Why entanglement of formation is not generally monogamous

Unlike correlation of classical systems, entanglement of quantum systems cannot be distributed at will: if one system A is maximally entangled with another system B, it cannot be entangled at all with a third system C. This concept, known as the monogamy of entanglement, is manifest when the entanglement of A with a pair BC can be divided as contributions of the entanglement between A and B and A and C, plus a term τABC involving genuine tripartite entanglement and so expected to be always positive. A very important measure in quantum information theory, the entanglement of formation (EOF), fails to satisfy this last requirement. Here we present the reasons for that and show a set of conditions that an arbitrary pure tripartite state must satisfy for the EOF to become a monogamous measure, i.e., for τABC≥0. The relation derived is connected to the discrepancy between quantum and classical correlations, τABC being negative whenever the quantum correlation prevails over the classical one. This result is employed to elucidate features of the distribution of entanglement during a dynamical evolution. It also helps to relate all monogamous instances of the EOF to the squashed sntanglement, an entanglement measure that is always monogamous. © 2013 American Physical Society.

Probing the degree of non-Markovianity for independent and common environments

We study the non-Markovianity of the dynamics of open quantum systems, focusing on the cases of independent and common environmental interactions. We investigate the degree of non-Markovianity quantified by two distinct measures proposed by Luo, Fu, and Song and Breuer, Laine, and Pillo. We show that the amount of non-Markovianity, for a single qubit and a pair of qubits, depends on the quantum process, the proposed measure, and whether the environmental interaction is collective or independent. In particular, we demonstrate that while the degree of non-Markovianity generally increases with the number of qubits in the system for independent environments, the same behavior is not always observed for common environments. In the latter case, our analysis suggests that the amount of non-Markovianity could increase or decrease depending on the properties of the considered quantum process. © 2013 American Physical Society.

Dinâmica de sistemas bipartites de spins no espaço de fase quântico discreto

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Estudo de sistemas quânticos não-hermitianos com espectro real

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Geração de soluções analíticas em sistemas quânticos com massa dependente da posição e funções de distribuição com limite clássico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O princípio de ação quântica de Schwinger: aspectos do tratamento de sistemas dependentes do tempo e interagentes

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

The structure of non-abelian kinks

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Extracting Information from Qubit-Environment Correlations

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Anderson localization and momentum-space entanglement

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Non-Markovianity through flow of information between a system and an environment

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Busca quântica de dados XML usando algoritmo de Grover

This paper presents a quantum search algorithm implementation with small modifications. The algorithm idea is to be hybrid, capable to run on classical systems and quantum systems. We present the concepts of quantum search and introduced a pseudo-framework able to generate code for classical computers (C++) and quantum computers (QCL). The algorithms were submitted to simulations, which resulted in a comparative study of the operation of Grover’s algorithm on both systems, carrying out searches in a mass of data in XML format files. As a result, we see very similar numbers between classical and quantum systems, this creates an expectation that the search in real quantum computers is much more efficient.

O estudo de caos na propagação do raio de som em um guia de onda no oceano

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dissipation effects in random transverse-field Ising chains

We study the effects of Ohmic, super-Ohmic, and sub-Ohmic dissipation on the zero-temperature quantum phase transition in the random transverse-field Ising chain by means of an (asymptotically exact) analytical strong-disorder renormalization-group approach. We find that Ohmic damping destabilizes the infinite-randomness critical point and the associated quantum Griffiths singularities of the dissipationless system. The quantum dynamics of large magnetic clusters freezes completely, which destroys the sharp phase transition by smearing. The effects of sub-Ohmic dissipation are similar and also lead to a smeared transition. In contrast, super-Ohmic damping is an irrelevant perturbation; the critical behavior is thus identical to that of the dissipationless system. We discuss the resulting phase diagrams, the behavior of various observables, and the implications to higher dimensions and experiments.

Spectral fluctuation and 1/f(alpha) noise in the energy level statistics of interacting trapped bosons

It has been recently shown numerically that the transition from integrability to chaos in quantum systems and the corresponding spectral fluctuations are characterized by 1/f(alpha) noise with 1 <= alpha <= 2. The system of interacting trapped bosons is inhomogeneous and complex. The presence of an external harmonic trap makes it more interesting as, in the atomic trap, the bosons occupy partly degenerate single-particle states. Earlier theoretical and experimental results show that at zero temperature the low-lying levels are of a collective nature and high-lying excitations are of a single-particle nature. We observe that for few bosons, the P(s) distribution shows the Shnirelman peak, which exhibits a large number of quasidegenerate states. For a large number of bosons the low-lying levels are strongly affected by the interatomic interaction, and the corresponding level fluctuation shows a transition to a Wigner distribution with an increase in particle number. It does not follow Gaussian orthogonal ensemble random matrix predictions. For high-lying levels we observe the uncorrelated Poisson distribution. Thus it may be a very realistic system to prove that 1/f(alpha) noise is ubiquitous in nature.

Entanglement of excited states in critical spin chains

Renyi and von Neumann entropies quantifying the amount of entanglement in ground states of critical spin chains are known to satisfy a universal law which is given by the conformal field theory (CFT) describing their scaling regime. This law can be generalized to excitations described by primary fields in CFT, as was done by Alcaraz et al in 2011 (see reference [1], of which this work is a completion). An alternative derivation is presented, together with numerical verifications of our results in different models belonging to the c = 1, 1/2 universality classes. Oscillations of the Renyi entropy in excited states are also discussed.