Quantum Non-Markovianity: Characterization, Quantification and Detection

We present a comprehensive and up to date review on the concept of quantum non-Markovianity, a central theme in the theory of open quantum systems. We introduce the concept of quantum Markovian process as a generalization of the classical definition of Markovianity via the so-called divisibility property and relate this notion to the intuitive idea that links non-Markovianity with the persistence of memory effects. A detailed comparison with other definitions presented in the literature is provided. We then discuss several existing proposals to quantify the degree of non-Markovianity of quantum dynamics and to witness non-Markovian behavior, the latter providing sufficient conditions to detect deviations from strict Markovianity. Finally, we conclude by enumerating some timely open problems in the field and provide an outlook on possible research directions.Comment: Review article. Close to published versio

The Role of Natriuretic peptides in Renovascular Hypertension and its correlation with the Evolution of Myocardial Hypertrophy

The interactions between pressure and volume overload that occur in hypertension lead to different patterns of cardiac hypertrophy and to increase in natriuretic peptides (NPs). The profiles of atrial natriuretic peptide (ANP) and brain natriuretic peptide (BNP) synthesis and secretion have been investigated in models of hypertension. However, the different evolution of these profiles during the acute and chronic periods of pressure overload-induced cardiac hypertrophy is still unknown. For this reason, we studied one-kidney, one clip model using Sprague-Dawley rats at weeks 2, 4, 6 and 12 and correlated the evolution of these profiles with cardiac hypertrophy and hypertension. We observed a positive correlation between blood pressure elevation and the degree of cardiac hypertrophy, with a time-dependent increase in both parameters from week 2. Levels of BNP expression showed an early increase after 2 weeks of treatment while ANP increased significantly after 6 weeks. Yet, the increase in ANP expression was gradual, allowing its correlation with hypertrophy and hypertension. The NP expression has a differential response in the early stages of the development of hypertrophy induced by the renovascular model, with an early increase in BNP expression. Once hypertrophy develops, BNP expression is no longer specific and the increase of both NPs depends on and correlates with the degree of cardiac hypertrophy.Fil: Cerrudo, Carolina Susana. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; ArgentinaFil: Cavallero, Carmen Susana. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; ArgentinaFil: Rodríguez Fermepin, Martin. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; ArgentinaFil: Hertig, Cecilia Margarita. Consejo Nacional de Investigaciones Científicas y Técnicas. Instituto de Investigaciones en Ingeniería Genética y Biología Molecular "Dr. Héctor N. Torres"; ArgentinaFil: Fernandez, Belisario Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Farmacia y Bioquímica; Argentin

Noise-enhanced classical and quantum capacities in communication networks

The unavoidable presence of noise is thought to be one of the major problems to solve in order to pave the way for implementing quantum information technologies in realistic physical platforms. However, here we show a clear example in which noise, in terms of dephasing, may enhance the capability of transmitting not only classical but also quantum information, encoded in quantum systems, through communication networks. In particular, we find analytically and numerically the quantum and classical capacities for a large family of quantum channels and show that these information transmission rates can be strongly enhanced by introducing dephasing noise in the complex network dynamics.Comment: 4 pages, 4 figures; See Video Abstract at http://www.quantiki.org/video_abstracts/1003587

Open systems with error bounds: spin boson model with spectral density variations

In the study of open quantum systems, one of the most common ways to describe environmental effects on the reduced dynamics is through the spectral density. However, in many models this object cannot be computed from first principles and needs to be inferred on phenomenological grounds or fitted to experimental data. Consequently, some uncertainty regarding its form and parameters is unavoidable; this in turn calls into question the accuracy of any theoretical predictions based on a given spectral density. Here, we focus on the spin-boson model as a prototypical open quantum system, and find two error bounds on predicted expectation values in terms of the spectral density variation considered, and state a sufficient condition for the strongest one to apply. We further demonstrate an application of our result, by bounding the error brought about by the approximations involved in the Hierarchical Equations of Motion resolution method for spin-boson dynamics.Comment: 5+5 pages, minor edits since last unpublished versio

Non-perturbative treatment of non-Markovian dynamics of open quantum systems

We identify the conditions that guarantee equivalence of the reduced dynamics of an open quantum system (OQS) for two different types of environments - one a continuous bosonic environment leading to a unitary system-environment evolution and the other a discrete-mode bosonic environment resulting in a system-mode (non-unitary) Lindbladian evolution. Assuming initial Gaussian states for the environments, we prove that the two OQS dynamics are equivalent if both the expectation values and two-time correlation functions of the environmental interaction operators are the same at all times for the two configurations. Since the numerical and analytical description of a discrete-mode environment undergoing a Lindbladian evolution is significantly more efficient than that of a continuous bosonic environment in a unitary evolution, our result represents a powerful, non-perturbative tool to describe complex and possibly highly non-Markovian dynamics. As a special application, we recover and generalize the well-known pseudomodes approach to open system dynamics.Comment: 5+4 pages, 2 figures, Close to the version accepted for publication in Physical Review Letter