We investigate the hierarchy of quantum correlations in a quadratic bosonic parity-time-symmetric system (PTSS) featuring distinct dissipation and amplification channels. The hierarchy includes global nonclassicality, entanglement, asymmetric quantum steering, and Bell nonlocality. We elucidate the interplay between the system physical nonlinearity (which serves as a source of quantumness) and the specific dynamics of bosonic PTSSs, which are qualitatively influenced by their damping and amplification characteristics. Using a set of quantifiers (including local and global nonclassicality depths, negativity, steering parameters, and the Bell parameter) we demonstrate that the standard PTSS typically exhibits weaker quantumness than its counterparts affected solely by damping or solely by amplification. Both the maximum values attained by these quantifiers and the speed and duration of their generation are generally lower in the standard PTSS. A comparative analysis of three two-mode PTSSs (standard, passive, and active) with identical eigenvectors and real parts of eigenfrequencies, but differing in their damping and amplification strengths, reveals the crucial role of quantum fluctuations associated with gain and loss. Among them, the passive PTSS yields the most strongly nonclassical states. Nevertheless, under suitable conditions, the standard PTSS can also generate highly nonclassical states. The supremacy of the passive PTSS is further supported by its fundamental advantages in practical realizations.We investigate the hierarchy of quantum correlations in a quadratic bosonic parity-time-symmetric system (PTSS) featuring distinct dissipation and amplification channels. The hierarchy includes global nonclassicality, entanglement, asymmetric quantum steering, and Bell nonlocality. We elucidate the interplay between the system physical nonlinearity (which serves as a source of quantumness) and the specific dynamics of bosonic PTSSs, which are qualitatively influenced by their damping and amplification characteristics. Using a set of quantifiers (including local and global nonclassicality depths, negativity, steering parameters, and the Bell parameter) we demonstrate that the standard PTSS typically exhibits weaker quantumness than its counterparts affected solely by damping or solely by amplification. Both the maximum values attained by these quantifiers and the speed and duration of their generation are generally lower in the standard PTSS. A comparative analysis of three two-mode PTSSs (standard, passive, and active) with identical eigenvectors and real parts of eigenfrequencies, but differing in their damping and amplification strengths, reveals the crucial role of quantum fluctuations associated with gain and loss. Among them, the passive PTSS yields the most strongly nonclassical states. Nevertheless, under suitable conditions, the standard PTSS can also generate highly nonclassical states. The supremacy of the passive PTSS is further supported by its fundamental advantages in practical realizations.

arXiv:2510.06171Physical Review ASep 23, 20253 citations

Nonclassical light at exceptional points of a quantum PT -symmetric two-mode system

Jan Peřina, A. Lukš, Joanna K. Kalaga +2 more

A two-mode optical parity-time ( $\mathcal{PT}$ ) symmetric system, with gain and damping, described by a quantum quadratic Hamiltonian with additional small Kerr-like nonlinear terms, is analyzed from the point of view of nonclassical-light generation. Two kinds of stationary states with different types of (in)stability are revealed. Properties of one of these are related to the presence of semiclassical exceptional points, i.e., exotic degeneracies of the non-Hermitian Hamiltonian describing the studied system without quantum jumps. The evolution of the logarithmic negativity, principal squeezing variances, and sub-shot-noise photon-number correlations, considered as entanglement and nonclassicality quantifiers, is analyzed in the approximation of linear-operator corrections to the classical solution. Suitable conditions for nonclassical-light generation are identified in the oscillatory regime, especially at and around exceptional points that considerably enhance the nonlinear interaction and, thus, the nonclassicality of the generated light. The role of quantum fluctuations, inevitably accompanying attenuation and amplification in the evolution of quantum states, is elucidated. The evolution of the system is analyzed for different initial conditions.A two-mode optical parity-time ($\mathcal{PT}$) symmetric system, with gain and damping, described by a quantum quadratic Hamiltonian with additional small Kerr-like nonlinear terms, is analyzed from the point of view of nonclassical-light generation. Two kinds of stationary states with different types of (in)stability are revealed. Properties of one of these are related to the presence of semiclassical exceptional points, i.e., exotic degeneracies of the non-Hermitian Hamiltonian describing the studied system without quantum jumps. The evolution of the logarithmic negativity, principal squeezing variances, and sub-shot-noise photon-number correlations, considered as entanglement and nonclassicality quantifiers, is analyzed in the approximation of linear-operator corrections to the classical solution. Suitable conditions for nonclassical-light generation are identified in the oscillatory regime, especially at and around exceptional points that considerably enhance the nonlinear interaction and, thus, the nonclassicality of the generated light. The role of quantum fluctuations, inevitably accompanying attenuation and amplification in the evolution of quantum states, is elucidated. The evolution of the system is analyzed for different initial conditions.

Physical Review ANov 11, 201943 citations

Nonclassical light at exceptional points of a quantum PT-symmetric two-mode system

Jan Peřina, A. Lukš, Joanna K. Kalaga +2 more

A two-mode optical parity-time (PT) symmetric system, with gain and damping, described by a quantum quadratic Hamiltonian with additional small Kerr-like nonlinear terms, is analyzed from the point of view of nonclassical-light generation. Two kinds of stationary states with different types of (in)stability are revealed. Properties of one of these are related to the presence of semiclassical exceptional points, i.e., exotic degeneracies of the non-Hermitian Hamiltonian describing the studied system without quantum jumps. The evolution of the logarithmic negativity, principal squeezing variances, and sub-shot-noise photon-number correlations, considered as entanglement and non-classicality quantifiers, is analyzed in the approximation of linear-operator corrections to the classical solution. Suitable conditions for nonclassical-light generation are identified in the oscillatory regime, especially at and around exceptional points that considerably enhance the nonlinear interaction and, thus, the non-classicality of the generated light. The role of quantum fluctuations, inevitably accompanying attenuation and amplification in the evolution of quantum states, is elucidated. The evolution of the system is analyzed for different initial conditions.A two-mode optical parity-time (PT) symmetric system, with gain and damping, described by a quantum quadratic Hamiltonian with additional small Kerr-like nonlinear terms, is analyzed from the point of view of nonclassical-light generation. Two kinds of stationary states with different types of (in)stability are revealed. Properties of one of these are related to the presence of semiclassical exceptional points, i.e., exotic degeneracies of the non-Hermitian Hamiltonian describing the studied system without quantum jumps. The evolution of the logarithmic negativity, principal squeezing variances, and sub-shot-noise photon-number correlations, considered as entanglement and non-classicality quantifiers, is analyzed in the approximation of linear-operator corrections to the classical solution. Suitable conditions for nonclassical-light generation are identified in the oscillatory regime, especially at and around exceptional points that considerably enhance the nonlinear interaction and, thus, the non-classicality of the generated light. The role of quantum fluctuations, inevitably accompanying attenuation and amplification in the evolution of quantum states, is elucidated. The evolution of the system is analyzed for different initial conditions.

arXiv:1910.10690Oct 23, 20191 citation

Unavoidability of nonclassicality loss in PT-symmetric systems

Jan Peřina, Adam Miranowicz, Joanna K. Kalaga +1 more

We show that the loss of nonclassicality (including quantum entanglement) cannot be compensated by the (incoherent) amplification of PT-symmetric systems. We address this problem by manipulating the quantum fluctuating forces in the Heisenberg-Langevin approach. Specifically, we analyze the dynamics of two nonlinearly coupled oscillator modes in a PT-symmetric system. An analytical solution allows us to separate the contribution of reservoir fluctuations from the evolution of quantum statistical properties of the modes. In general, as reservoir fluctuations act constantly, the complete loss of nonclassicality and entanglement is observed for long times. To elucidate the role of reservoir fluctuations in a long-time evolution of nonclassicality and entanglement, we consider and compare the predictions from two alternative models in which no fatal long-time detrimental effects on the nonclassicality and entanglement are observed. This is so as, in the first semiclassical model, no reservoir fluctuations are considered at all. This, however, violates the fluctuation-dissipation theorem. The second, more elaborated, model obeys the fluctuation-dissipation relations as it partly involves reservoir fluctuations. However, to prevent from the above long-time detrimental effects, the reservoir fluctuations have to be endowed with the nonphysical properties of a sink model. In both models, additional incorporation of the omitted reservoir fluctuations results in their physically consistent behavior. This behavior, however, predicts the gradual loss of the nonclassicality and entanglement. Thus the effects of reservoir fluctuations related to damping cannot be compensated by those related to amplification.We show that the loss of nonclassicality (including quantum entanglement) cannot be compensated by the (incoherent) amplification of PT-symmetric systems. We address this problem by manipulating the quantum fluctuating forces in the Heisenberg-Langevin approach. Specifically, we analyze the dynamics of two nonlinearly coupled oscillator modes in a PT-symmetric system. An analytical solution allows us to separate the contribution of reservoir fluctuations from the evolution of quantum statistical properties of the modes. In general, as reservoir fluctuations act constantly, the complete loss of nonclassicality and entanglement is observed for long times. To elucidate the role of reservoir fluctuations in a long-time evolution of nonclassicality and entanglement, we consider and compare the predictions from two alternative models in which no fatal long-time detrimental effects on the nonclassicality and entanglement are observed. This is so as, in the first semiclassical model, no reservoir fluctuations are considered at all. This, however, violates the fluctuation-dissipation theorem. The second, more elaborated, model obeys the fluctuation-dissipation relations as it partly involves reservoir fluctuations. However, to prevent from the above long-time detrimental effects, the reservoir fluctuations have to be endowed with the nonphysical properties of a sink model. In both models, additional incorporation of the omitted reservoir fluctuations results in their physically consistent behavior. This behavior, however, predicts the gradual loss of the nonclassicality and entanglement. Thus the effects of reservoir fluctuations related to damping cannot be compensated by those related to amplification.

arXiv:2302.04235Feb 8, 20230 citations

Hierarchy and robustness of multilevel two-time temporal quantum correlations

Dawid Maskalaniec, Karol Bartkiewicz

Quantum steering refers to correlations that can be classified as intermediate between entanglement and Bell nonlocality. Every state exhibiting Bell nonlocality exhibits also quantum steering and every state exhibiting quantum steering is also entangled. In low dimensional cases similar hierarchical relations have been observed between the temporal counterparts of these correlations. Here, we study the hierarchy of such temporal correlations for a general multilevel quantum system. We demonstrate that the same hierarchy holds for two definitions of state over time. In order to compare different types of temporal correlations, we show that temporal counterparts of Bell nonlocality and entanglement can be quantified with a temporal nonlocality robustness and temporal entanglement robustness. Our numerical result reveal that in contrast to temporal steering, for temporal nonlocality to manifest itself we require the initial state not to be in a completely mixed state.Quantum steering refers to correlations that can be classified as intermediate between entanglement and Bell nonlocality. Every state exhibiting Bell nonlocality exhibits also quantum steering and every state exhibiting quantum steering is also entangled. In low dimensional cases similar hierarchical relations have been observed between the temporal counterparts of these correlations. Here, we study the hierarchy of such temporal correlations for a general multilevel quantum system. We demonstrate that the same hierarchy holds for two definitions of state over time. In order to compare different types of temporal correlations, we show that temporal counterparts of Bell nonlocality and entanglement can be quantified with a temporal nonlocality robustness and temporal entanglement robustness. Our numerical result reveal that in contrast to temporal steering, for temporal nonlocality to manifest itself we require the initial state not to be in a completely mixed state.

arXiv:2106.02844Jun 5, 20212 citations

Hierarchy of average correlation, quantum steering and Bell nonlocality in two-qubit systems

Qinglong Tian, GUO Youneng

Abstract Nonclassicality is seen as an important physical resource and offers quantum advantages in modern quantum information processing. Motivated by recent work on the interplay between Bell nonlocality and nonclassicality quantified by average correlation [ Phys. Rev. Res. 5 023063 (2023)], in this paper we aim to establish the intrinsic relationship between the average correlation and the violation of the three-setting linear steering inequality for arbitrary two-qubit states. The results suggest that average correlation is closely related to the violation of the three-setting linear steering inequality, like its relationship with Bell inequality violation. Moreover, the dynamical behaviors of average correlation and steering are carefully analyzed under the influence of local unital and nonunital noisy channels. Particularly, for any two-qubit states, the hierarchy of average correlation-steering-Bell nonlocality is demonstrated by using the singular value decomposition theorem.Abstract Nonclassicality is seen as an important physical resource and offers quantum advantages in modern quantum information processing. Motivated by recent work on the interplay between Bell nonlocality and nonclassicality quantified by average correlation [ Phys. Rev. Res. 5 023063 (2023)], in this paper we aim to establish the intrinsic relationship between the average correlation and the violation of the three-setting linear steering inequality for arbitrary two-qubit states. The results suggest that average correlation is closely related to the violation of the three-setting linear steering inequality, like its relationship with Bell inequality violation. Moreover, the dynamical behaviors of average correlation and steering are carefully analyzed under the influence of local unital and nonunital noisy channels. Particularly, for any two-qubit states, the hierarchy of average correlation-steering-Bell nonlocality is demonstrated by using the singular value decomposition theorem.

Chinese Physics BMay 11, 20260 citations

A two-mode optical parity-time (

\mathcal{PT}

) symmetric system, with gain and damping, described by a quantum quadratic Hamiltonian with additional small Kerr-like nonlinear terms, is analyzed from the point of view of nonclassical-light generation. Two kinds of stationary states with different types of (in)stability are revealed. Properties of one of these are related to the presence of semiclassical exceptional points, i.e., exotic degeneracies of the non-Hermitian Hamiltonian describing the studied system without quantum jumps. The evolution of the logarithmic negativity, principal squeezing variances, and sub-shot-noise photon-number correlations, considered as entanglement and nonclassicality quantifiers, is analyzed in the approximation of linear-operator corrections to the classical solution. Suitable conditions for nonclassical-light generation are identified in the oscillatory regime, especially at and around exceptional points that considerably enhance the nonlinear interaction and, thus, the nonclassicality of the generated light. The role of quantum fluctuations, inevitably accompanying attenuation and amplification in the evolution of quantum states, is elucidated. The evolution of the system is analyzed for different initial conditions.