We investigate the role of continuous measurement and postselection in the dynamics and entanglement of a transmon-cavity-transmon coupled system. In the dispersive regime, characterized by a large detuning between the transmons and the cavity, the two transmons interact via virtual excitation of the cavity, giving rise to an effective transmon-transmon coupling. In addition to this coherent interaction, each transmon undergoes spontaneous emission, which is continuously monitored through independent detection channels. By incorporating realistic detector inefficiencies, we analyze both efficient and imperfect monitoring scenarios and demonstrate that postselection significantly slows down the decay of entanglement compared to the unmonitored case. We formulate the stochastic master equation for the coupled system, derive the corresponding postselected master equation, and investigate the dynamics through the Liouvillian superoperator spectrum. In the interaction frame, we identify the emergence of an exceptional point and characterize the associated broken and unbroken PT-symmetric phases. We show how these phases influence the system dynamics and the corresponding entanglement behavior. Our results provide insight into how continuous measurement and postselection affect entanglement in dissipative quantum systems, with potential applications in quantum information processing.
Continuous weak measurements of quantum systems are of great relevance in quantum foundations and applications. They can be achieved by probing the quantum system of interest by repeatedly measuring an auxiliary system weakly coupled to it. Here we study two qubits coupled in different points to a common one-dimensional electromagnetic field and simultaneously monitored in the right- and left-propagating output channels by homodyne detection. Using a collision-model description, we derive an analytical Stochastic Master Equation (SME) governing the resulting diffusive quantum trajectories, including the interference between the two measurement channels. For nonlinear functions of the quantum state, such as entropies, averages over quantum trajectories generally differ from the corresponding quantities evaluated on the unconditional state. Through this mechanism, we show that continuous monitoring generates entanglement, absent in the unconditional dynamics, and enhances quantum magic in the qubit pair during the decay. Both resources can be tuned through the optical phase accumulated between the qubits and the phases of homodyne local oscillators. Our results establish continuous homodyne monitoring of multiple emitters as a tunable mechanism for generating quantum resources.
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.
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.
Open quantum systems interacting with an environment exhibit dynamics described by the combination of dissipation and coherent Hamiltonian evolution. Taken together, these effects are captured by a Liouvillian superoperator. The degeneracies of the (generically non-Hermitian) Liouvillian are exceptional points, which are associated with critical dynamics as the system approaches steady state. We use a superconducting transmon circuit coupled to an engineered environment to observe two different types of Liouvillian exceptional points that arise either from the interplay of energy loss and decoherence or purely due to decoherence. By dynamically tuning the Liouvillian superoperators in real time we observe a non-Hermiticity-induced chiral state transfer. Our study motivates a new look at open quantum system dynamics from the vantage of Liouvillian exceptional points, enabling applications of non-Hermitian dynamics in the understanding and control of open quantum systems.
this study significantly emphasizes on the entanglement engineering using a transmon qubit. A transmon qubit is created with two superconducting islands coupled with two Josephson Junction embedded into a transmission line. The transmon qubit energies are manipulated through its coupling to the transmission line. The key factor here is the coupling factor between transmission line and qubit by which the quantum features of the system such as transmon decay rate, energy dispersion, and related coherence time are controlled. To complete knowledge about the design, the system is quantum mechanically analyzed and the related Hamiltonian is derived. Accordingly, the dynamics equation of motions is derived and so the energy dispersion and the coupled system coherence time are investigated. The system engineering should be established in such a way that satisfies the energy dispersion and the coherence time. However, to analyze the entanglement between modes, it needs to calculate the number of photons of the transmission lines and the transmon qubit, and also the phase sensitive cross-correlation. The important section of this study emphasizes on engineering the coupling between the transmon qubit and transmission line to enhance the entanglement. The results show that around the Josephson Junction location where the more coupling is established the more entanglement between modes is created.
A quantum system subject to continuous measurement and postselection evolves according to a non-Hermitian Hamiltonian. We show that, as one increases the strength of postselection, this non-Hermitian Hamiltonian can undergo a spectral phase transition. On one side of this phase transition (for weak postselection), an initially mixed density matrix remains mixed at all times, and an initially unentangled state develops volume-law entanglement; on the other side, an arbitrary initial state approaches a unique pure state with low entanglement. We identify this transition with an exceptional point in the spectrum of the non-Hermitian Hamiltonian, at which PT symmetry is spontaneously broken. We characterize the transition as well as the nontrivial steady state that emerges at late times in the mixed phase using exact diagonalization and an approximate, analytically tractable mean-field theory; these methods yield consistent conclusions.