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We investigate the dynamics of information among the parties of tripartite systems. We start by proving two results concerning the monogamy of mutual information. The first one states that mutual information is monogamous for generic tripartite pure states. The second shows that in general mutual information is monogamous only if the amount of genuine tripartite correlations is large enough. Then, we analyze the internal dynamics of tripartite systems whose parties do not exchange energy. In particular, we allow for one of the subsystems to play the role of a finite thermal bath. As a result, we find a typical scenario in which local information tends to be converted into delocalized information. Moreover, we show that (i) the information flow is reversible for finite thermal baths at low temperatures, (ii) monogamy of mutual information is respected throughout the dynamics, and (iii) genuine tripartite correlations are typically present. Finally, we analytically calculate a quantity capable of revealing favorable regimes for non-Markovianity in our model., Comment: 9 pages, 4 figures

The covariance of the Schr\"odinger equation under Galilei boosts and the compatibility of nonrelativistic quantum mechanics with Einstein's equivalence principle have been constrained for so long to the existence of a superselection rule which would prevent a quantum particle from being found in superposition states of different masses. In an effort to avoid this expedient, and thus allow nonrelativistic quantum mechanics to account for unstable particles, recent works have suggested that the usual Galilean transformations are inconsistent with the nonrelativistic limit implied by the Lorentz transformation. Here we approach the issue in a fundamentally different way. Using a formalism of unitary transformations and employing quantum reference frames rather than immaterial coordinate systems, we show that the Schr\"odinger equation, although form variant, is fully compatible with the aforementioned principles of relativity., Comment: 7 pages, thoroughly revised, published version

Generalized quantum discord $(D_q)$, Einstein-Podolsky-Rosen steering $(S)$, entanglement $(E)$, and Bell nonlocality ($N$), are logically distinct quantifiers of quantum correlations. All these measures capture nonclassical aspects of quantum states and play some role as resources in quantum information processing. In this work, we look for the hierarchy satisfied by these quantum correlation witnesses for a class of two-qubit states. We show that $N \triangleright S\triangleright E\triangleright D_q$, meaning that nonlocality implies steering, which in turn implies entanglement, which then implies $q$-discord. For the quantum states under concern, we show that the invariance of this hierarchy under noisy quantum channels directly implies a death chronology. Additionally, we have found that sudden death of all quantum resources except discord is absent only for a subset of states of measure zero. At last, we provide an illustration of another consequence of the aforementioned hierarchy, namely, the existence of a sudden birth chronology under non-Markovian channels., Comment: Substantially revised version, title changed, new stuff and references added

Recently, Bohr's complementarity principle was assessed in setups involving delayed choices. These works argued in favor of a reformulation of the aforementioned principle so as to account for situations in which a quantum system would simultaneously behave as wave and particle. Here we defend a framework that, supported by well-known experimental results and consistent with the decoherence paradigm, allows us to interpret complementarity in terms of correlations between the system and an {\em informer}. Our proposal offers formal definition and operational interpretation for the dual behavior in terms of both nonlocal resources and the couple work-information. Most importantly, our results provide a generalized information-based trade-off for the wave-particle duality and a causal interpretation for delayed-choice experiments., Comment: 14 pages, title changed, text expanded, to appear in Found. Phys

The laws of friction are reasonably well understood for the case of blocks in contact with rough plane surfaces. However, as far as bodies with circular sections are concerned, the physics of friction becomes more involving and it is not possible to adopt a simple conceptual framework to explain all phenomena. In particular, there is no approach so far to the problem of the resistance force that opposes to circular bodies that remain at rest while acted upon by small forces. Here we fill this gap by introducing a mechanical model based on both the elasticity theory and Hertz contact mechanics. Our approach furnishes a quantitative expression for the critical force beyond which rest can no longer be maintained. Besides confirming the expected proportionality of the resistance force with the load, our result contains no free parameters and is expressed solely in terms of physical properties of the problem, such as the pressure of the body per unit of superficial area, a relation between the Young modulus of the surface and its Poisson ratio, and the symmetry of the contact., Comment: 6 pages, 3 figures (published version)

Generalized measures of quantum correlations are derived by taking Bayes' rule as the only fundamental principle. The resulting quantifiers satisfy several desirable conditions for a measure of quantum correlations and are shown to admit operational interpretation in terms of the difference in efficiency of quantum and classical demons in allowing for the extraction of generalized work from a heat bath. The link with discord is established by adopting the $q$ entropy as entropic principle. This allows us to reproduce, within a one-parameter formalism, both the entropic and the geometric measures of discord and physically distinguish them within the context of the nonextensive thermodynamics. Besides offering a unified view of several measures of correlations in terms of the Bayesian principle and its connection with thermodynamics, our approach unveils a bridge to the nonextensive statistical mechanics., Comment: 5+2 pages, 1 figure, appendix added, published version

From the principle that there is no absolute description of a physical state, we advance the approach according to which one should be able to describe the physics from the perspective of a quantum particle. The kinematics seen from this frame of reference is shown to be rather unconventional. In particular, we discuss several subtleties emerging in the relative formulation of central notions such as vector states, the classical limit, entanglement, uncertainty relations, and the complementary principle. A Hamiltonian formulation is derived as well which correctly encapsulates effects of fictitious forces associated with the accelerated motion of the frame. Our approach shows, therefore, how to formulate nonrelativistic quantum mechanics within noninertial reference frames which can be consistently described by the theory, with no appeal to classical elements., Comment: 20 pages, 2 figures, published version

We analyze the dynamical generation of entanglement in systems of two interacting spins initially prepared in a product of spin coherent states. For arbitrary time-independent Hamiltonians, we derive a semiclassical expression for the purity of the reduced density matrix as function of time. The final formula, subsidiary to the linear entropy, shows that the short-time dynamics of entanglement depends exclusively on the stability of trajectories governed by the underlying classical Hamiltonian. Also, this semiclassical measure is shown to reproduce the general properties of its quantum counterpart and give the expected result in the large spin limit. The accuracy of the semiclassical formula is further illustrated in a problem of phase exchange for two particles of spin $j$., Comment: 10 pages

The notion of integrability is discussed for classical nonautonomous systems with one degree of freedom. The analysis is focused on models which are linearly spanned by finite Lie algebras. By constructing the autonomous extension of the time-dependent Hamiltonian we prove the existence of two invariants in involution which are shown to obey the criterion of functional independence. The implication of this result is that chaotic motion cannot exist in these systems. In addition, if the invariant manifold is compact, then the system is Liouville integrable. As an application, we discuss regimes of integrability in models of dynamical tunneling and parametric resonance, and in the dynamics of two-level systems under generic classical fields. A corresponding quantum algebraic structure is shown to exist which satisfies analog conditions of Liouville integrability and reproduces the classical dynamics in an appropriate limit within the Weyl-Wigner formalism. The quantum analog is then conjectured to be integrable as well., Comment: extended version; title changed; 10 pages; 4 figures; accepted in J. Phys. A

The dynamical generation of entanglement in closed bipartite systems is investigated in the semiclassical regime. We consider a model of two particles, initially prepared in a product of coherent states, evolving in time according to a generic Hamiltonian, and derive a formula for the linear entropy of the reduced density matrix using the semiclassical propagator in the coherent-state representation. The formula is explicitly written in terms of quantities that define the stability of classical trajectories of the underlying classical system. The formalism is then applied to the problem of two nonlinearly coupled harmonic oscillators and the result is shown to be in remarkable agreement with the exact quantum measure of entanglement in the short-time regime. An important byproduct of our approach is a unified semiclassical formula which contemplates both the coherent-state propagator and its complex conjugate., Comment: 10 pages

The classical limit of quantum mechanics is discussed for closed quantum systems in terms of observational aspects. Initially, the failure of the limit h->0 is explicitly demonstrated in a model of two quantum mechanically interacting oscillators by showing that neither quantum expectations reduce to Newtonian trajectories nor entanglement vanishes. This result suggests that the quantum-to-classical transition occurs only at an approximative level, which is regulated by the low accuracy of the measurements. In order to verify the consistence of these ideas we take into account the experimental resolution of physical measurements by introducing a discretized formulation for the quantum structure of wave functions. As a result, in the low-resolution limit the quasi-determinism is recovered and hence the quantum-to-classical transition is shown to occur adequately. Other puzzling problems, such as the classical limit of quantum superpositions and nonlocal correlations, are naturally address as well., Comment: 12 pages, 2 figures

The polemical term "interaction-free measurement" (IFM) is analyzed in its interpretative nature. Two seminal works proposing the term are revisited and their underlying interpretations are assessed. The role played by nonlocal quantum correlations (entanglement) is formally discussed and some controversial conceptions in the original treatments are identified. As a result the term IFM is shown to be consistent neither with the standard interpretation of quantum mechanics nor with the lessons provided by the EPR debate., Comment: accepted in Found. Phys

A phase damping reservoir composed by $N$-bosons coupled to a system of interest through a cross-Kerr interaction is proposed and its effects on quantum superpo sitions are investigated. By means of analytical calculations we show that: i-) the reservoir induces a Gaussian decay of quantum coherences, and ii-) the inher ent incommensurate character of the spectral distribution yields irreversibility . A state-independent decoherence time and a master equation are both derived an alytically. These results, which have been extended for the thermodynamic limit, show that nondissipative decoherence can be suitably contemplated within the EI D approach. Finally, it is shown that the same mechanism yielding decoherence ar e also responsible for inducing dynamical disentanglement., Comment: 8 pages, 3 figures

We investigate the correlations of initially separable probability distributions in a globally pure bipartite system with two degrees of freedom for classical and quantum systems. A classical version of the quantum linear mutual information is introduced and the two quantities are compared for a system of oscillators coupled with both linear and non-linear interactions. The classical correlations help to understand how much of the quantum loss of purity are due to intrinsic quantum effects and how much is related to the probabilistic character of the initial states, a characteristic shared by both the classical and quantum pictures. Our examples show that, for initially localized Gaussian states, the classical statistical mutual linear entropy follows its quantum counterpart for short times. For non-Gaussian states the behavior of the classical and quantum measures of information are still qualitatively similar, although the fingerprints of the non-classical nature of the initial state can be observed in their different amplitudes of oscillation., Comment: (16 pages, 4 figures)

An exactly soluble non-linear interaction Hamiltonian is proposed to study fundamental properties of the entanglement dynamics for a coupled non-linear oscillators. The time-evolved state is obtained analytically for initial products of two coherent and two number states and relevant informations are extracted from the dynamics of various quantities like subsystem linear and Von Neumann entropies, quadrature mean values, variances and Q-functions. We determined the re-coherence time scales and found among the interaction terms present in the Hamiltonian the one responsible for the entanglement in both cases. We identify the existence of two regimens for the entanglement dynamics in the case of initially coherent states: the short time, phase spread regimen where the entropy rises monotonically and the self-interference regimen where the entropy oscillates and re-coherence phenomenon can be observed. We also found that the break time from the first regimen to the second one becomes longer, as well as the re-coherence and reversibility times, as the Planck's constant becomes much smaller than a typical action in phase space., Comment: 8 pages, 7 figures