arXiv subjects

R. Tarrach

Publications and source records attributed to R. Tarrach.

17 recordsLinked to original sources

arXiv2000

Optimal encoding and decoding of a spin direction

For a system of N spins 1/2 there are quantum states that can encode a direction in an intrinsic way. Information on this direction can later be decoded by means of a quantum measurement. We present here the optimal encoding and decoding procedure using the fidelity as a figure of merit. We compute the maximal fidelity and prove that it is directly related to the largest zeroes of the Legendre and Jacobi polynomials. We show that this maximal fidelity approaches unity quadratically in 1/N. We also discuss this result in terms of the dimension of the encoding Hilbert space.

quant-ph↗

arXiv2000

Neutral Kaons in Medium: Decoherence Effects

We consider departures from hamiltonian dynamics in the evolution of neutral kaons due to their interactions with environment that generate entanglement among them. We propose a phenomenological model of stochastic re-scattering and estimate the coefficients of the effective hamiltonian and decoherence terms. Finally we analyze the interplay between the weak interaction and matter effects and propose the observables suitable to measure the matter characteristics of CPT violation and decoherence.

hep-ph↗

arXiv2000

Optimal strategies for sending information through a quantum channel

Quantum states can be used to encode the information contained in a direction, i.e., in a unit vector. We present the best encoding procedure when the quantum state is made up of $N$ spins (qubits). We find that the quality of this optimal procedure, which we quantify in terms of the fidelity, depends solely on the dimension of the encoding space. We also investigate the use of spatial rotations on a quantum state, which provide a natural and less demanding encoding. In this case we prove that the fidelity is directly related to the largest zeros of the Legendre and Jacobi polynomials. We also discuss our results in terms of the information gain.

quant-ph↗

arXiv2000

Separability and distillability in composite quantum systems -a primer-

Quantum mechanics is already 100 years old, but remains alive and full of challenging open problems. On one hand, the problems encountered at the frontiers of modern theoretical physics like Quantum Gravity, String Theories, etc. concern Quantum Theory, and are at the same time related to open problems of modern mathematics. But even within non-relativistic quantum mechanics itself there are fundamental unresolved problems that can be formulated in elementary terms. These problems are also related to challenging open questions of modern mathematics; linear algebra and functional analysis in particular. Two of these problems will be discussed in this article: a) the separability problem, i.e. the question when the state of a composite quantum system does not contain any quantum correlations or entanglement and b) the distillability problem, i.e. the question when the state of a composite quantum system can be transformed to an entangled pure state using local operations (local refers here to component subsystems of a given system). Although many results concerning the above mentioned problems have been obtained (in particular in the last few years in the framework of Quantum Information Theory), both problems remain until now essentially open. We will present a primer on the current state of knowledge concerning these problems, and discuss the relation of these problems to one of the most challenging questions of linear algebra: the classification and characterization of positive operator maps.

quant-ph↗

arXiv2000

Three-qubit pure-state canonical forms

In this paper we analyze the canonical forms into which any pure three-qubit state can be cast. The minimal forms, i.e. the ones with the minimal number of product states built from local bases, are also presented and lead to a complete classification of pure three-qubit states. This classification is related to the values of the polynomial invariants under local unitary transformations by a one-to-one correspondence.

quant-ph↗

arXiv2000

Generalized Schmidt decomposition and classification of three-quantum-bit states

We prove for any pure three-quantum-bit state the existence of local bases which allow to build a set of five orthogonal product states in terms of which the state can be written in a unique form. This leads to a canonical form which generalizes the two-quantum-bit Schmidt decomposition. It is uniquely characterized by the five entanglement parameters. It leads to a complete classification of the three-quantum-bit states. It shows that the right outcome of an adequate local measurement always erases all entanglement between the other two parties.

quant-ph↗

arXiv2000

Effective Quark Models in QCD at low and intermediate energies

The effective quark models are employed to describe the hadronization of QCD in the quark sector. They reveal a different structure depending on how the spontaneous chiral symmetry breaking (CSB) is implemented. When the generation of light pseudoscalar mesons is manifestly incorporated one deals with an extension of the chiral quark model (CQM) with the non-linear realization of chiral symmetry. If a model is built at the CSB scale by means of perturbation theory it generalizes the Nambu-Jona-Lasinio (NJL) one with chiral symmetry broken due to attractive 4-fermion forces in the scalar channel. The matching to high-energy QCD is realized at CSB scale by means of Chiral Sum Rules. Two types of models are compared in their fitting of meson physics. In particular, if the lowest scalar meson is sufficiently heavy approaching the mass of heavy π'(1300) then QCD favours an effective theory which is dominated by the simplest CQM. On the contrary, the light scalar quarkonium with a mass of order 500MeV, supports the NJL mechanism.

hep-ph↗

arXiv2000

Triviality of GHZ operators of higher spin

We prove that local observables of the set of GHZ operators for particles of spin higher than 1/2 reduce to direct sums of the spin 1/2 operators $σ_x$, $σ_y$ and, therefore, no new contradictions with local realism arise by considering them.

quant-ph↗

arXiv1999

Separability and distillability of multiparticle quantum systems

We present a family of 3--qubit states to which any arbitrary state can be depolarized. We fully classify those states with respect to their separability and distillability properties. This provides a sufficient condition for nonseparability and distillability for arbitrary states. We generalize our results to $N$--particle states.

quant-ph↗

arXiv1999

Optimal estimation of two-qubit pure-state entanglement

We present optimal measuring strategies for the estimation of the entanglement of unknown two-qubit pure states and of the degree of mixing of unknown single-qubit mixed states, of which N identical copies are available. The most general measuring strategies are considered in both situations, to conclude in the first case that a local, although collective, measurement suffices to estimate entanglement, a non-local property, optimally.

quant-ph↗

arXiv1999

The Extended Chiral Quark Model confronts QCD

We discuss the truncation of low energy effective action of QCD below the chiral symmetry breaking (CSB) scale, including all operators of dimensionality less or equal to 6 which can be built with quark and chiral fields. We perform its bosonization in the scalar, pseudoscalar, vector and axial-vector channels in the large-N_c and leading-log approximation. Constraints on the coefficients of the effective lagrangian are derived from the requirement of Chiral Symmetry Restoration (CSR) at energies above the CSB scale in the scalar-pseudoscalar and vector-axial-vector channels, from matching to QCD at intermediate scales, and by fitting some hadronic observables. In this truncation two types of pseudoscalar states (massless pions and massive Pi'-mesons), as well as a scalar, vector and axial-vector one arise as a consequence of dynamical chiral symmetry breaking. Their masses and coupling constants as well as a number of chiral structural constants are derived. A reasonable fit of all parameters supports a relatively heavy scalar meson (quarkonium) with the mass \sim 1 GeV and a small value of axial pion-quark coupling constant g_A \simeq 0.55.

hep-ph↗

arXiv1998

Optimal minimal measurements of mixed states

The optimal and minimal measuring strategy is obtained for a two-state system prepared in a mixed state with a probability given by any isotropic a priori distribution. We explicitly construct the specific optimal and minimal generalized measurements, which turn out to be independent of the a priori probability distribution, obtaining the best guesses for the unknown state as well as a closed expression for the maximal mean averaged fidelity. We do this for up to three copies of the unknown state in a way which leads to the generalization to any number of copies, which we then present and prove.

quant-ph↗

arXiv1998

The Extended Chiral Quark Model and QCD

We consider the low energy effective action of QCD below the chiral symmetry breaking scale, including, in Wilson's spirit, all operators of dimensionality less or equal to 6 which can be built with quark and chiral fields. The effect of the residual gluon interactions is contained in a number of coupling constants, whose running is studied. The resulting model is an extension of both the chiral quark model and the Nambu-Jona-Lasinio one. Constraints on the coefficients of the effective lagrangian are derived from the requirement of chiral symmetry restoration at energies above the chiral symmetry breaking scale, from matching to QCD at intermediate scales, and by fitting some hadronic observables. In this model two types of pseudoscalar states (massless pions and massive Π-mesons), as well as one scalar one arise as a consequence of dynamical chiral symmetry breaking. Their masses and coupling constants are studied. We also predict a number of low energy structural constants. We find out that QCD favours a low-energy effective theory which is largely dominated by the simplest chiral quark model, whereas higher dimensional operators (such as those of the Nambu-Jona-Lasinio type) can be assumed to be small.

hep-ph↗

arXiv1998

Minimal optimal generalized quantum measurements

Optimal and finite positive operator valued measurements on a finite number $N$ of identically prepared systems have been presented recently. With physical realization in mind we propose here optimal and minimal generalized quantum measurements for two-level systems. We explicitly construct them up to N=7 and verify that they are minimal up to N=5. We finally propose an expression which gives the size of the minimal optimal measurements for arbitrary $N$.

quant-ph↗

arXiv1996

Ambiguities in QED: Renormalons versus Triviality

We point out that, contrary to what is believed to hold for QCD, renormalons are genuine in QED; i.e. the ambiguities which come with them do not require cancellation by hypothetical non-perturbative contributions. They are just the ambiguities characteristic of any trivial ---and thus effective--- theory. If QED remained an isolated theory up to an energy close to its triviality scale, these ambiguities would surely hint at new physics. This not being so, the renormalon ambiguities in QED lead to no new physics, not even to non-perturbative contributions within QED itself.

hep-ph↗

arXiv1995

The regulated four parameter one dimensional point interaction

The general four parameter point interaction in one dimensional quantum mechanics is regulated. It allows the exact solution, but not the perturbative one. We conjecture that this is due to the interaction not being asymptotically free. We then propose a different breakup of unperturbed theory and interaction, which now is asymptotically free but leads to the same physics. The corresponding regulated potential can be solved both exactly and perturbatively, in agreement with the conjecture.

hep-th↗

arXiv1994

Speed of Light in Non--Trivial Vacua

We unify all existing results on the change of the speed of low--energy photons due to modifications of the vacuum, finding that it is given by a universal constant times the quotient of the difference of energy densities between the usual and modified vacua over the mass of the electron to the fourth power. Whether photons move faster or slower than $c$ depends only on the lower or higher energy density of the modified vacuum, respectively. Physically, a higher energy density is characterized by the presence of additional particles (real or virtual) in the vacuum whereas a lower one stems from the absence of some virtual modes. We then carry out a systematic study of the speed of propagation of massless particles for several field theories up to two loops on a thermal vacuum. Only low--energy massless particles corresponding to a massive theory show genuine modifications of their speed while remaining massless. All other modifications are mass-related, or running mass-related. We also develop a formalism for the Casimir vacuum which parallels the thermal one and check that photons travel faster than $c$ between plates.

hep-th↗