Minimal, open quantum systems that are governed by non-Hermitian Hamiltonians have been realized across multiple platforms in the past two years. Here we investigate the dynamics of open systems with Hermitian or anti-Hermitian Hamiltonians, both of which can be implemented in such platforms. For a single system, the subject to unitary and thermal dynamics in a periodic manner, we show that the corresponding Floquet Hamiltonian has a rich phase diagram with numerous exceptional-point (EP) degeneracy contours. This protocol can be used to realize a quantum Hatano-Nelson model that is characterized by asymmetric tunneling. For one unitary and one thermal qubit, we show that the concurrence is maximized at the EP that is controlled by the strength of Hermitian coupling between them. Surprisingly, the entropy of each qubit is also maximized at the EP. Our results point to the multifarious phenomenology of systems undergoing unitary and thermal dynamics.
Minimal, open quantum systems that are governed by non-Hermitian Hamiltonians have been realized across multiple platforms in the past two years. Here we investigate the dynamics of open systems with Hermitian or anti-Hermitian Hamiltonians, both of which can be implemented in such platforms. For a single system, the subject to unitary and thermal dynamics in a periodic manner, we show that the corresponding Floquet Hamiltonian has a rich phase diagram with numerous exceptional-point (EP) degeneracy contours. This protocol can be used to realize a quantum Hatano-Nelson model that is characterized by asymmetric tunneling. For one unitary and one thermal qubit, we show that the concurrence is maximized at the EP that is controlled by the strength of Hermitian coupling between them. Surprisingly, the entropy of each qubit is also maximized at the EP. Our results point to the multifarious phenomenology of systems undergoing unitary and thermal dynamics.
We investigate the relation between non-Hermitian Hamiltonian and Lindblad dynamics in nonequilibrium open quantum systems. Non-Hermitian models can extend phase diagrams and enable sensing advantages, but such effects often rely on postselection, raising questions about their relevance for unconditional dynamics. Using a minimal two-qubit setup mediating a heat current, we compare local and global Markovian master equations with their non-Hermitian counterparts. We observe that exceptional points emerge only in the local master equation and in the corresponding non-Hermitian Hamiltonian at sufficiently strong nonequilibrium. We further consider hybrid configurations, where one bath is treated with a Lindblad description and the other with a non-Hermitian approach, interpolating between the two extremes. Our results contribute understanding the role of quantum jumps and exceptional points in nonequilibrium open quantum systems and identify a simple, experimentally accessible architecture, realizable, for instance, in circuit-QED platforms, for their exploration.
Although non-Hermitian dynamics near exceptional points (EPs) provide a route to accelerated entanglement generation, entanglement can also be generated far from EPs at comparable or even higher rates. However, the behavior of such entanglement in open systems remains largely unexplored, rendering it highly susceptible to environmental noise. Here, we study entanglement dynamics in two coupled qubits described by a non-Hermitian Hamiltonian, where the dissipative rates are subject to stochastic noise. We focus on the regime away from EPs. Our approach demonstrates that, even in the presence of classical noise, rich dynamical control can be achieved, enabling highly efficient entanglement generation with a timescale that is significantly shorter than that of both Hermitian systems and EP-based non-Hermitian protocols. Additionally, the timescale is independent of the number of qubits, highlighting favorable scalability for multipartite entanglement generation and facilitating integration into future photonic quantum processors.
This study investigates the dynamics of two-qubit systems in open quantum environments, with a focus on the influence of exceptional points (EPs) and phase angle on entanglement dynamics. Two-qubit systems are pivotal in quantum information science, as they are the simplest system that reveals quantum entanglement, a crucial resource for quantum computing and communication. The research explores the effects of coupling, spontaneous emission, and environment on two-qubit states, specifically the X-states, within the framework of the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) or Lindblad master equation. EPs are unique to non-Hermitian systems. They affect the system’s dynamics significantly when the system approaches EP. Analytical and numerical analyses reveal that third-order EPs occur at specific parameters for two-qubit system, leading to critical changes in eigenvalues and eigenvectors of the Liouvillian superoperator. The study demonstrates that EPs can enhance or suppress entanglement. The concurrence, a quantitative measure of entanglement, peaks around the EPs under certain initial conditions. Furthermore, the impact of phase angle, θ, that parameterizes the relative phase of maximally entangled states is analyzed. For initial states labeled as ρΨ(θ,p) in this thesis, the phase angle significantly influences concurrence evolution, enabling tunability of entanglement dynamics. In contrast, for other class of initial states labeled as ρΦ(θ,p), concurrence exhibits phase invariance, ensuring stability across the variations in θ. Besides this, the analysis shows that the maximum concurrence occurs around EP for some states, the phase angle can also be tuned to increase the concurrence for some initial states. These findings highlight the importance of both EPs and phase angle in optimizing entanglement generation and control. This research offers valuable insights into the interplay between non-Hermitian physics and quantum entanglement, paving the way for advancements in quantum technologies. The outcomes provide possible practical implications in the field of quantum computation.
The exploration of the effect of non-Hermitian (NH) in quantum systems is gaining renewed momentum as a result of the recent progress in experiments. It has been indicated that the ability to engineer the orders of exceptional points (EPs) can be fundamental to its applications in quantum control, such as accelerating entanglement generation; however, an initial survey of the interactions between different orders of EPs is still missing. In this work, we try to partially address this issue by employing a non-reciprocally coupled cavity system which can be experimentally realizable with a two-dimensional reconfigurable NH gauged laser array. With deliberate design, our systems display both second and third orders of EPs. The sign of a novel, purely quantum continuous entanglement phase transition is observed, which reveals how multi-EP interactions alter entanglement dynamics across different regimes while maintaining accelerated generation. Our findings reveil the genuinely quantum NH physics of higher-order EPs, which has opened up a new avenue for future investigations of the higher-order degeneracy application and the dynamic phase transitions of quantum systems.
This study investigates the dynamics of two-qubit systems in open quantum environments, with a focus on the influence of exceptional points (EPs) and phase angle on entanglement dynamics. Two-qubit systems are pivotal in quantum information science, as they are the simplest system that reveals quantum entanglement, a crucial resource for quantum computing and communication. The research explores the effects of coupling, spontaneous emission, and environment on two-qubit states, specifically the X-states, within the framework of the Gorini–Kossakowski–Sudarshan–Lindblad (GKSL) or Lindblad master equation. EPs are unique to non-Hermitian systems. They affect the system’s dynamics significantly when the system approaches EP. Analytical and numerical analyses reveal that third-order EPs occur at specific parameters for two-qubit system, leading to critical changes in eigenvalues and eigenvectors of the Liouvillian superoperator. The study demonstrates that EPs can enhance or suppress entanglement. The concurrence, a quantitative measure of entanglement, peaks around the EPs under certain initial conditions. Furthermore, the impact of phase angle, θ, that parameterizes the relative phase of maximally entangled states is analyzed. For initial states labeled as ρΨ(θ,p) in this thesis, the phase angle significantly influences concurrence evolution, enabling tunability of entanglement dynamics. In contrast, for other class of initial states labeled as ρΦ(θ,p), concurrence exhibits phase invariance, ensuring stability across the variations in θ. Besides this, the analysis shows that the maximum concurrence occurs around EP for some states, the phase angle can also be tuned to increase the concurrence for some initial states. These findings highlight the importance of both EPs and phase angle in optimizing entanglement generation and control. This research offers valuable insights into the interplay between non-Hermitian physics and quantum entanglement, paving the way for advancements in quantum technologies. The outcomes provide possible practical implications in the field of quantum computation.
Theoretical analysis of a prototypical two-qubit effective non-Hermitian system characterized by asymmetric Heisenberg XY interactions in the absence of external magnetic fields demonstrates that maximal bipartite entanglement and quantum phase transitions can be induced exclusively through non-Hermiticity. At thermal equilibrium as T→0, the system attains maximal entanglement C=1 for values of the non-Hermiticity parameter greater than a critical value γ>γc=J(1−δ2), where J denotes the exchange interaction and δ represents the anisotropy of the system; conversely, for γ<γc, entanglement is nonmaximal and given by C=(1−(γ/J)2). The entanglement undergoes a discontinuous transition to zero precisely at γ=γc. This phase transition originates from the closing of the energy gap at a non-Hermiticity-driven ground state degeneracy, which is fundamentally different from an exceptional point. This work suggests the use of singular-value-decomposition generalized density matrix for the computation of entanglement in bi-orthogonal systems.