arXiv subjects

Pawel Caban

Publications and source records attributed to Pawel Caban.

10 recordsLinked to original sources

arXiv2026

Violation of Bell inequalities in $2\times3$ dimensional systems

We consider the Clauser-Horn (CH) inequality for a qubit-qutrit system. We derive the necessary and sufficient conditions for the violation of the inequality as well as some sufficient conditions. Remarkably, we demonstrate the importance of local parameters in violation of the inequality. In other words, there are some families of mixed states violating the inequality for which the correlation part alone is useless in the Bell-CH test.

quant-ph↗

arXiv2023

Bell-type inequalities for systems of relativistic vector bosons

We perform a detailed analysis of the possible violation of various Bell-type inequalities for systems of vector boson-antiboson pairs. Considering the general case of an overall scalar state of the bipartite system, we identify two distinct classes of such states, and determine the joint probabilities of spin measurement outcomes for each them. We calculate the expectation values of the CHSH, Mermin and CGLMP inequalities and find that while the generalised CHSH inequality is not expected to be violated for any of the scalar states, in the case of the Mermin and CGLMP inequalities the situation is different -- these inequalities can be violated in certain scalar states while they cannot be violated in others. Moreover, the degree of violation depends on the relative speed of the two particles.

quant-ph↗

arXiv2013

Spin operator in the Dirac theory

We find all spin operators for a Dirac particle satisfying the following very general conditions: (i) spin does not convert positive (negative) energy states into negative (positive) energy states, (ii) spin is a pseudo-vector, and (iii) eigenvalues of the projection of a spin operator on an arbitrary direction are independent of this direction (isotropy condition). We show that there are four such operators and all of them fulfill the standard su(2) Lie algebra commutation relations. Nevertheless, only one of them has a proper non-relativistic limit and acts in the same way on negative and positive energy states. We show also that this operator is equivalent to the Newton-Wigner spin operator and Foldy-Wouthuysen mean-spin operator. We also discuss another operators proposed in the literature.

quant-ph↗

arXiv2008

Helicity correlations of vector bosons

We calculate the helicity and polarization correlation functions in the Einstein-Podolsky-Rosen-type experiments with relativistic vector bosons. We show that the linear polarization correlation function in the appriopriately chosen state in the massless limit is the same as the correlation function in the scalar two-photon state. We show also that the polarization correlation function violate the Clauser-Horne-Shimony-Holt inequality and that the degree of this violation can increase with the particle momentum.

quant-ph↗

arXiv2006

Einstein-Podolsky-Rosen correlations of Dirac particles - quantum field theory approach

We calculate correlation function in the Einstein--Podolsky--Rosen type of experiment with massive relativistic Dirac particles in the framework of the quantum field theory formalism. We perform our calculations for states which are physically interesting and transforms covariantly under the full Lorentz group action, i.e. for pseudoscalar and vector state.

quant-ph↗

arXiv2005

Entanglement and Tensor Product Decomposition for Two Fermions

The problem of the choice of tensor product decomposition in a system of two fermions with the help of Bogoliubov transformations of creation and annihilation operators is discussed. The set of physical states of the composite system is restricted by the superselection rule forbidding the superposition of fermions and bosons. It is shown that the Wootters concurrence is not proper entanglement measure in this case. The explicit formula for the entanglement of formation is found and its dependence on tensor product decompositions of the Hilbert space is discussed. It is shown that the set of separable states is narrower than in two-qubit case. Moreover, there exist states which are separable with respect to all tensor product decompositions of the Hilbert space.

quant-ph↗

arXiv2003

Photon polarization and Wigner's little group

To discuss one-photon polarization states we find an explicit form of the Wigner's little group element in the massless case for arbitrary Lorentz transformation. As is well known, when analyzing the transformation properties of the physical states, only the value of the phase factor is relevant. We show that this phase factor depends only on the direction of the momentum $\vec{k}/|\vec{k}|$ and does not depend on the frequency $k^0$. Finally, we use this observation to discuss the transformation properties of the linearly polarized photons and the corresponding reduced density matrix. We find that they transform properly under Lorentz group.

quant-ph↗

arXiv1998

Lorentz-covariant quantum mechanics and preferred frame

In this paper the relativistic quantum mechanics is considered in the framework of the nonstandard synchronization scheme for clocks. Such a synchronization preserves Poincar{é} covariance but (at least formally) distinguishes an inertial frame. This enables to avoid the problem of a noncausal transmision of information related to breaking of the Bell's inequalities in QM. Our analysis has been focused mainly on the problem of existence of a proper position operator for massive particles. We have proved that in our framework such an operator exists for particles with arbitrary spin. It fulfills all the requirements: it is Hermitean and covariant, it has commuting components and moreover its eigenvectors (localised states) are also covariant. We have found the explicit form of the position operator and have demonstrated that in the preferred frame our operator coincides with the Newton--Wigner one. We have also defined a covariant spin operator and have constructed an invariant spin square operator. Moreover, full algebra of observables consisting of position operators, fourmomentum operators and spin operators is manifestly Poincaré covariant in this framework. Our results support expectations of other authors (Bell, Eberhard) that a consistent formulation of quantum mechanics demands existence of a preferred frame.

quant-ph↗

arXiv1997

Decays of spacelike neutrinos

In this paper we consider the hypothesis that neutrinos are fermionic tachyons with helicity 1/2. We propose an effective model of interactions of these neutrinos and analyze dominant effects under the above hypothesis: the three-body neutrino decay, the radiative decay and briefly discuss beta-decay with tachyonic antineutrino. We calculate the corresponding amplitudes and the mean life time for decays, as well as the differential decay width. In addition we apply the neutrino three-body decay to the solar neutrino problem and we obtain a remarkable change of energy spectrum of the neutrino flux at the Earth ground (assuming no neutrino oscillation). We compare the results with the Standard Solar Model predictions and solar neutrino experiments to estimate an upper bound for the taonic neutrino.

hep-ph↗

arXiv1996

The Preferred Frame and Poincare Symmetry

In this paper we describe a covariant canonical formalism for a free time-like (massive) as well as space-like (tachyonic) particle in the framework of nonstandard synchronization scheme. In this scheme one is able to introduce absolute causality without breaking the Poincaré invariance.

hep-th↗