In this work we introduce a nonlinear witness that is a sufficient condition for detecting the vanishment of quantum correlation of bipartite states. Our result directly generalizes the result of [J. Maziero, R. M. Serra, arXiv:1012.3075] to arbitrary dimension based on the Bloch representation of density matrices.

Zhi-Hao Ma Zhi-Hua Chen Jing-Ling Chen

Given a family of locally Lipschitz vector fields $X(x)=(X_1(x),\dots,X_m(x))$ on $\mathbb{R}^n$, $m\leq n$, we study functionals depending on $X$. We prove an integral representation for local functionals with respect to $X$ and a result of $\Gamma$-compactness for a class of integral functionals depending on $X$.

Alberto Maione Andrea Pinamonti Francesco Serra Cassano

We present a reliable scheme for engineering arbitrary motional ionic states through an adaptation of the projection synthesis technique for trapped-ion phenomena. Starting from a prepared coherent motional state, the Wigner function of the desired state is thus sculpted from a Gaussian distribution. The engineering process has also been developed to take into account the errors arising from intensity fluctuations in the exciting-laser pulses required for manipulating the electronic and vibrational states of the trapped ion. To this end, a recently developed phenomenological-operator approach that allows for the influence of noise will be applied. This approach furnishes a straightforward technique to estimate the fidelity of the prepared state in the presence of errors, precluding the usual extensive ab initio calculations. The results obtained here by the phenomenological approach, to account for the effects of noise in our engineering scheme, can be directly applied to any other process involving trapped-ion phenomena.

R. M. Serra P. B. Ramos N. G. de Almeida W. D. Jose M. H. Y. Moussa

We investigate the mechanism of damping and heating of trapped ions associated with the polarization of the residual background gas induced by the oscillating ions themselves. Reasoning by analogy with the physics of surface electrons in liquid helium, we demonstrate that the decay of Rabi oscillations observed in experiments on 9Be+ can be attributed to the polarization phenomena investigated here. The measured sensitivity of the damping of Rabi oscillations with respect to the vibrational quantum number of a trapped ion is also predicted in our polarization model.

R. M. Serra N. G. de Almeida W. B. da Costa M. H. Y. Moussa

We analyse the geometric phase due to the Stark shift in a system composed of a bosonic field, driven by time-dependent linear amplification, interacting dispersively with a two-level (fermionic) system. We show that a geometric phase factor in the joint state of the system, which depends on the fermionic state (resulting form the Stark shift), is introduced by the amplification process. A clear geometrical interpretation of this phenomenon is provided. We also show how to measure this effect in an interferometric experiment and to generate geometric "Schrodinger cat"-like states. Finally, considering the currently available technology, we discuss a feasible scheme to control and measure such geometric phases in the context of cavity quantum electrodynamics.

E. I. Duzzioni C. J. Villas-Boas S. S. Mizrahi M. H. Y. Moussa R. M. Serra

Based only on the parallel transport condition, we present a general method to compute Abelian or non-Abelian geometric phases acquired by the basis states of pure or mixed density operators, which also holds for nonadiabatic and noncyclic evolution. Two interesting features of the non-Abelian geometric phase obtained by our method stand out: i) it is a generalization of Wilczek and Zee's non-Abelian holonomy, in that it describes nonadiabatic evolution where the basis states are parallelly transported between distinct degenerate subspaces, and ii) the non-Abelian character of our geometric phase relies on the transitional evolution of the basis states, even in the nondegenerate case. We apply our formalism to a two-level system evolving nonadiabatically under spontaneous decay to emphasize the non-Abelian nature of the geometric phase induced by the reservoir. We also show, through the generalized invariant theory, that our general approach encompasses previous results in the literature.

E. I. Duzzioni R. M. Serra M. H. Y. Moussa

We investigate pairwise quantum correlation as measured by the quantum discord as well as its classical counterpart in the thermodynamic limit of anisotropic XY spin-1/2 chains in a transverse magnetic field for both zero and finite temperatures. Analytical expressions for both classical and quantum correlations are obtained for spin pairs at any distance. In the case of zero temperature, it is shown that the quantum discord for spin pairs farther than second-neighbors is able to characterize a quantum phase transition, even though pairwise entanglement is absent for such distances. For finite temperatures, we show that quantum correlations can be increased with temperature in the presence of a magnetic field. Moreover, in the XX limit, the thermal quantum discord is found to be dominant over classical correlation while the opposite scenario takes place for the transverse field Ising model limit.

J. Maziero H. C. Guzman L. C. Celeri M. S. Sarandy R. M. Serra

Non-classical correlations play a crucial role in the development of quantum information science. The recent discovery that non-classical correlations can be present even in separable (unentangled) states has broadened this scenario. This generalized quantum correlation has been increasing relevance in several fields, among them quantum communication, quantum computation, quantum phase transitions, and biological systems. We demonstrate here the occurrence of the sudden-change phenomenon and immunity against some sources of noise for the quantum discord and its classical counterpart, in a room temperature nuclear magnetic resonance setup. The experiment is performed in a decohering environment causing loss of phase relations among the energy eigenstates and exchange of energy between system and environment, resulting in relaxation to a Gibbs ensemble.

R. Auccaise L. C. Celeri D. O. Soares-Pinto E. R. deAzevedo J. Maziero A. M. Souza T. J. Bonagamba R. S. Sarthour I. S. Oliveira R. M. Serra

Maxwell's demon explores the role of information in physical processes. Employing information about microscopic degrees of freedom, this "intelligent observer" is capable of compensating entropy production (or extracting work), apparently challenging the second law of thermodynamics. In a modern standpoint, it is regarded as a feedback control mechanism and the limits of thermodynamics are recast incorporating information-to-energy conversion. We derive a trade-off relation between information-theoretic quantities empowering the design of an efficient Maxwell's demon in a quantum system. The demon is experimentally implemented as a spin-1/2 quantum memory that acquires information, and employs it to control the dynamics of another spin-1/2 system, through a natural interaction. Noise and imperfections in this protocol are investigated by the assessment of its effectiveness. This realization provides experimental evidence that the irreversibility on a non-equilibrium dynamics can be mitigated by assessing microscopic information and applying a feed-forward strategy at the quantum scale.

P. A. Camati J. P. S. Peterson T. B. Batalhão K. Micadei A. M. Souza R. S. Sarthour I. S. Oliveira R. M. Serra

Heat spontaneously flows from hot to cold in standard thermodynamics. However, the latter theory presupposes the absence of initial correlations between interacting systems. We here experimentally demonstrate the reversal of heat flow for two quantum correlated spins-1/2, initially prepared in local thermal states at different effective temperatures, employing a Nuclear Magnetic Resonance setup. We observe a spontaneous energy flow from the cold to the hot system. This process is enabled by a trade off between correlations and entropy that we quantify with information-theoretical quantities. These results highlight the subtle interplay of quantum mechanics, thermodynamics and information theory. They further provide a mechanism to control heat on the microscale.

Kaonan Micadei John P. S. Peterson Alexandre M. Souza Roberto S. Sarthour Ivan S. Oliveira Gabriel T. Landi Tiago B. Batalhão Roberto M. Serra Eric Lutz