We examine the entanglement dynamics of two initially entangled qubits coupled to independent photon reservoirs and undergoing continuous matter-state–photon population transitions. We represent the decay and replenishment of matter-based bit states via photons by time-dependent generalized conversion functions. For the specific case of a sinusoidal function, we show that sudden death events in qubit–qubit entanglement anti-correlate (correlate) exactly with sudden birth events in photon–photon entanglement for the symmetric (anti-symmetric) mode of quantum conversions. We show the invariance in dynamics of all possible bipartite concurrences for various configurations of qubit–reservoir systems and highlight its crucial role in identifying a global concurrence of the multipartite system. We study the coherently driven quantum dot-cavity system as a specific application of our approach, including an analysis of evolution of its Meyer–Wallach measure with time.
We examine the entanglement dynamics of two initially entangled qubits coupled to independent photon reservoirs and undergoing continuous matter-state–photon population transitions. We represent the decay and replenishment of matter-based bit states via photons by time-dependent generalized conversion functions. For the specific case of a sinusoidal function, we show that sudden death events in qubit–qubit entanglement anti-correlate (correlate) exactly with sudden birth events in photon–photon entanglement for the symmetric (anti-symmetric) mode of quantum conversions. We show the invariance in dynamics of all possible bipartite concurrences for various configurations of qubit–reservoir systems and highlight its crucial role in identifying a global concurrence of the multipartite system. We study the coherently driven quantum dot-cavity system as a specific application of our approach, including an analysis of evolution of its Meyer–Wallach measure with time.
Within the framework of semi-classical theory of light and matter, we investigate the entanglement dynamics of the bipartite system consisting of two identical and interacting two-level atoms by means of concurrence, which are coupled to the common reservoir and driven by external time-dependent laser field. Numerical results reveal that for these initially entangled states, the bipartite system undergoes entanglement sudden death (ESD) and birth (ESB), and stable entanglement always occur irrespective of dissipation. Besides, the coupling strength of the electric dipole-dipole will have remarkable effects on the entanglement dynamics, like accelerating the ESD and ESB. However, these conclusions are not applicable to other initially entangled states.
Entanglement plays a crucial role in quantum information protocols; thus the dynamical behavior of entangled states is of great importance. In this paper, we suggest a useful scheme that permits a direct measure of entanglement in a two-qubit cavity system. It is realized through cavity-QED technology utilizing atoms as flying qubits. To quantify entanglement we use the concurrence. We derive the conditions that ensure that the state remains entangled in spite of the interaction with the reservoir. The phenomenon of entanglement sudden death in a bipartite system subjected to a squeezed vacuum reservoir is examined. We show that the sudden death time of the entangled states depends on the initial preparation of the entangled state and the parameters of the squeezed vacuum reservoir.
We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state. For a composite system consisting of three cavities interacting with independent reservoirs, it is shown that the entanglement evolution is restricted by a set of monogamy relations. Furthermore, as quantified by the negativity, the entanglement dynamical property of the mixed entangled state of cavity photons is investigated. It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death (ESD). However, compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement, the ESD time of mixed states is later than that of the pure state. Finally, we discuss the entanglement distribution in the multipartite system, and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.
Entanglement is a key resource in quantum information. It can be destroyed or sometimes created by interactions with a reservoir. In recent years, much attention has been devoted to the phenomena of entanglement sudden death and sudden birth, i.e., the sudden disappearance or revival of entanglement at finite times resulting from a coupling of the quantum system to its environment [1, 2, 3]. We investigate the evolution of the entanglement of noninteracting qubits coupled to reservoirs under monitoring of the reservoirs by means of continuous measurements. Because of these measurements, the qubits remain at all times in a pure state, which evolves randomly. To each measurement result (or "realization") corresponds a quantum trajectory in the Hilbert space of the qubits. We show that for two qubits coupled to independent baths subjected to local measurements, the average of the qubits' concurrence over all quantum trajectories is either constant or decays exponentially. The corresponding decay rate depends on the measurement scheme only. This result contrasts with the entanglement sudden death phenomenon exhibited by the qubits' density matrix in the absence of measurements. Our analysis applies to arbitrary quantum jump dynamics (photon counting) as well as to quantum state diffusion (homodyne or heterodyne detections) in the Markov limit. We discuss the best measurement schemes to protect the entanglement of the qubits. We also analyze the case of two qubits coupled to a common bath. Then, the average concurrence can vanish at discrete times and may coincide with the concurrence of the density matrix. The results explained in this article have been presented during the "Fifth International Workshop DICE2010" by the first author and have been the subject of a prior publication [4].
We analyze the multipartite entanglement evolution of three-qubit mixed states composed of a GHZ state and a W state. For a composite system consisting of three cavities interacting with independent reservoirs, it is shown that the entanglement evolution is restricted by a set of monogamy relations. Furthermore, as quantified by the negativity, the entanglement dynamical property of the mixed entangled state of cavity photons is investigated. It is found that the three cavity photons can exhibit the phenomenon of entanglement sudden death (ESD). However, compared with the evolution of a generalized three-qubit GHZ state which has the equal initial entanglement, the ESD time of mixed states is later than that of the pure state. Finally, we discuss the entanglement distribution in the multipartite system, and point out the intrinsic relation between the ESD of cavity photons and the entanglement sudden birth of reservoirs.
We investigate entanglement dynamics of bipartite as well multipartite systems beyond Markov approximation. We study two pairs of cavity–reservoir systems, modeled as four qubits and track the change of entanglement among cavity–cavity qubits, reservoir–reservoir qubits, and also for genuine entanglement of all four qubits. For cavity–cavity qubits, we find that non-Markovianity prolongs the life of entanglement besides collapse/revival phenomenon. For reservoir–reservoir qubits, entanglement sudden birth is delayed accordingly along with oscillations. For all four qubits, with a specific initial state, we find that genuine entanglement develops gradually, reaches to a maximum constant value and then freezes at this value for some time before decaying. This sudden change in dynamics of genuine entanglement occurs for a time window where neither cavities nor reservoirs are entangled. In contrast to Markov process, sudden change phenomenon may be recurrent in non-Markovian regime.