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Taking quantum formalism as a point of reference and connection, we explore the various possibilities that arise in the construction of physical theories. Analyzing the distinct physical phenomena that each of them may describe, we introduce the different types of hidden variables theories that correspond to these physical phenomena. A hierarchical classification of the offered theories, based on the degree of correlation between dichotomic observables in bipartite systems, as quantified by a Bell type inequality, is finally proposed., Comment: 13 pages, 2 figures

The preparation procedure, an undefined notion in quantum theory, has not had the relevance that it deserves in the interpretation of quantum mechanical formalism. Here we utilize the concepts of identical and similar preparation procedures to show the conceptual differences and mutual interconnections between the statistical and the conventional interpretation of quantum formalism. Although the statistical understanding, and its final logical consequence, hidden variables theories (this connexion being explained in the text), have a great intuitive appeal due to its fewer ontological difficulties, both recent experimental results and some theoretical developments seem to support an epistemic alternative closer to the conventional one. Nevertheless, we must not rule out the possibility that new theorems or new explanatory principles may modify the reigning supremacy of this interpretation., Comment: Updated version. 12 pages, 2 figures

It is argued that the traditional "realist" methodology of physics, according to which human concepts, laws and theories can grasp the essence of reality, is incompatible with the most fruitful interpretation of quantum formalism. The proof rests on the violation by quantum mechanics of the foundational principles of that methodology. An alternative methodology, in which the construction of sciences finishes at the level of human experience, as standard quantum theory strongly suggests, is then conjectured., Comment: 25 pages, 1 figure

Exploiting the cone structure of the set of unnormalized mixed quantum states, we offer an approach to detect separability independently of the dimensions of the subsystems. We show that any mixed quantum state can be decomposed as $\rho=(1-\lambda)C_{\rho}+\lambda E_{\rho}$, where $C_{\rho}$ is a separable matrix whose rank equals that of $\rho$ and the rank of $E_{\rho}$ is strictly lower than that of $\rho$. With the simple choice $C_{\rho}=M_{1}\otimes M_{2}$ we have a necessary condition of separability in terms of $\lambda$, which is also sufficient if the rank of $E_{\rho}$ equals 1. We give a first extension of this result to detect genuine entanglement in multipartite states and show a natural connection between the multipartite separability problem and the classification of pure states under stochastic local operations and classical communication (SLOCC). We argue that this approach is not exhausted with the first simple choices included herein., Comment: 22 pages, 1 figure

We show that quantum mechanics is the first theory in human history that violates the basic a priori principles that have shaped human thought since immemorial times. Therefore although it is more contrary to magic than any body of knowledge could be, what could be called its magic precisely resides in this violation., Comment: 20 pages, 1 figure. Typos corrected

We show how the separability problem is dual to that of decomposing any given matrix into a conic combination of rank-one partial isometries, thus offering a duality approach different to the positive maps characterization problem. Several inmediate consequences are analyzed: (i) a sufficient criterion for separability for bipartite quantum systems, (ii) a complete solution to the separability problem for pure states also of bipartite systems independent of the classical Schmidt decomposition method and (iii) a natural generalization of these results to multipartite systems., Comment: 12 pages, no figures

We revise the 'no-signaling' condition for the supraluminal communication between two spatially separated finite quantum systems of arbitrary dimensions, thus generalizing a similar preceding approach for two-qubits: non-linear evolution does not necessarily imply the possibility of supraluminal communication between any sort of finite quantum systems., Comment: 6 pages, no figures

We generalize a preceding simple proof of the Jamiolkowski criterion to check whether a given linear map between algebras of operators is completely positive or not. The generalization is performed to embrace all algebras of Hilbert-Schmidt class operators, thus possibly infinite-dimensional., Comment: 9 pages, no figures. Latex class svmult.cls required

We give a simple direct proof of the Jamiolkowski criterion to check whether a linear map between matrix algebras is completely positive or not. This proof is more accesible for physicists than others found in the literature and provides a systematic method to give any set of Kraus matrices of its Kraus decomposition., Comment: 12 pages (double space), no figures. Some points further clarified

Using the Bloch representation of an N-dimensional quantum system and immediate results from quantum stochastic calculus, we establish a closed formula for the Bloch vector, hence also for the density operator, of a quantum system following a Lindblad evolution with selfadjoint Lindblad operators., Comment: Accepted in Phys. Lett. A (shorter version than original)

We suggest a novel proposal to express decoherence in open quantum systems by jointly employing spectral and stochastic methods. This proposal, which basically perturbs the unitary evolution operator in a random fashion, allows us to embrace both markovian and nonmarkovian situations with little extra effort. We argue that it can be very suitable to deal with models where an approximation neglecting some degrees of freedom is undertaken. Mathematical simplicity is also obtained both to solve some master equations and to arrive at experimentally measured decoherence functions., Comment: 15 pages, no figures

We correct a mistake in a result reported in [PRA 64, 062106 (2001)], where it is rightfully argued that initial correlations between a system and its environment may render the system reduced dynamics not completely positive. We prove how not only these initial correlations but also the specific joint dynamics does play a significant role in the question of the complete positivy of the reduced dynamics., Comment: 2 pages, no figures

It is shown how any Lindbladian evolution with selfadjoint Lindblad operators, either Markovian or nonMarkovian, can be understood as an averaged random unitary evolution. Both mathematical and physical consequences are analyzed. First a simple and fast method to solve this kind of master equations is suggested and particularly illustrated with the phase-damped master equation for the multiphoton resonant Jaynes-Cummings model in the rotating-wave approximation. A generalization to some intrinsic decoherence models present in the literature is included. Under the same philosophy a proposal to generalize the Jaynes-Cummings model is suggested whose predictions are in accordance with experimental results in cavity QED and in ion traps. A comparison with stochastic dynamical collapse models is also included., Comment: 16 pages, 4 ps figures

It is shown how the phase-damping master equation, either in Markovian and nonMarkovian regimes, can be obtained as an averaged random unitary evolution. This, apart from offering a common mathematical setup for both regimes, enables us to solve this equation in a straightforward manner just by solving the Schrodinger equation and taking the stochastic expectation value of its solutions after an adequate modification. Using the linear entropy as a figure of merit (basically the loss of quantum coherence) the distinction of four kinds of environments is suggested., Comment: 7 pages, 1 ps figure

A formalism is presented to express decoherence both in the markovian and nonmarkovian regimes and both dissipative and nondissipative in isolated systems. The main physical hypothesis, already contained in the literature, amounts to allowing some internal parameters of the system to evolve in a random fashion. This formalism may also be applicable to open quantum systems., Comment: 4 pages, no figures, REVTex4

Three basic postulates for Quantum Theory are proposed, namely the Probability, Maximum-Speed and Hilbert-Space postulates. Subsequently we show how these postulates give rise to well-known and widely used quantum results, as the probability rule and the linearity of quantum evolution. A discussion of the postulates in the light of Bell's theorem is included which points towards yet unsolved conceptual problems in the Foundations of Quantum Mechanics., Comment: LaTeX2e, 13 pages, 1 eps figure

We consider the simple hypothesis of letting quantum systems have an inherent random nature. Using well-known stochastic methods we thus derive a stochastic evolution operator which let us define a stochastic density operator whose expectation value under certain conditions satisfies a Lindblad equation. As natural consequences of the former assumption decoherence and spontaneous emission processes are obtained under the same conceptual scheme. A temptative solution for the preferred basis problem is suggested. All this is illustrated with a comprehensive study of a two-level quantum system evolution., Comment: LaTeX2e, 26 pages, 3 eps figures

The stochastic methods in Hilbert space have been used both from a fundamental and a practical point of view. The result we report here concerns only the idea of applying these methods to model the evolution of quantum systems and does not enter into the question of their fundamental or practical status. It can be easily stated as follows: Once a quantum stochastic evolution scheme is assumed, the incompatibility between the Markov property and the notion of quantum jump is rapidly established., Comment: LaTeX2e, 3 pages, no figures. Included in the Proceedings of the 3rd Workshop on Mysteries, Puzzles and Paradoxes in Quantum Mechanics, Gargnano, Italy, September 17-23, 2000

A brief analysis of the compatibility between the quantum jump and the Markov property for quantum systems described by a stochastic evolution scheme is presented., Comment: 10 pages, no figures, submitted to Letters in Mathematical Physics

We study the time evolution of decaying particles in renormalizable models of Relativistic Quantum Field Theory. Significant differences between the latter and Non Relativistic Quantum Mechanics are found -in particular, the Zeno effect seems to be absent in such RQFT models. Conventional renormalization yields finite time behavior in some cases but fails to produce finite survival probabilities in others., Comment: Revised version of the paper Time evolution and Zeno effect in relativistic quantum field theory. To appear in Phys. Lett. A