Hellinger geometric quantum discord and interferometric power are investigated for an open system consisting of two bosonic modes interacting with four different environments: vacuum, squeezed vacuum, thermal and squeezed thermal, taking the initial state of the system either a single-mode squeezed state, which presents no correlations, or a squeezed vacuum state. The description of the evolution of the correlations is formulated in the framework of the theory of open systems, based on completely positive quantum dynamical semigroups, using the Gorini-Kossakowski-Lindblad-Sudarshan master equation. We show that both quantum correlations can be generated from an initial factorized state and even amplified, while also studying the back and forth impact of the squeezing parameters on the considered correlations; specifically, for the squeezed vacuum environment, the competition between the influences exerted by the squeezing of the initial state and the squeezing of the environment leads to the decreasing, and even destruction of the correlations, or to their enhancement. In the case of an initial squeezed vacuum state in interaction with the squeezed vacuum environment, for specific conditions one can achieve decoherence-free states (DFS), while for the interaction with a thermal environment there exist regimes of enhancing or decreasing the considered correlations, depending on the parameters of both open system and environment.

Abstract The quantum dynamics of a double quantum dot placed in an optical cavity and interacting with thermally distributed phonons have been investigated. We demonstrate that quantum features of the cavity quantum electrodynamics are destroyed due to the double-quantum-dot-phonon interaction. Namely, sub-Poissonian distributed cavity photons are no longer obtained when phonons are included into the quantum system.

Quantum Fisher Information (QFI), which sets the fundamental bound on parameter estimation precision via the quantum Cramér-Rao inequality, is investigated for a general single-mode Gaussian state before and after teleportation. Using a two-mode squeezed vacuum state as a shared entanglement resource between Alice and Bob, we analyze the teleportation protocol under environmental noise, focusing on diffusion and dissipation induced by a thermal bath. By comparing QFI for several parameters of the input state before and after teleportation, we evaluate the effectiveness of QFI transfer. We find that increasing the squeezing of the shared state enhances QFI preservation. Notably, under certain conditions, environmental interactions can help maintain QFI, particularly for shared states with high frequency, suggesting a subtle interplay between system dynamics and decoherence.

We investigate the dynamical evolution of quantum discord, entanglement and purity in an open quantum system of two coupled asymmetric harmonic oscillators interacting with a thermal environment. Using the Kossakowski-Lindblad master equation we analyze the time evolution starting with a squeezed vacuum state. In contrast to our previous study on entanglement evolution in asymmetric oscillators, the present work introduces XY-type position-position coupling together with a systematic joint analysis of quantum discord and purity alongside entanglement. We examine the combined effects of the squeezing parameter, asymmetry parameter, coupling constant, dissipation rate and temperature. We find that quantum discord and entanglement exhibit, in general, a non-monotonic decrease over time. Increasing temperature consistently accelerates the degradation of both quantum correlations and purity, whereas increasing dissipation accelerates the degradation of quantum correlations but leads to higher steady-state purity. Increasing the squeezing parameter provides a protective effect by enhancing initial correlations and prolonging entanglement survival time, while increasing the coupling constant leads to higher quantum correlations. The asymmetry parameter exhibits only a weak influence on the correlation evolution. Our analysis reveals that quantum discord demonstrates stronger resilience than entanglement, which can present more complex behaviour including entanglement sudden death and possible temporary revivals and re-suppressions. These findings provide valuable insights for developing robust quantum information protocols and strategies for preserving quantum correlations in realistic open quantum systems, with potential extensions to non-Markovian regimes and multi-mode architectures.

The quantum dynamics of a double quantum dot two-level system, coupled to a leaking microwave resonator mode, is theoretically investigated. The double quantum dot is driven by applying a continuous field giving rise to time-dependent modulations of its energy separation between the ground levels of each dot, forming the qubit. Therefore, the cavity resonances occur when the difference between the resonator and the qubit frequencies equals the multiple of the modulation frequency, respectively. In the strong Coulomb interaction limit and the weak couplings of the combined system, i.e. the qubit and the single-mode cavity, to corresponding electronic, phononic or photonic reservoirs, we have demonstrated that the output cavity electromagnetic field is formed of a single-photon flux obeying the sub-Poissonian quantum photon statistics. This was proved via Fano's factor behaviour or by comparing the resonator's second- and third-order photon correlation functions, respectively. The phonon, the cavity mode dephasing or the environmental temperatures influence on the quantum properties of the photons are also discussed.

The steady-state quantum dynamics of a compound sample consisting of a semiconductor double-quantum-dot (DQD) system, non-linearly coupled with a leaking superconducting transmission line resonator, is theoretically investigated. Particularly, the transition frequency of the DQD is taken to be equal to the doubled resonator frequency, whereas the inter-dot Coulomb interaction is considered weak. As a consequence, the steady-state quantum dynamics of this complex non-linear system exhibit sudden changes in its features, occurring at a critical DQD-cavity coupling strength, suggesting perspectives for designing on-chip microwave quantum switches. Furthermore, we show that, above the threshold, the electrical current through the double-quantum dot follows the mean photon number into the microwave mode inside the resonator. This might not be the case any more below that critical coupling strength. Lastly, the photon quantum correlations vary from super-Poissonian to Poissonian photon statistics, i.e., towards single-qubit lasing phenomena at microwave frequencies.

The steady-state quantum dynamics of a compound sample consisting of a semiconductor double quantum dot (DQD) system nonlinearly coupled with a leaking single-mode microresonator is theoretically investigated. The focus is on the resonance condition when the transition frequency of the DQD equals to the doubled resonator frequency, respectively, and the resulting interplay among the involved phonon or photon decay channels. As a result, the steady-state quantum dynamics of this complex nonlinear system exhibits a variety of possible effects that have been demonstrated here. Particularly, we have found the relationship between the electrical current through the double quantum dot and the microwave field inside the resonator, which is nonlinearly coupled to it, with a corresponding emphasis on their critical behaviours. Additionally, the quantum correlations of the photon flux generated into the resonator mode vary from super-Poissonian to Poissonian photon statistics, leading to single-qubit lasing phenomena at microwave frequencies.

Quantum teleportation is a fundamental protocol in quantum information science. It represents a critical resource for quantum communication and distributed quantum computing. We derive an analytical expression of the fidelity of teleportation of an input squeezed thermal state using for teleportation a bipartite Gaussian resource state shared between Alice and Bob. Each mode of the resource state is susceptible to the influence of the environment. We employ the characteristic function approach in conjunction with the covariance matrix formalism. The fidelity of teleportation is expressed in terms of input and resource state covariance matrices. We investigate, as an example, the feasibility of secure quantum teleportation of a squeezed thermal state using a two-mode resource state whose modes are placed in separate thermal baths. A successful quantum teleportation requires meeting two criteria: the presence of two-way quantum steering and a teleportation fidelity exceeding the classical threshold. The quantum steering is by nature asymmetric and has found applications in quantum cryptography and secure quantum teleportation. Weak squeezing and a high number of average thermal photons in the input states lead to an increase in the fidelity of teleportation. Generally, steering disappears much faster than the fidelity of teleportation decreases below its classical limit.

The time evolution of Gaussian quantum entanglement of two bosonic modes associated with a scalar quantum field in de Sitter space and in interaction with a thermal reservoir is investigated in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. We show that quantum entanglement strongly depends on the squeezing of the bimodal state, the parameters characterizing the thermal environment, the curvature parameter of de Sitter space, and the mass parameter. The thermal environment and the curvature have a destructive influence on the entanglement, whose survival time depends on the competition between the contrary effects provided by the squeezing of the bimodal state, the curvature, and the thermal bath. The entanglement is minimized for values 1/2 and 3/2 of the mass parameter, corresponding to the conformally coupled scalar field, respectively, minimally coupled massless field.

Entanglement of formation is a measure that has a clear physically motivated definition, namely, it provides a lower bound over all pure-state entanglement decompositions required to create a given state. We investigate the open system dynamics of entanglement of formation of a two-mode Gaussian state interacting with a common bosonic environment. In the framework of the theory based on completely positive dynamical semigroups, the open system dynamics leads to a master equation in Lindblad form, which preserves the positivity and the Gaussian form of an initially Gaussian state at all times. For an initially separable state we witness the generation of entanglement, and its preservation in the limit of asymptotic times.

Quantum communication networks can be built on quantum teleportation, which is the transmission of an unknown quantum state from a sending station to a remote receiving station supported by entangled states and classical communication. We use a continuous variable two-mode squeezed vacuum state as a resource state for the quantum teleportation. This state is shared by Alice and Bob, and their system comes into contact with a squeezed thermal environment. The conditions for a secure quantum teleportation require a teleportation fidelity larger than 2/3 and two-way steering of the resource state. We investigate the time evolution of the steering and the fidelity of teleportation in order to determine the values of the parameters required for a successful secure quantum teleportation of a coherent Gaussian state. We show that the temperature, dissipation rate and squeezing parameter of the squeezed thermal reservoir limit the feasible duration for secure quantum teleportation, while by increasing the squeezing parameter of the initial state one can effectively expand the temporal range for a successful secure quantum teleportation.

An active area of research in quantum information theory is expanding the operational approach of resource theory (RT) to all quantum correlations. In the context of quantum resource theories we define a measure using resource destroying maps that can be interpreted as the upper bound on any information present in dynamical systems.

We investigate the Markovian time evolution of the entropy production rate as a measure of irreversibility created in a quantum system consisting of two coupled bosonic modes interacting with a common thermal environment. We consider a general bilinear interaction between the modes, which accounts for the excitation exchange coupling and the two-mode squeezing coupling. The dynamics of the system is described in the framework of the theory of open quantum systems based on completely positive quantum dynamical semigroups. We provide an analytical and numerical investigation of this model for initial two-mode squeezed thermal states and show that the entropy production rate strongly depends on the two considered types of coupling between the modes.

We present a short review on the subject of witnesses based on second moments as a primary tool for the efficient detection of entanglement and steering. In particular, we focus on the example of Gaussian states, which represent the core toolbox for the vast domain of continuous variable states. We fully define and characterise the entanglement and steering Gaussian witnesses, respectively, and then present a set of linear constraints as an alternative characterisation that allows for the implementation of a numerical optimisation semidefinite programming algorithm. We have the great pleasure to dedicate this paper in the honour of Professor Dan Tiba on the occasion of his 70th Anniversary and to wish him a long life in good health and further success in his scientific activity.

Implementing of high efficiency quantum teleportation protocols is in the key task for development of accessible and secure quantum communication. For a successful quantum teleportation two conditions should be satisfied: fidelity of teleportation greater then 1/2 for pure states and the existence of the entanglement between resource state modes during all teleportation process. Quantum teleportation using Gaussian states is a perspective direction because they can be easily implemented and manipulated using laser radiation. The simplest case for the continuous variable quantum teleportation represent teleportation of a pure state. However the thermal noise cannot be eliminated from the system, and the thermal component should be taken into account. In this work we put in evidence how the increase of average thermal photon number influence the fidelity of teleportation of a Gaussian state. We use Lindblad master equation and covariance matrix formalism to describe the temporal evolution of studied system and to put in evidence dependence of the fidelity of teleportation on the environment conditions and resource state parameters. As well we calculated the entanglement between the resource state modes to check if all conditions for a successful teleportation are satisfied.

We define and fully characterize the witnesses based on second moments detecting steering in Gaussian states by means of Gaussian measurements. All such tests, which arise from linear combination of variances or second moments of canonical operators, are easily implemented in experiments. We propose also a set of linear constraints fully characterizing steering witnesses when the steered party has one bosonic mode, while in the general case the constraints restrict the set of tests detecting steering. Given an unknown quantum state we implement a semidefinite program providing the appropriate steering test with respect to the number of random measurements performed. Thus, it is a ‘repeat-until-success’ method allowing for steering detection with less measurements than in full tomography. We study the efficiency of steering detection for two-mode squeezed vacuum states, for two-mode general unknown states, and for three-mode continuous variable GHZ states. In addition, we discuss the robustness of this method to statistical errors.

"We investigate the collective quantum dynamics of an ensemble of two-level emitters, embedded in a crystal, and coherently pumped by a moderately intense, and externally applied coherent electromagnetic field. The ensemble is damped preponderantly via the surrounding phonon reservoir which mediates the inter-particle collective interactions. We have found that generally phonon transitions among the corresponding dressed states are taking place involving simultaneously many single emitters or pairs of two-level emitters, respectively. In both cases the phonon intensity can be proportional to the squared number of involved two-level emitters."

Quantum correlations represent one of the most characteristic traits of quantum mechanics [...]

We investigate the influence of the seed of measurement on the performance of a Szilard engine based on a two-mode Gaussian state evolving in a noisy channel. Quantum work is extracted by performing a positive operator-valued measurement (POVM) on one of the two modes, after which this mode reaches equilibrium with the environment. As the seed of measurement, we use a single-mode squeezed thermal state. We employ the Markovian Kossakowski-Lindblad master equation to determine the evolution in time of the considered open system and the quantum work is defined based on the Rényi entropy of order 2. We show that the extracted quantum work and information-work efficiency strongly depend on the characteristic parameters of the system (frequency, average thermal photons number, and squeezing), the noisy channel (temperature and squeezing of the bath), and the seed of measurement (average thermal photons number and strength of the measurement).

Different types of geometric and entropic quantum correlation quantifiers are studied for a system composed of two resonant bosonic modes embedded in a thermal bath. The description of the evolution of the correlation measures is formulated in the framework of the theory of open systems, based on completely positive quantum dynamical semigroups, by using both a geometric and entropic quantification of total nonclassical correlations of Gaussian states. We consider the special case when the initial squeezed thermal state of the system preserves its form in time. We show that time evolution of the measures strongly depends on the parameters characterising the initial state of the system (squeezing parameter and average thermal photon numbers of the two modes) and of the thermal environment (temperature of the thermal bath and dissipation rate). In the limit of large times all the considered measures asymptotically tend to zero value, corresponding to an asymptotic bimodal uncorrelated product state. We make a comparison between the behaviour of the evolution in time of the Gaussian geometric quantum correlations and Gaussian entropic quantum correlations.