Marcos C. de Oliveira

Multipartite entanglement signature of quantum phase transitions.

We derive a general relation between the nonanalyticities of the ground state energy and those of a subclass of the multipartite generalized global entanglement (GGE) measure defined by de Oliveira et al. [Phys. Rev. A 73, 010305(R) (2006)] for many-particle systems. We show that GGE signals both a critical point location and the order of a quantum phase transition (QPT). We also show that GGE allows us to study the relation between multipartite entanglement and QPTs, suggesting that multipartite but not bipartite entanglement is favored at the critical point. Finally, using GGE we were able, at a second-order QPT, to define a diverging entanglement length (EL) in terms of the usual correlation length. We exemplify this with the XY spin-1/2 chain and show that the EL is half the correlation length.

Genuine multipartite entanglement in quantum phase transitions

We demonstrate that the global-entanglement (GE) measure defined by Meyer and Wallach [J. Math. Phys. 43, 4273 (2002)] is maximal at the critical point for the Ising chain in a transverse magnetic field. Our analysis is based on the equivalence of GE to the averaged linear entropy, allowing an understanding of multipartite entanglement (ME) features through a generalization of GE for bipartite blocks of qubits. Moreover, in contrast to GE, the proposed ME measure can distinguish three paradigmatic entangled states: GHZ{sub N} (Greenberger-Horne-Zeilinger), W{sub N}, and EPR{sup xN/2}. As such the generalized measure can detect a genuine ME and is maximal at the critical point.

Operational classification and quantification of multipartite entangled states

We formalize and extend an operational multipartite entanglement measure introduced by T. R. Oliveira, G. Rigolin, and M. C. de Oliveira, Phys. Rev. A 73, 010305(R) (2006), through the generalization of global entanglement (GE) [D. A. Meyer and N. R. Wallach, J. Math. Phys. 43, 4273 (2002)]. Contrarily to GE the main feature of this measure lies in the fact that we study the mean linear entropy of all possible partitions of a multipartite system. This allows the construction of an operational multipartite entanglement measure which is able to distinguish among different multipartite entangled states that GE failed to discriminate. Furthermore, it is also maximum at the critical point of the Ising chain in a transverse magnetic field, being thus able to detect a quantum phase transition.

Symmetry-breaking effects upon bipartite and multipartite entanglement in the X Y model

We analyze the bipartite and multipartite entanglement for the ground state of the one-dimensional

P-representable subset of all bipartite Gaussian separable states

XY

Quantum walks on a circle with optomechanical systems

model in a transverse magnetic field in the thermodynamical limit. We explicitly take into account the spontaneous symmetry breaking in order to explore the relation between entanglement and quantum phase transitions. As a result we show that while both bipartite and multipartite entanglement can be enhanced by spontaneous symmetry breaking deep into the ferromagnetic phase, only the latter is affected by it in the vicinity of the critical point. This result adds to the evidence that multipartite, and not bipartite, entanglement is the fundamental indicator of long-range correlations in quantum phase transitions.

Quantification of continuous variable entanglement with only two types of simple measurements

P-representability is a necessary and sufficient condition for separability of bipartite Gaussian states only for the special subset of states whose covariance matrix are Sp(2,R)xSp(2,R) locally invariant. Although this special class of states can be reached by a convenient Sp(2,R)xSp(2,R) transformation over an arbitrary covariance matrix, it represents a loss of generality, avoiding inference of many general aspects of separability of bipartite Gaussian states.

Complete state reconstruction of a two-mode Gaussian state via local operations and classical communication

We propose an implementation of a quantum walk on a circle in an optomechanical system by encoding the walker on the phase space of a radiation field and the coin on a two-level state of a mechanical resonator. The dynamics of the system is obtained by applying Suzuki–Trotter decomposition. We numerically show that the system displays typical behaviors of quantum walks, namely the probability distribution evolves ballistically and the standard deviation of the phase distribution is linearly proportional to the number of steps. We also analyze the effects of decoherence by using the phase-damping channel on the coin space, showing the possibility to implement the quantum walk with present-day technology.

Erratum: Minimal Set of Local Measurements and Classical Communication for Two-Mode Gaussian State Entanglement Quantification [Phys. Rev. Lett.98, 150501 (2007)]

Abstract Here we propose an experimental set-up in which it is possible to obtain the entanglement of a two-mode Gaussian state, be it pure or mixed, using only simple linear optical measurement devices. After a proper unitary manipulation of the two-mode Gaussian state only number and purity measurements of just one of the modes suffice to give us a complete and exact knowledge of the state’s entanglement.

Characterization and quantification of symmetric Gaussian state entanglement through a local classicality criterion

We propose a strictly local quantum tomography protocol for a bipartite system. We show that the joint density matrix of an arbitrary two-mode Gaussian state, entangled or not, is obtained via local operations and classical communication only. In contrast to previous proposals, simultaneous homodyne measurements (HM) on both modes are replaced by local homodyne detections and a set of local projective measurements.