entanglement, Gaussian quantum discord, and mutual information obtained by the detectors change with the temperature of the field. While (as expected) the harvested entanglement rapidly decays to zero as temperature is increased, we find remarkably that both the mutual information and the discord can actually be increased by multiple orders of magnitude via increasing the temperature. We go on to explain this phenomenon by taking advantage of the translational invariance of the field and use this to make accurate predictions of the behavior of thermal amplification; by this we also introduce a new perspective on field-correlation harvesting that we feel is worthy of consideration in its own right. The thermal amplification of discord harvesting represents an exciting prospect for discord-based quantum computation, including its use in entanglement activation.

Quantum Discord of Two Bosonic Modes in Two-Reservoir Model

In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the continuous variable quantum discord for a system consisting of two non-interacting bosonic modes embedded in two independent thermal environments. We describe the evolution of discord in terms of the covariance matrix for Gaussian input states. In the case of an entangled initial squeezed vacuum state, we analyze the time evolution of the Gaussian quantum discord, which is a measure of all quantum correlations in the bipartite state, including entanglement, and show that quantum discord decays asymptotically in time under the effect of the thermal reservoirs. For an initial separable pure state, the Gaussian quantum discord is zero and it keeps this value during the whole evolution of the system.

Effect of excess noise on continuous variable entanglement sudden death and Gaussian quantum discord

A symmetric two-mode Gaussian entangled state is used to investigate the effect of excess noise on entanglement sudden death and Gaussian quantum discord with continuous variables. The results show that the excess noise in the channel can lead to entanglement sudden death of a symmetric two-mode Gaussian entangled state, while Gaussian quantum discord never vanishes. As a practical application, the security of a quantum key distribution (QKD) scheme based on a symmetric two-mode Gaussian entangled state against collective Gaussian attacks is analyzed. The calculation results show that the secret key cannot be distilled when entanglement vanishes and only quantum discord exists in such a QKD scheme.