arXiv subjects

Antonio Di Lorenzo

Publications and source records attributed to Antonio Di Lorenzo.

32 records · Page 2Linked to original sources

arXiv2012

Full counting statistics of weak measurement

A weak measurement consists in coupling a system to a probe in such a way that constructive interference generates a large output. So far, only the average output of the probe and its variance were studied. Here, the characteristic function for the moments of the output is provided. The outputs considered are not limited to the eigenstates of the pointer or of its conjugate variable, so that the results apply to any observable $\Hat{o}$ of the probe. Furthermore, a family of well behaved complex quantities, the normal weak values, is introduced, in terms of which the statistics of the weak measurement can be described. It is shown that, within a good approximation, the whole statistics of weak measurement is described by a complex parameter, the weak value, and a real one.

quant-ph↗

arXiv2011

Reproducing entanglement through local classical resources with no communication

Entanglement is one of the most intriguing features of quantum mechanics. It gives rise to peculiar correlations which cannot be reproduced by a large class of alternative theories, the so-called hidden-variable models, that use parameters in addition to the wave-function. This incompatibility was quantified through the celebrated Bell inequalities, and more recently through new inequalities due to Leggett. Experiments confirm the predictions of quantum mechanics. However, this does not imply that quantum mechanics is the ultimate theory, unsusceptible of improvement, nor that quantum mechanics is essentially non-local. The theories ruled out by Bell and Leggett inequalities are required to satisfy some hypotheses, none of which is implied by locality alone. By dropping one or more hypotheses, it is possible not only to violate said inequalities, but to reproduce the quantum mechanical predictions altogether. So far, the models proposed were only mathematical constructs. In this paper we provide a classical realization of two of these models, using local classical resources, without recurring to any type of communication among the involved parties. The resources consist in two baseballs, two bats, and a number of synchronized watches. Our results demonstrate the possibility of reproducing the quantum mechanical correlations, and even creating stronger correlations which provide the maximum violation of the Bell inequality, beyond the Cirel'son bound for quantum mechanics.

quant-ph↗

arXiv2011

Free will and quantum mechanics

A simple example is provided showing that violation of free will allows to reproduce the quantum mechanical predictions, and that the Clauser-Horne parameter can take the maximum value 4 for a proper choice.

quant-ph↗

arXiv2011

A short note on conflicting definitions of locality

There are various non-equivalent definitions of locality. Three of them, impossibility of instantaneous communication, impossibility of action-at-a-distance, and impossibility of faster-than-light travel, while not fully implying each other, have a large overlap. When the term non-locality is used, most physicists think that one of these three conditions is being violated. There is a minority of physicists, however, who uses "locality" with a fourth meaning, the satisfaction of the hypotheses underlying Bell inequality. This definition devoids Bell's theorem of its profoundness, reducing it to a mere tautology. It is demonstrated here, through a classical example using a deck of cards, that this latter definition of "locality" is untenable.

quant-ph↗

arXiv2011

Hidden-variable models for the spin singlet. II. Local theories violating Bell and Leggett inequalities

Three classes of local hidden-variable models that violate both Bell and Leggett inequalities are presented. The models, however, do not reproduce the quantum mechanical predictions, hence they are experimentally testable. It is concluded that on one hand neither Bell or Leggett inequality fully captures the essential counterintuitiveness of quantum mechanics, while on the other hand the hypothesis of outcome independence and that of locality are uncorrelated.

quant-ph↗

arXiv2010

Strong correspondence principle for joint measurement of conjugate observables

It is demonstrated that the the statistics for a joint measurement of two conjugate variables in Quantum Mechanics are expressed through an equation identical to the classical one, provided that joint classical probabilities are substituted by Wigner functions and that the interaction between system and detectors is accounted for. This constitutes an extension of Ehrenfest correspondence principle, and it is thereby dubbed strong correspondence principle. Furthermore, it is proved that the detectors provide an additive term to all the cumulants, and that if they are prepared in a Gaussian state they only contribute to the first and second cumulant.

quant-ph↗

arXiv2008

Weak measurement: Effect of the detector dynamics

A general approach to the measurement of an observable with pre- and post-selection is presented. The limit of weak measurement is studied in detail, and it is shown that the phase of the probe, including a Hamiltonian contribution to it, gives rise to observable effects, since the coherence of the probe is essential for the concept of complex weak value to be meaningful. As a particular example, the measurement of a spin component is considered. We find that the contribution of the imaginary part of the weak value is sizeable in this case.

quant-ph↗

arXiv2006

Does the wavefunction describe individual systems?

We analyze the issue of the interpretation of the wavefunction, namely whether it should be interpreted as describing individual systems or ensembles of identically prepared systems. We propose an experiment which can decide the issue, based on the simultaneous measurement of the same observable with different detectors, and we discuss the theoretical implications of the possible experimental outcomes.

quant-ph↗

arXiv2005

Full Counting Statistics of Non-Commuting Variables: the Case of Spin Counts

We discuss the Full Counting Statistics of non-commuting variables with the measurement of successive spin counts in non-collinear directions taken as an example. We show that owing to an irreducible detector back-action, the FCS in this case may be sensitive to the dynamics of the detectors, and may differ from the predictions obtained with using a naive version of the Projection Postulate. We present here a general model of detector dynamics and path-integral approach to the evaluation of FCS. We concentrate further on a simple "diffusive" model of the detector dynamics where the FCS can be evaluated with transfer-matrix method. The resulting probability distribution of spin counts is characterized by anomalously large higher cumulants and substantially deviates from Gaussian Statistics.

cond-mat.mes-hall↗

arXiv2005

Full Counting Statistics with Spin-sensitive Detectors reveals Spin-singlets

We study the full counting statistics of electric current to several drain terminals with spin-dependent entrance conductances. We show that the statistics of charge transfers can be interpreted in terms of single electrons and spin-singlet pairs coming from the source. If the source contains transport channels of high transparency, a significant fraction of electrons comes in spin-singlet pairs.

cond-mat.mes-hall↗

arXiv2003

Full Counting Statistics of Spin Currents

We discuss how to detect fluctuating spin currents and derive full counting statistics of electron spin transfers. It is interesting to consider several detectors in series that simultaneously monitor different components of the spins transferred. We have found that in general the statistics of the measurement outcomes cannot be explained with the projection postulate and essentially depends on the quantum dynamics of the detectors.

cond-mat↗

arXiv2002

Quasi-classical descendants of disordered vertex models with boundaries

We study descendants of inhomogeneous vertex models with boundary reflections when the spin-spin scattering is assumed to be quasi--classical. This corresponds to consider certain power expansion of the boundary-Yang-Baxter equation (or reflection equation). As final product, integrable $su(2)$-spin chains interacting with a long range with $XXZ$ anisotropy are obtained. The spin-spin couplings are non uniform, and a non uniform tunable external magnetic field is applied; the latter can be obtained when the boundary conditions are assumed to be quasi-classical as well. The exact spectrum is achieved by algebraic Bethe ansatz. Having realized the $su(2)$ operators in terms of fermions, the class of models we found turns out to describe confined fermions with pairing force interactions. The class of models presented in this paper is a one-parameter extension of certain Hamiltonians constructed previously. Extensions to $su(n)$-spin open chains are discussed.

cond-mat.stat-mech↗

arXiv2001

Integrable models for confined fermions: applications to metallic grains

We study integrable models for electrons in metals when the single particle spectrum is discrete. The electron-electron interactions are BCS-like pairing, Coulomb repulsion, and spin exchange coupling. These couplings are, in general, nonuniform in the sense that they depend on the levels occupied by the interacting electrons. By using the realization of spin 1/2-operators in terms of electrons the models describe spin 1/2 models with nonuniform long range interactions and external magnetic field. The integrability and the exact solution arise since the model Hamiltonians can be constructed in terms of Gaudin models. Uniform pairing and the resulting orthodox model correspond to an isotropic limit of the Gaudin Hamiltonians. We discuss possible applications of this model to a single grain and to a system of few interacting grains.

cond-mat.supr-con↗

arXiv2001

Integrable model for interacting electrons in metallic grains

We find an integrable generalization of the BCS model with non-uniform Coulomb and pairing interaction. The Hamiltonian is integrable by construction since it is a functional of commuting operators; these operators, which therefore are constants of motion of the model, contain the anisotropic Gaudin Hamiltonians. The exact solution is obtained diagonalizing them by means of Bethe Ansatz. Uniform pairing and Coulomb interaction are obtained as the ``isotropic limit'' of the Gaudin Hamiltonians. We discuss possible applications of this model to a single grain and to a system of few interacting grains.

cond-mat.supr-con↗