arXiv subjects

Jakub Rembieliński

Publications and source records attributed to Jakub Rembieliński.

17 recordsLinked to original sources

arXiv2026

Quasilinear evolution versus von Neumann selective measurement

In this article, we introduce a new form of quantum selective measurement in which the von Neumann projection postulate is replaced by quasilinear evolution, governed by a nonlinear generalization of the von Neumann equation. We demonstrate that this equation preserves the equivalence of quantum ensembles and, consequently, satisfies the no-signalling principle, ensuring consistency with both quantum mechanics and Einstein causality. Our approach eliminates the need for instantaneous, discontinuous state collapse and provides a unified description of the postmeasurement quantum state reduction as a form of quantum state evolution. Notably, it does not require invoking concepts such as the quantum state assigned to a classical apparatus. At the same time, the stochastic character of selective measurement and the Born rule remain unchanged. We present several numerical solutions of the evolution equation for quasilinear selective measurement in two-level quantum systems and compare them with the standard von Neumann projection. The results demonstrate agreement between the two measurement schemes in their fundamental properties. Furthermore, we investigate phenomena associated with the structural instability of the evolution equation and identify very narrow parameter regions in which the outcomes deviate from those predicted by the von Neumann projection. These regions may offer opportunities to test the proposed approach experimentally. Finally, using specific analytical solutions, we discuss the Stern-Gerlach experiment within the framework of quasilinear measurement.

quant-ph↗

arXiv2026

Quantum selective measurement as a quasilinear evolution

We propose replacing the instantaneous state reduction in von Neumann selective measurement with continuous nonlinear evolution. Despite its nonlinearity, this evolution preserves the equivalence of quantum ensembles and hence obeys the no-signaling principle. Its final states coincide with those produced by the von Neumann projection. The defining features of rank-one projective measurement are retained: convergence to the eigenstate of the observable associated with the selected outcome, independence of this final state from the initial state, and consistent action on entangled states.

quant-ph↗

arXiv2025

Entanglement and Bell inequality violation in vector diboson systems produced in decays of spin-0 particles

We discuss entanglement and the violation of the CGLMP inequality in a system of two vector bosons produced in the decay of a spin-0 particle. We assume the most general CPT conserving, Lorentz-invariant coupling of the spin-0 particle with the daughter bosons. We compute the most general two-boson density matrix obtained by averaging over kinematical configurations with an appropriate probability distribution (which can be obtained when both bosons subsequently decay into fermion-antifermion). We show that the two-boson state is entangled and violates the CGLMP inequality for all values of the (anomalous) coupling constants and that in this case the state is entangled iff it can violate the CGLMP inequality. As an exemplary process of this kind we use the decay $H\to ZZ$ with anomalous coupling.

hep-ph↗

arXiv2025

Minimal extension of the Standard Model with a mirror symmetry between fundamental fermions and a possible origin of dark matter

In this paper, we propose a specific, nontrivial extension of the Standard Model of weak interactions based on the ${SU(2)}_L\times{U(1)}_Y\times{U(1)}_C$ group. Our motivation follows from the identification of the globally conserved charge $Ω=\mathrm{B}-\mathrm{L}-\mathrm{Q}$ as a neutrino charge. An intriguing feature of the model is the emergence of a mirror symmetry between neutrinos and electrically charged leptons, as well as between up and down quarks. Following the spontaneous breaking of the weak gauge symmetry with the use of the Goldstone-Higgs iso-doublet, all elementary fermions acquire Dirac masses from Yukawa interaction. The $W^\pm$ and $Z$ bosons also acquire masses, although with a modified relationship between their respective masses, as compared to the Standard Model. Our model accounts for both chiral components of the neutrino and offers an explanation for the non-observability of the right-chiral neutrino. Additionally, it forbids neutrinoless double-beta decay. Spontaneous breaking of the local $U(1)$ symmetry leads to the new gauge boson $ \mathitΩ_μ$ mass $M_\mathitΩ$, which we assume to be greater than the mass $m_χ$ of a new scalar, Higgs-like field $χ$. The cosmological stability of $χ$, predicted under this condition, allows for its interpretation as dark matter, interacting exclusively with $\mathitΩ_μ$ and gravity. From this perspective, we solve and analyze a system of Boltzmann equations that describe the thermal evolution of the number density of $χ$ dark matter and the $\mathitΩ_μ$ mediator field within the context of the $\mathrm{ΛCDM}$ cosmological model. Specifically, we estimate the coupling constant $q$ to be in the range of $\sim 10^{-8.5}\ g$ to $\sim 10^{-6}\ g$ which ensures cosmological stability of the $χ$ particles.

hep-ph↗

arXiv2024

Entanglement and Bell inequalities violation in $H\to ZZ$ with anomalous coupling

We discuss entanglement and violation of Bell-type inequalities for a system of two $Z$ bosons produced in Higgs decays. We take into account beyond the Standard Model (anomalous) coupling between $H$ and daughter bosons but we limit ourselves to an overall scalar $ZZ$ state (we exclude the possibility that $H$ contains a pseudo-scalar component). In particular we consider the case when each $Z$ decays further into fermion-antifermion pair. We find that a $ZZ$ state is entangled and violates the CGLMP inequality for all values of the (anomalous) coupling constant.

hep-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↗

arXiv2021

Quantum Field Theory of Space-like Neutrino

We performed a Lorentz covariant quantization of the spin-1/2 fermion field assuming the space-like energy-momentum dispersion relation. We a\-chieved the task in the following steps: ($i$) determining the unitary realizations of the inhomogenous Lorentz group in the preferred frame scenario by means of the Wigner-Mackey induction procedure and constructing the Fock space; ($ii$) formulating the theory in a manifestly covariant way by constructing the field amplitudes according to the Weinberg method; ($iii$) obtaining the final constraints on the amplitudes by postulating a Dirac-like free field equation. Our theory allows to predict all chiral properties of the neutrinos, preserving the Standard Model dynamics. We discussed the form of the fundamental observables, energy and helicity, and show that non-observation of the $+\tfrac{1}{2}$ helicity state of the neutrino and the $-\tfrac{1}{2}$ helicity state of the antineutrino could be a direct consequence of the "tachyoneity" of neutrinos at the free level. We found that the free field theory of the space-like neutrino is not invariant under the C and P transformations separately but is CP-invariant. We calculated and analyzed the electron energy spectrum in tritium decay within the framework of our theory and found an excellent agreement with the recent measurement of KATRIN. In our formalism the questions of negative/imaginary energies and the causality problem does not appear.

hep-ph↗

arXiv2021

Nonlinear extension of the quantum dynamical semigroup

In this paper we consider deterministic nonlinear time evolutions satisfying so called convex quasi-linearity condition. Such evolutions preserve the equivalence of ensembles and therefore are free from problems with signaling. We show that if family of linear non-trace-preserving maps satisfies the semigroup property then the generated family of convex quasi-linear operations also possesses the semigroup property. Next we generalize the Gorini-Kossakowski-Sudarshan-Lindblad type equation for the considered evolution. As examples we discuss the general qubit evolution in our model as well as an extension of the Jaynes-Cummings model. We apply our formalism to spin density matrix of a charged particle moving in the electromagnetic field as well as to flavor evolution of solar neutrinos.

quant-ph↗

arXiv2019

Nonlinear evolution and signaling

We propose a condition, called convex quasi-linearity, for deterministic nonlinear quantum evolutions. Evolutions satisfying this condition do not allow for arbitrary fast signaling, therefore, they cannot be ruled out by a standard argument. We also give an explicit example of a nonlinear qubit evolution satisfying quasi-linearity.

quant-ph↗

arXiv2013

Relativistic Einstein-Podolsky-Rosen correlations and localization

We calculate correlation functions for a relativistic Einstein-Podolsky-Rosen-type experiment with massive Dirac particles. We take the influence of the Newton-Wigner localization into account and perform the calculations for a couple of physically interesting states.

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↗

arXiv2012

Relativistic spin operator and Dirac equation

We give a direct link between description of Dirac particles in the abstract framework of unitary representation of the Poincaré group and description with the help of the Dirac equation. In this context we discuss in detail the spin operator for a relativistic Dirac particle. We show also that the spin operator used in quantum field theory for spin $s=1/2$ corresponds to the Foldy-Woutheysen mean-spin operator.

math-ph↗

arXiv2010

Einstein-Podolsky-Rosen correlations in a hybrid system

We calculate the relativistic correlation function for a hybrid system of a photon and a Dirac-particle. Such a system can be produced in decay of another spin-1/2 fermion. We show, that the relativistic correlation function, which depends on particle momenta, may have local extrema for fermion velocity of order 0.5 c. This influences the degree of violation of CHSH inequality.

quant-ph↗

arXiv2010

Relativistic Einstein-Podolsky-Rosen correlations for vector and tensor states

We calculate and investigate the relativistic correlation function for bipartite systems of spin-1/2 in vector and spin-1 particles in tensor states. We show that the relativistic correlation function, which depends on particles momenta, may have local extrema. What is more, the momentum dependance of the correlation functions for two choices of relativistic spin operator may be significantly different.

quant-ph↗

arXiv2009

Strange behavior of the relativistic Einstein-Podolsky-Rosen correlations

We show that configurations exist in which the correlation functions and the degree of violation of Bell-type inequalities in the relativistic Einstein-Podolsky-Rosen (EPR) experiment have local extrema for some values of the velocities of the EPR particles. Moreover, this strange behavior can be observed for both discussed relativistic spin operators and for spin-1/2 as well as spin-1 particles.

quant-ph↗

arXiv2008

Einstein-Podolsky-Rosen correlations of vector bosons

We calculate the joint probabilities and the correlation function in Einstein--Podolsky--Rosen type experiments with a massive vector boson in the framework of quantum field theory. We report on the strange behavior of the correlation function (and the probabilities) -- the correlation function, which in the relativistic case still depends on the particle momenta, for some fixed configurations has local extrema. We also show that relativistic spin-1 particles violate some Bell inequalities more than nonrelativistic ones and that the degree of violation of the Bell inequality is momentum dependent.

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↗