No abstract

A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multiqubits states. In particular, our present results are compared with those recently reported by Brown et al (J. Phys. A: Math. Gen. 2005 38 1119). The statistical distribution of entanglement values for the aforementioned multiqubit systems is also explored.

In a recent paper, the generalization of the Jensen Shannon divergence (JSD) in the context of quantum theory has been studied (Phys. Rev. A 72, 052310 (2005)). This distance between quantum states has shown to verify several of the properties required for a good distinguishability measure. Here we investigate the metric character of this distance. More precisely we show, formally for pure states and by means of a numerical procedure for mixed states, that its square root verifies the triangle inequality.

. Mn, 89.70.ϩc, 03.65.Ϫw, 02.50.Ϫr, 99.10.Cd In Sec. II, Fig. 1 should be replaced by a new Fig. 1. This, in turn, originates small changes in the comments placed below Eq. ͑14͒. The specific origin of the errors in the previous ͑wrong͒ version of Fig. 1 was equationappearing in the second line after Eq. ͑14͒. This equation, corresponding to the upper curve in the previous Fig. 1, is wrong because it was wrongly derived from Eq. ͑13͒ ͑which is indeed correct͒. A similar mistake led to Eq. ͑26͒ which must also be deleted. It affects the old Fig. 2. According to the new Fig. 1, for all values of the concurrence C ͓0,1͔ the largest possible evolution time is given by / T min = ͱ 2. This maximum value corresponds to ␣ = and ⌫ =1/4 ͓see Eq. ͑14͔͒. On the other hand, the minimum possible value of / T min is a monotonically decreasing function of C. Consequently, the difference between the maximum and the minimum evolution times augments as the concurrence grows. In Sec. III, Fig. 2 must be replaced by a new Fig. 2 as well, without changes in the caption. Furthermore, Eq. ͑23͒ must now be changed toAs in the previously mentioned case of two distinguishable particles ͑qubits͒, when we have two identical bosons the maximum evolution time is again ͑for all values of C ͓0,1͔͒ given by / T min = ͱ 2. As a consequence, Eq. ͑26͒ must now be deleted. Summing up, the amendments that have to be made in the paper are as follows: Figs. 1 and 2 have to be replaced by the corresponding new ones; equation ⌫ = ͱ C 2 / 2 in the second line after Eq. ͑14͒ has to be deleted; Eq. ͑23͒ has to be modified; and Eq. ͑26͒ has to be deleted.The main conclusions of the paper remain unchanged. Indeed, for systems of either two qubits or two identical bosons, the lower bound for the evolution time to an orthogonal state is a monotonically decreasing function of the concurrence. All separable states ͑C =0͒ that evolve to an orthogonal state do so in the slowest ͑"worst"͒ possible way, associated with / T min = ͱ 2. In order to achieve faster ͑"better"͒ evolution speeds ͑associated with smaller values of / T min ͒ one necessarily needs to increase the concurrence C ͑that is, the amount of entanglement of the state͒. To achieve the fastest kind of possible evolution ͑ / T min =1͒, states of maximum entanglement ͑C =1͒ are required.FIG. 1. Curves in the ͑C , T / T min ͒ϵ͑C , / T min ͒ plane corresponding, for each value of C, to the states of two ͑distinguishable͒ qubits with maximum and minimum / T min . The points represent randomly generated individual states that evolve to an orthogonal state. All depicted quantities are dimensionless. FIG. 2. Curves in the ͑C, T / T min ͒ϵ͑C , / T min ͒ plane corresponding, for each value of C, to the states of two bosons with maximum and minimum / T min . The points represent randomly generated individual states that evolve to an orthogonal state. All depicted quantities are dimensionless.PHYSICAL REVIEW A 73, 049904͑E͒ ͑2006͒

The concept of quantum speed limit-time (QSL) was initially introduced as a lower bound to the time interval that a given initial state ψ I may need so as to evolve into a state orthogonal to itself. Recently [V. Giovannetti, S. Lloyd, and L. Maccone, Phys. Rev. A 67, 052109 (2003)] this bound has been generalized to the case where ψ I does not necessarily evolve into an orthogonal state, but into any other ψ F . It was pointed out that, for certain classes of states, quantum entanglement enhances the evolution "speed" of composite quantum systems. In this work we provide an exhaustive and systematic QSL study for pure and mixed states belonging to the whole 15-dimensional space of two qubits, with ψ F a not necessarily orthogonal state to ψ I . We display convincing evidence for a clear correlation between concurrence, on the one hand, and the speed of quantum evolution determined by the action of a rather general local Hamiltonian, on the other one.

We investigate the decay of entanglement, due to decoherence, of multi-qubit systems that are initially prepared in highly (in some cases maximally) entangled states. We assume that during the decoherence processes each qubit of the system interacts with its own, independent environment.We determine, for systems with a small number of qubits and for various decoherence channels, the initial states exhibiting the most robust entanglement. We also consider a restricted version of this robustness-optimization problem that only involves states equivalent, under local unitary transformations, to the |GHZ

Nonlocality and quantum entanglement constitute two special features of quantum systems of paramount importance in quantum information theory (QIT). Essentially regarded as identical or equivalent for many years, they constitute different concepts. Describing nonlocality by means of the maximal violation of two Bell inequalities, we study both entanglement and nonlocality for two and three spins in the XY model. Our results shed a new light into the description of nonlocality and the possible information-theoretic task limitations of entanglement in an infinite quantum system. Schrödinger 's reply [1] to the paradox posed by Einstein, Podolsky and Rosen (EPR) [2] motivated the modern notion of entanglement in a quantum system. EPR suggested a description of nature, called "local realism", which assigned independent properties to distant parties of a composite physical system, to conclude that QM was an incomplete theory. Schrödinger, instead, did not recognise such conflict and regarded entanglement as the characteristic feature of QM.The most significant progress toward the resolution of the EPR debate was made by Bell [3]. Bell showed that local realism, in the form of local variable models (LVM), implied constraints on the predictions of spin correlations, known as Bell inequalities. Spatially separated observers sharing an entangled state and performing measurements on them may induce (nonlocal) correlations which cannot be simulated by local means (violate Bell inequalities). This limitation to our physical understanding is nowadays exploited for implementing informationtheoretic tasks.Ever since Bell's contribution, entanglement and nonlocality were essentially identified as the same thing. With the advent QIT, interest in entanglement dramatically increased over the years for it lies at the basis of several important processes and applications which possess no classical counterpart [4,5].Confusion between nonlocality and entanglement arose when the usefulness of quantum correlations was put in doubt (see [6]). The nonlocal character of entangled states was clear for pure states since all entangled pure states of two qubits violate the CHSH inequality and are therefore nonlocal (Gisin's theorem) [7]. However, the situation became more involved when Werner [8] discovered that while entanglement is necessary for a state to be nonlocal, for mixed states is not sufficient.Entanglement is commonly viewed as a useful resource for various information-processing tasks. Yet, there exist certain procedures, such as device-independent quantum key distribution [9] and quantum communication complexity problems [10], which can only be carried out provided the corresponding entangled states exhibit nonlocal correlations. Therefore we are naturally led to the question whether nonlocality and entanglement constitute two different resources.The purpose of the present work is to shed some light upon the relation between entanglement and nonlocality, through the maximal violation of a Bell inequality, in an infinite system, n...

Abstract. The elementary dipole excitations of the ionized clusters Na~-, Na~ and Na~ are investigated by solving the equations of the Random-Phase Approximation. The ground and excited states are described using the jellium model for the ionic background and a non-local energy density functional for the valence electrons. Non-local effects are specifically analyzed. The excitation energies thus obtained approach better than those of the Local Density Approximation both the full Hartree-Fock and the experimental results.