Papers by Kordian Smoliński
arXiv (Cornell University), Apr 23, 2003
It is shown that the hypothesis of tachyonic neutrinos leads to the same oscillations effect as i... more It is shown that the hypothesis of tachyonic neutrinos leads to the same oscillations effect as if they were usual massive particles. Therefore, the experimental evidence of neutrino oscillations does not distinguish between massive and tachyonic neutrinos.
On the Kraus representation of destruction of states for one qudit
arXiv (Cornell University), Jul 10, 2003
Quantum operations arise naturally in many fields of quantum information theory and quantum compu... more Quantum operations arise naturally in many fields of quantum information theory and quantum computing. One of the simplest example of quantum operation is the von Neumann-Lueders measurement. Destruction of states in quantum mechanics can be treated as a supplement to the von Neumann-Lueders measurement [P. Caban, J. Rembielinski, K. A. Smolinski and Z. Walczak, J. Phys. A: Math. Gen. 35, 3265 (2002)]. We show that destruction of states in one-qudit system is a quantum operation by finding its Kraus representation.
A Model of Quantum Space-Time Symmetry in Two Dimensions
arXiv (Cornell University), Aug 12, 1993
An example of a toy model of $D=2$ Minkowski space and Poincaré group with real deformation para... more An example of a toy model of $D=2$ Minkowski space and Poincaré group with real deformation parameter $q$ is considered. A notion of free motion is defined. The kinematics and phase-space are constructed and the ``uncertainity'' ralations are found.
A pr 2 00 3 Flavor change of tachyonic neutrinos
It is shown that the hypothesis of tachyonic neutrinos leads to the same oscillations effect as i... more It is shown that the hypothesis of tachyonic neutrinos leads to the same oscillations effect as if they were usual massive particles. Therefore, the expe rimental evidence of neutrino oscillations does not distinguish between massive and tach yonic neutrinos.
Quantum poincar� group for isotropic quantum space-time
Czech J Phys, 1994
A Model of Quantum Space-Time Symmetry in Two Dimensions
An example of a toy model of $D=2$ Minkowski space and Poincar\'e group with real deformation... more An example of a toy model of $D=2$ Minkowski space and Poincar\'e group with real deformation parameter $q$ is considered. A notion of free motion is defined. The kinematics and phase-space are constructed and the ``uncertainity'' ralations are found.
Spin Correlations in Nonrelativistic Quantum Mechanics
International Journal of Theoretical Physics, 2003
Einstein—Podolsky—Rosen spin correlations in the framework of nonrelativistic quantum mechanics f... more Einstein—Podolsky—Rosen spin correlations in the framework of nonrelativistic quantum mechanics for moving observers are calculated. The measurements are performed in bounded regions of space (detectors), not necessarily simultaneously. The resulting correlation function depends not only on the directions of spin measurements but also on the relative velocity of the observers.
International Journal of Theoretical Physics, 2003
The description of destruction in bipartite quantum systems in terms of quantum mechanics rather ... more The description of destruction in bipartite quantum systems in terms of quantum mechanics rather than quantum field theory is presented. The maps called supertraces are defined and used in the definition of the destruction procedure, which can be treated as a supplement to the von Neumann—Lüders reduction postulate. The presented formalism is illustrated by several examples that may be helpful
A kind of doubly special relativity theory proposed by J. Magueijo and L. Smolin [Phys. Rev. Lett... more A kind of doubly special relativity theory proposed by J. Magueijo and L. Smolin [Phys. Rev. Lett. 88, 190403 (2002)] is analysed. It is shown that this theory leads to serious physical difficulties in interpretation of kinematical quantities. Moreover, it is argued that statistical mechanics and thermodynamics cannot be resonably formulate within the model proposed in the mentioned paper.
Physical review, Aug 31, 2007
The Lorentz covariant classical and quantum statistical mechanics and thermodynamics of an ideal ... more The Lorentz covariant classical and quantum statistical mechanics and thermodynamics of an ideal relativistic gas of bradyons (particles slower than light), luxons (particles moving with the speed of light) and tachyons (hypothetical particles faster than light) is discussed. The Lorentz covariant formulation is based on the preferred frame approach which among others enables consistent, free of paradoxes description of tachyons. The thermodynamic functions within the covariant approach are obtained both in classical and quantum case.
The idea of the preferred frame as a remedy for difficulties of the relativistic quantum mechanic... more The idea of the preferred frame as a remedy for difficulties of the relativistic quantum mechanics in description of the non-local quantum phenomena was undertaken by such physicists as J. S. Bell and D. Bohm. The possibility of the existence of preferred frame was also seriously treated by P. A. M. Dirac. In this paper, we propose an Einstein-Podolsky-Rosen-type experiment for testing the possible existence of a quantum preferred frame. Our analysis suggests that to verify whether a preferred frame of reference in the quantum world exists it is enough to perform an EPR type experiment with pair of observers staying in the same inertial frame and with use of the massive EPR pair of spin one-half or spin one particles.
We describe a q-deformed dynamical system corresponding to the quantum free particle moving along... more We describe a q-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system. 1
We described a q-deformation of a quantum dynamics in one dimension. We prove that there exists o... more We described a q-deformation of a quantum dynamics in one dimension. We prove that there exists only one essential deforamtion of quantum dynamics. 1
The formula for the correlation function of spin measurements of two particles in two moving iner... more The formula for the correlation function of spin measurements of two particles in two moving inertial frames is derived within Lorentz-covariant quantum mechanics formulated in the absolute synchronization framework. These results are the first exact Einstein-Podolsky-Rosen correlation functions obtained for Lorentz-covariant quantum-mechanical systems in moving frames under physically acceptable conditions, i.e., taking into account the localization of the particles during the detection and using the spin operator with proper transformation properties under the action of the Lorentz group. Some special cases and approximations of the calculated correlation function are given. The resulting correlation function can be used as a basis for a proposal of a decisive experiment for a possible existence of a quantum-mechanical preferred frame.
Unstable particles as open quantum systems (9 pages)
Quantum Information Processing, 2018
We formulate a covariant description of a relativistic qubit identified with an irreducible set o... more We formulate a covariant description of a relativistic qubit identified with an irreducible set of quantum spin states of a Majorana particle with a sharp momentum. We treat the particle's four-momentum as an external parameter. We show that it is possible to define an interesting time evolution of the spin density matrix of such a qubit. This evolution is manifestly Lorentz covariant in the bispinor representation and unitary in the spin representation. Moreover, during this evolution the Majorana particle undergoes an uniformly accelerated motion. We classify possible types of such motions, and finally we illustrate the behaviour of the polarization vector of the Majorana qubit during the evolution in some special cases.
Quantum Information Processing, 2017
We study selected aspects of non-classical correlations of arbitrary states from the stochastic l... more We study selected aspects of non-classical correlations of arbitrary states from the stochastic local operations and classical communication orbit of rankdeficient two-qubit states. In particular, we find explicitly entanglement of formation and quantum discord for these states. Moreover, we determine and analyze the Einstein-Podolsky-Rosen steering ellipsoids corresponding to these states.
Physical Review A, 2015
We have shown that it is possible to formulate the consistent and probability-preserving descript... more We have shown that it is possible to formulate the consistent and probability-preserving description of the CP -symmetry-violating evolution of a system of decaying particles. This has been done within the framework of quantum mechanics of open systems. This approach allows the description of both the exponential decay and flavour oscillations. We have solved explicitly the Kossakowski-Lindblad master equation for a system of particles with violated CP symmetry and found the evolution of any observable bilinear in creation and annihilation operators. The choice of a concrete observable can be done by the proper choice of initial conditions for the system of differential equations. We have calculated the evolution as well as mean values of the observables most interesting from the physical point of view, and we have found their lowest order difference with the CP -preserved values.
International Journal of Theoretical Physics
The correlation function of spin measurements of two spin-1 2 particles in two moving inertial fr... more The correlation function of spin measurements of two spin-1 2 particles in two moving inertial frames is derived within the framework of the Lorentz covariant quantum mechanics with the preferred frame. The localization of the particles during the detection and proper transformation properties under the action of the Lorentz group of the spin operator are taken into account. Some special cases and approximations of the calculated correlation function are discussed.
Quantum Information Processing, 2015
Verstraete, Dehaene and DeMoor showed that each of the two-qubit states can be generated from one... more Verstraete, Dehaene and DeMoor showed that each of the two-qubit states can be generated from one of two canonical families of two-qubit states by means of transformations preserving the tensor structure of the state space. Precisely, each of such states can be generated from a three-parameter family of Bell-diagonal states or from three-parameter rank-deficient states. In this paper, we show that this classification of two-qubit states can be refined. In particular, we show that the latter canonical family of states can be reduced to three fixed states and a two-parameter family of two-qubit states. For this family of states, we provide a simple parametrization that guarantees positive semidefiniteness of the states and enables easier calculation of the Wootters concurrence and quantum discord. Moreover, we present a new general parametrization of all two-qubit states generated from the canonical families of states using sets of (pseudo)orthogonal four-vectors (frames). An advantage of the presented approach lies in the fact that the standard conditions for positive semidefiniteness of states are equivalent to (pseudo)orthogonality conditions for four-vectors serving as
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Papers by Kordian Smoliński