Sudden Birth versus Sudden Death of Entanglement in Multipartite Systems

Abstract

We study the entanglement dynamics of two cavities interacting with independent reservoirs. Expectedly, as the cavity entanglement is depleted, it is transferred to the reservoir degrees of freedom. We find also that when the cavity entanglement suddenly disappear, the reservoir entanglement suddenly and necessarily appears. Surprisingly, we show that this entanglement sudden birth can manifest before, simultaneously, or even after entanglement sudden death. Finally, we present an explanatory study of other entanglement partitions and of higher dimensional systems. Dynamical behavior of entanglement under the action of the environment is a central issue in quantum information [1,2,3,4]. Recently, it has been observed that two qubits affected by uncorrelated reservoirs can experience disentanglement in a finite time despite coherence is lost asymptotically [2,3,4,5,6]. This phenomenon, called entanglement sudden death (ESD), has recently deserved a great attention [7,8,9,10,11,12,13], and has been observed in the lab for entangled photon pairs [14], and atomic ensembles [15].To our knowledge ESD has been studied mainly in relation to bipartite systems, while a deeper understanding is associated to the question of where does the lost entanglement finally go. This question would be properly answered by enlarging the system to include reservoir degrees of freedom. Intuitively, we may think that the lost entanglement has to be transferred to the reservoir degrees of freedom. However, is this entanglement swapped continuously? If the bipartite entanglement suffers ESD, what can we say about the transferred entanglement? Should there be a simultaneous entanglement sudden birth (ESB) on reservoir states, or when would this entanglement be created? In this work, we thoroughly study the entanglement transfer from the bipartite system to their independent reservoirs. We show that ESD of a bipartite system state is intimately linked to ESB of entanglement between the reservoirs, though their apparition times follow counterintuitive rules.To illustrate the problem we have chosen the case of entangled cavity photons being affected by dissipation, as in the case of two modes inside the same dissipative cavity or single modes in two different ones. The present study could certainly be extended to other physical systems like matter qubits. First we study the case of qubits for two uncoupled (cavity) modes having up to one photon. Then, we extend our treatment to investigate wether or not the effect is present in higher dimensions (qudits).Since each mode evolves independently, we can learn how to characterize the evolution of the overall system from the mode-reservoir dynamics. The interaction between a single cavity mode and an N -mode reservoir is described through the HamiltonianLet us consider the case when a cavity mode is containing a single photon and its corresponding reservoir is in the vacuum state,where, |0 r = N k=1 |0 k r . It is not difficult to realize that the evolution given by (1) leads to the statewhere the st...

System-environment dynamics of X-type states in noninertial frames

“…At the same time, it is interesting to note that this interaction also generates environment-environment entanglement between the environments E A and ER, and such entanglement exhibits entanglement sudden birth (SB) [36] at some certain r and p. It is worthy to notice that when p = 0, the entanglement of the system (Fig. 1a) is 1 while the system-environment entanglement (Fig.…”

Entanglement evolution of three-qubit mixed states in multipartite cavity—reservoir systems

“…where |1 r = (1/χ(t)) N k=1 λ k (t)|1 k r with the amplitude converging to χ(t) = [1−exp(−κt)] 1/2 [14]. Thus, the cavity and reservoir evolve as an effective two-qubit system.…”

“…The interaction between a single cavity and its N-mode reservoir is characterized by the Hamiltonian [14] …”

“…Recently, Lopez et al analyzed the entanglement dynamics of two cavities interacting with independent reservoirs [14]. They showed that when the cavity entanglement experiences the ESD phenomenon, the reservoir entanglement suddenly and necessarily appears.…”

Quantum entanglement and disentanglement of multi-atom systems

“…The required initial correlations were created by the parametric down-conversion process. Although the sudden death feature is concerned with the disentangled properties of spontaneous emission there is an interesting "sudden" feature in the temporal creation of entanglement from initially independent qubits [32,33]. The phenomenon termed as sudden birth of entanglement, as it is opposite to the sudden death of entanglement arises dynamically during the spontaneous evolution of an initially separate qubits.…”