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...

We propose a general scheme to measure the concurrence of an arbitrary two-qubit pure state in atomic systems. The protocol is based on one-and two-qubit operations acting on two available copies of the bipartite system, and followed by a global qubit readout. We show that it is possible to encode the concurrence in the probability of finding all atomic qubits in the ground state. Two possible scenarios are considered: atoms crossing 3D microwave cavities and trapped ion systems. [7], among others. On the other hand, the quantification of the degree of entanglement for an arbitrary number of qubits is still an open problem in quantum information [8]. Arguably, the most valuable entanglement measure is the entanglement of formation (EOF) [9], which quantifies the minimal cost needed to prepare a certain quantum state in terms of EPR pairs. Many efforts have been devoted to the derivation of the EOF through analytical and numerical approaches. In an important contribution it has been shown that EOF E f (ρ) for an arbitrary two-qubit state ρ can be defined in terms of an exactly calculable quantity: the concurrence C [10]. This quantity can be defined as C(ρ) = max{0, λ 1 − λ 2 − λ 3 − λ 4 }, where the λ i 's are square roots in decreasing order of the eigenvalues of matrix ρρ withρ = σ y ⊗ σ y ρ * σ y ⊗ σ y , σ y being the usual Pauli operator. Remarkably, for a pure state this concurrence is reduced to the simple expressionA straightforward method for measuring entanglement would be a complete tomographic reconstruction of the quantum state [11]. In this case, the reconstruction of a two-qubit state requires the readout of 15 parameters. Additionally, theoretical proposals based on entanglement Witness operator [12], positive maps [13], and two-particle interference [14], have been introduced. Recently, the direct measurement of concurrence of a twophoton entangled state was implemented in the lab [15]. This experiment is based on the fact that the concurrence information of a two-qubit pure state is encoded in the probability of observing the two copies of the first subsystem in an antisymmetric state [16]. Without any doubt, it would be desirable to translate these ideas to the case of matter qubits where diverse physical setups have reached high level of quantum control.In this work, we propose a method to measure the concurrence of a two-qubit pure state in matter qubits. The proposed technique relies on the availability of two copies of the bipartite state and the direct measurement of the occupation probability of the collective state of both copies. We illustrate this protocol with two examples, Rydberg atoms crossing 3D microwave cavities [6] and confined ions in a linear Paul trap [4].The central idea of this proposal is the transformation of the separable state of two copies into a state where the value of the concurrence will be loaded in the probability amplitude to have all the qubits in the ground state. The required operations are σ y unitaries and local rotations R, as well as a controlled-not ga...

The evolution of the lower bound of entanglement proposed by Chen et al. ͓Phys. Rev. Lett. 95, 210501 ͑2005͔͒ in high-dimensional bipartite systems under dissipation is studied. Discontinuities for the time derivative of this bound are found depending on the initial conditions for entangled states. These abrupt changes along the evolution of the entanglement bound appear as precursors of sudden death.Entanglement is a cornerstone of modern quantum physics ͓1,2͔. The evolution of entanglement in open quantum systems is a matter of increasing interest, and new phenomena have been predicted ͓3-10͔. One of the most outstanding effects arises when entanglement vanishes long before coherence is lost. It has been pointed out that systems composed of two qubits in a noisy environment can lose their entanglement in finite time, a phenomenon named entanglement sudden death ͑ESD͒, even though full decoherence happens asymptotically. This feature appears for certain classes of states of two qubits under the action of independent reservoirs. Examples of these classes are the so-called X mixed states as well as some particular types of nonmaximally entangled pure states ͓7͔.The purpose of this work is to explore the dynamical behavior of entangled states in larger bipartite systems under the action of independent reservoirs. We show that unlike the case of two qubits, 3 3 systems may present not only sudden death, but also intermediate abrupt changes in the lower bound of entanglement ͑LBOE͒ dynamics; i.e., the decay rate of the LBOE may change throughout the dissipative process even though coherence is lost at a constant rate. We show that these rate changes are associated with sudden changes in the rank of the partially transposed density matrix, which also provides an explanation for the ESD for the two-qubit case and for the sudden death of the LBOE in the two-qutrit case.We analyze the LBOE dynamics for different initial states and show that abrupt changes may be present or not depending on the variation of a small number of parameters. We also recover the result for two qubits when preparing the initial state in a 2 2 subspace of the whole system. Finally, we interpret these results in terms of changes in the set of entanglement witnesses appropriated for the characterization of the entangled state in each part of the dynamics.In this work we use a general measurement for the lower bound of entanglement of formation ͑EOF͒ for a mixed state in m n dimensions, which has been recently proposed ͓11͔. This proposal is based on the comparison between two major criteria: ͑i͒ the positivity under partial transposition ͑PPT criterion͒ ͓12,13͔ and ͑ii͒ the realignment criterion ͓14,15͔. The EOF for m n-dimensional systems ͑m Յ n͒ is defined as ͓11͔where m is the dimension of the first subsystem and ␥ is given byThe trace norm ʈ · ʈ is defined by ʈ G ʈ =tr͑GG † ͒ 1/2 . The matrix T A is the partial transpose with respect to the subsystem A-that is, ik,jl T A = jk,il -and the matrix R͑͒ is defined as R͑͒ ij,kl = ik,jl .The PPT crite...

Starting from the requirement of distinguishability of two atoms by their positions, it is shown that photon recoil has a strong influence on finite-time disentanglement and in some cases prevents its appearance. At near-field inter atomic distances well localized atoms -with maximally one atom being initially excitedmay suffer disentanglement at a single finite time or even at a series of equidistant finite times, depending on their mean inter atomic distance and their initial electronic preparation.

We develop an analytical model for describing the dynamics of a donor-based charge quantum bit (qubit). As a result, the quantum decoherence of the qubit is analytically obtained and shown to reveal non-Markovian features: The decoherence rate varies with time and even attains negative values, generating a non-exponential decay of the electronic coherence and a later recoherence. The resulting coherence time is inversely proportional to the temperature, thus leading to low decoherence below a material dependent characteristic temperature.