Characterizing and measuring multipartite Entanglement

A method is proposed to characterize and quantify multipartite entanglement in terms of the probability density function of bipartite entanglement over all possible balanced bipartitions of an ensemble of qubits. The method is tested on a class of random pure states.Comment: 7 pages, 5 figures. Submitted to "International Journal of Quantum Information

Multipartite entanglement characterization of a quantum phase transition

A probability density characterization of multipartite entanglement is tested on the one-dimensional quantum Ising model in a transverse field. The average and second moment of the probability distribution are numerically shown to be good indicators of the quantum phase transition. We comment on multipartite entanglement generation at a quantum phase transition.Comment: 10 pages, 6 figures, final versio

Feynman graphs and the large dimensional limit of multipartite entanglement

We are interested in the properties of multipartite entanglement of a system composed by $n$ $d$-level parties (qudits). Focussing our attention on pure states we want to tackle the problem of the maximization of the entanglement for such systems. In particular we effort the problem trying to minimize the purity of the system. It has been shown that not for all systems this function can reach its lower bound, however it can be proved that for all values of $n$ a $d$ can always be found such that the lower bound can be reached. In this paper we examine the high-temperature expansion of the distribution function of the bipartite purity over all balanced bipartition considering its optimization problem as a problem of statistical mechanics. In particular we prove that the series characterizing the expansion converges and we analyze the behavior of each term of the series as $d\to \infty$.Comment: 29 pages, 11 figure

Flashing annihilation term of a logistic kinetic as a mechanism leading to Pareto distributions

It is shown analytically that the flashing annihilation term of a Verhulst kinetic leads to the power--law distribution in the stationary state. For the frequency of switching slower than twice the free growth rate this provides the quasideterministic source of a Levy noises at the macroscopic level.Comment: 1 fi

Experimental estimation of entanglement at the quantum limit

Entanglement is the central resource of quantum information processing and the precise characterization of entangled states is a crucial issue for the development of quantum technologies. This leads to the necessity of a precise, experimental feasible measure of entanglement. Nevertheless, such measurements are limited both from experimental uncertainties and intrinsic quantum bounds. Here we present an experiment where the amount of entanglement of a family of two-qubit mixed photon states is estimated with the ultimate precision allowed by quantum mechanics.Comment: 4 pages, 3 figure

Statistical mechanics of multipartite entanglement

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over all balanced bipartitions. We search for those (maximally multipartite entangled) states whose purity is minimum for all bipartitions and recast this optimization problem into a problem of statistical mechanics.Comment: final versio

Classical Statistical Mechanics Approach to Multipartite Entanglement

We characterize the multipartite entanglement of a system of n qubits in terms of the distribution function of the bipartite purity over balanced bipartitions. We search for maximally multipartite entangled states, whose average purity is minimal, and recast this optimization problem into a problem of statistical mechanics, by introducing a cost function, a fictitious temperature and a partition function. By investigating the high-temperature expansion, we obtain the first three moments of the distribution. We find that the problem exhibits frustration.Comment: 38 pages, 10 figures, published versio

Multipartite Entanglement and Frustration

Some features of the global entanglement of a composed quantum system can be quantified in terms of the purity of a balanced bipartition, made up of half of its subsystems. For the given bipartition, purity can always be minimized by taking a suitable (pure) state. When many bipartitions are considered, the requirement that purity be minimal for all bipartitions can engender conflicts and frustration arises. This unearths an interesting link between frustration and multipartite entanglement, defined as the average purity over all (balanced) bipartitions.Comment: 15 pages, 7 figure

Entanglement of two blocks of spins in the critical Ising model

We compute the entropy of entanglement of two blocks of L spins at a distance d in the ground state of an Ising chain in an external transverse magnetic field. We numerically study the von Neumann entropy for different values of the transverse field. At the critical point we obtain analytical results for blocks of size L=1 and L=2. In the general case, the critical entropy is shown to be additive when d goes to infinity. Finally, based on simple arguments, we derive an expression for the entropy at the critical point as a function of both L and d. This formula is in excellent agreement with numerical results.Comment: published versio

Adverse Childhood Life Events and Postpartum Mood Episodes in Bipolar Disorder

Background: The early postpartum has been established as a period of increased vulnerability for psychiatric mood illness. Women with bipolar disorder (BD) in particular are at elevated risk of postnatal depression (PND) and of postpartum psychosis (PP). Though adverse childhood life events (ACLEs) have been implicated in the aetiology of PND, this has rarely been studied in relation to PP. Furthermore, despite being at high risk of relapse following childbirth, little research has assessed the relationship between ACLEs and postnatal mood episodes (PNEs) exclusively in women with BD. Therefore, our aim was to explore associations between ACLEs and occurrence of both PND and PP in a large sample of women with BD. Methods: Participants were 665 parous women with BD who had been recruited into the Bipolar Disorder Research Network study. Diagnoses and lifetime psychopathology were obtained via a semi-structured interview (SCAN). Postnatal psychiatric history and experience of 7 ACLEs were also assessed. Where available, all information obtained at interview was confirmed from psychiatric case notes. Women were classified into three groups according to postnatal psychiatric history: 1) those who had experienced no postnatal mood episode (no PNE, n=224), 2) women with a history of PND (n=223) and 3) women who had experienced PP (n=208). A Pearson’s chi-square test was used to compare the prevalence of each type of ACLE between women in the no PNE group and those with a history of PND or PP. Results: Women with PND were significantly more likely to have experienced emotional, sexual or physical abuse in childhood compared with women who had no history of a PNE (p<0.05). In particular, childhood sexual abuse was reported significantly more in the PND than the no PNE group (P<0.05). In contrast, there were no significant differences in the frequency of reporting of any ACLEs between women who had no PNE and those with PP. Conclusions: Our findings indicate that childhood abuse, sexual abuse in particular, is associated with PND among women with BD. In contrast, we found no evidence for an association between any ACLE and PP, suggesting that biological factors are likely to play a more important role in the aetiology of psychosis in the early postpartum