Dynamical Reduction Models with General Gaussian Noises

We consider the effect of replacing in stochastic differential equations leading to the dynamical collapse of the statevector, white noise stochastic processes with non white ones. We prove that such a modification can be consistently performed without altering the most interesting features of the previous models. One of the reasons to discuss this matter derives from the desire of being allowed to deal with physical stochastic fields, such as the gravitational one, which cannot give rise to white noises. From our point of view the most relevant motivation for the approach we propose here derives from the fact that in relativistic models the occurrence of white noises is the main responsible for the appearance of untractable divergences. Therefore, one can hope that resorting to non white noises one can overcome such a difficulty. We investigate stochastic equations with non white noises, we discuss their reduction properties and their physical implications. Our analysis has a precise interest not only for the above mentioned subject but also for the general study of dissipative systems and decoherence.Comment: 22 pages, Late

Does quantum nonlocality irremediably conflict with Special Relativity?

We reconsider the problem of the compatibility of quantum nonlocality and the requests for a relativistically invariant theoretical scheme. We begin by discussing a recent important paper by T. Norsen [arXiv:0808.2178] on this problem and we enlarge our considerations to give a general picture of the conceptually relevant issue to which this paper is devoted.Comment: 18 pages, 1 figur

Selective cloning of Gaussian states by linear optics

We investigate the performances of a selective cloning machine based on linear optical elements and Gaussian measurements, which allows to clone at will one of the two incoming input states. This machine is a complete generalization of a 1 to 2 cloning scheme demonstrated by U. L. Andersen et al. [Phys. Rev. Lett. vol. 94, 240503 (2005)]. The input-output fidelity is studied for generic Gaussian input state and the effect of non-unit quantum efficiency is also taken into account. We show that if the states to be cloned are squeezed states with known squeezing parameter, then the fidelity can be enhanced using a third suitable squeezed state during the final stage of the cloning process. A binary communication protocol based on the selective cloning machne is also discussed.Comment: 6 pages, 6 figure

Quantum and Superquantum Nonlocal Correlations

We present a simple hidden variable model for the singlet state of a pair of qubits, characterized by two kinds, hierarchically ordered, of hidden variables. We prove that, averaging over both types of variables, one reproduces all the quantum mechanical correlations of the singlet state. On the other hand, averaging only over the hidden variables of the lower level, one obtains a general formal theoretical scheme exhibiting correlations stronger than the quantum ones, but with faster-than-light communication forbidden. This result is interesting by itself since it shows that a violation of the quantum bound for nonlocal correlations can be implemented in a precise physical manner and not only mathematically, and it suggests that resorting to two levels of nonlocal hidden variables might led to a deeper understanding of the physical principles at the basis of quantum nonlocality.Comment: 5 pages, 1 figure. Submitted for publicatio

Hardy's proof of nonlocality in the presence of noise

We extend the validity of Hardy's nonlocality without inequalities proof to cover the case of special one-parameter classes of non-pure statistical operators. These mixed states are obtained by mixing the Hardy states with a completely chaotic noise or with a colored noise and they represent a realistic description of imperfect preparation processes of (pure) Hardy states in nonlocality experiments. Within such a framework we are able to exhibit a precise range of values of the parameter measuring the noise affecting the non-optimal preparation of an arbitrary Hardy state, for which it is still possible to put into evidence genuine nonlocal effects. Equivalently, our work exhibits particular classes of bipartite mixed states whose constituents do not admit any local and deterministic hidden variable model reproducing the quantum mechanical predictions.Comment: 9 pages, 2 figures, RevTex, revised versio

The Conway-Kochen argument and relativistic GRW models

In a recent paper, Conway and Kochen proposed what is now known as the "Free Will theorem" which, among other things, should prove the impossibility of combining GRW models with special relativity, i.e., of formulating relativistically invariant models of spontaneous wavefunction collapse. Since their argument basically amounts to a non-locality proof for any theory aiming at reproducing quantum correlations, and since it was clear since very a long time that any relativistic collapse model must be non-local in some way, we discuss why the theorem of Conway and Kochen does not affect the program of formulating relativistic GRW models.Comment: 16 pages, RevTe

A general hidden variable model for the two-qubits system

We generalize Bell's hidden variable model describing the singlet state of a two-qubits system by extending it to arbitrary states and observables. As in the original work, we assume a uniform, state-independent probability distribution for the hidden variables which are identified with the unit vectors of a 3-dimensional real space. By slightly modifying our model, we provide also a minimal hidden variable description of the two-qubits system, relying on a single hidden variable. We discuss the main features and the implications of the model.Comment: 4 pages, submitted for publicatio

Greenberger-Horne-Zeilinger argument of nonlocality without inequalities for mixed states

We generalize the Greenberger-Horne-Zeilinger nonlocality without inequalities argument to cover the case of arbitrary mixed statistical operators associated to three-qubits quantum systems. More precisely, we determine the radius of a ball (in the trace distance topology) surrounding the pure GHZ state and containing arbitrary mixed statistical operators which cannot be described by any local and realistic hidden variable model and which are, as a consequence, noncompletely separable. As a practical application, we focus on certain one-parameter classes of mixed states which are commonly considered in the experimental realization of the original GHZ argument and which result from imperfect preparations of the pure GHZ state. In these cases we determine for which values of the parameter controlling the noise a nonlocality argument can still be exhibited, despite the mixedness of the considered states. Moreover, the effect of the imperfect nature of measurement processes is discussed.Comment: 8 pages, RevTex; added references, corrected typo

Stochastic Collapse and Decoherence of a Non-Dissipative Forced Harmonic Oscillator

Careful monitoring of harmonically bound (or as a limiting case, free) masses is the basis of current and future gravitational wave detectors, and of nanomechanical devices designed to access the quantum regime. We analyze the effects of stochastic localization models for state vector reduction, and of related models for environmental decoherence, on such systems, focusing our analysis on the non-dissipative forced harmonic oscillator, and its free mass limit. We derive an explicit formula for the time evolution of the expectation of a general operator in the presence of stochastic reduction or environmentally induced decoherence, for both the non-dissipative harmonic oscillator and the free mass. In the case of the oscillator, we also give a formula for the time evolution of the matrix element of the stochastic expectation density matrix between general coherent states. We show that the stochastic expectation of the variance of a Hermitian operator in any unraveling of the stochastic process is bounded by the variance computed from the stochastic expectation of the density matrix, and we develop a formal perturbation theory for calculating expectation values of operators within any unraveling. Applying our results to current gravitational wave interferometer detectors and nanomechanical systems, we conclude that the deviations from quantum mechanics predicted by the continuous spontaneous localization (CSL) model of state vector reduction are at least five orders of magnitude below the relevant standard quantum limits for these experiments. The proposed LISA gravitational wave detector will be two orders of magnitude away from the capability of observing an effect.Comment: TeX; 34 page

A realist interpretation of quantum mechanics based on undecidability due to gravity

We summarize several recent developments suggesting that solving the problem of time in quantum gravity leads to a solution of the measurement problem in quantum mechanics. This approach has been informally called "the Montevideo interpretation". In particular we discuss why definitions in this approach are not "for all practical purposes" (fapp) and how the problem of outcomes is resolved.Comment: 7 pages, IOPAMS style, no figures, contributed to the proceedings of DICE 2010, Castiglioncello, slightly improved versio