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Superfast Algorithms and the Halting Problem in Geometric AlgebraNov 05 2006A new type of algorithms is presented that combine the advantages of quantum and classical ones. Those combined advantages along with aspects of Geometric Algebra that open possibilities unavailable to both of these computations are exploited to obtain ... More

The influence of the choice of post-processing method on Bell inequalitiesOct 19 2017Dec 07 2017In every experimental test of a Bell inequality, we are faced with the problem of inefficient detectors. How we treat the events when no particle was detected has a big influence on the properties of the inequality. In this work, we study this influence. ... More

Robustness of quantum randomness expansion protocols in the presence of noiseMay 01 2013In this paper we investigate properties of several randomness generation protocols in the device independent framework. Using Bell-type inequalities it is possible to certify that the numbers generated by an untrusted device are indeed random. We present ... More

Structure of quantum and broadcasting nonlocal correlationsApr 20 2015Jan 03 2016The multipartite setting offers much more complexity of nonlocality than the bipartite one. We analyze the structure of tripartite nonlocal correlations by proposing inequalities satisfied by each type: bilocal, broadcasting and quantum, but violated ... More

Experimentally feasible semi-device-independent certification of $4$ outcome POVMsNov 30 2018In this paper we construct a semi-device-independent protocol able to certify the presence of the generalized measurements. We show robustness of the protocol and conclude that it allows for experimental realisations using current technology.

Information CausalityDec 06 2011We review the literature on Information Causality. Since it's for a book, we don't think an abstract will be needed at all, so we have written this one just for the sake of the arXiv.

Universe's memory and spontaneous coherence in loop quantum cosmologyJul 14 2016The quantum bounce a priori connects several (semi)classical epochs of Universe evolution, however determining if and how well the semiclassicality is preserved in this transition is highly nontrivial. We review the present state of knowledge in that ... More

Geometric time in quantum cosmologyMar 16 2014Various choices of the geometry degrees of freedom as the emergent time are tested on the model of an isotropic universe with a scalar field of $\phi^2$ potential. Potential problems with each choices as well as possible applications in loop quantization ... More

Spin-valley two-qubit system in a gated MoS$_2$-monolayer quantum dotJul 07 2019The aim of presented research is to design a nanodevice based on a gate-defined quantum dot within a MoS$_2$ monolayer in which we confine a single electron. By applying control voltages to the device gates we modulate the confinement potential and force ... More

Testing dimension and non-classicality in communication networksMay 07 2015Sep 14 2015We consider networks featuring preparation, transformation, and measurement devices, in which devices exchange communication via mediating physical systems. We investigate the problem of testing the dimension of the mediating systems in the device-independent ... More

Self-testing of unsharp measurementsMar 29 2019We consider unsharp quantum measurements as a recourse in scenarios where one faces the trade-off between information gain and disturbance. We analyse in detail the case of two-outcome qubit measurements and show that generalized measurements allow for ... More

Properties of dimension witnesses and their semi-definite programming relaxationsMay 15 2014In this paper we develop a method for investigating semi-device-independent randomness expansion protocols that was introduced in [Li et al., Phys. Rev. A $\mathbf{87}$, 020302(R) (2013)]. This method allows to lower-bound, with semi-definite programming, ... More

State independent contextuality advances one-way communicationAug 16 2017Apr 29 2018Despite 'quantum contextuality' being one of the most fundamental non-classical features, its generic role in information processing and computation is an open quest. This article shows that quantum contextuality is a potential resource for communication. ... More

When Are Popescu-Rohrlich Boxes and Random Access Codes Equivalent?Jul 30 2013Sep 11 2014We study a problem of interconvertibility of two supra-quantum resources: one is so called PR-box, which violates CHSH inequality up to maximal algebraic bound, and second is so called random access code (RAC). The latter is a functionality that enables ... More

Device-independent quantum key distribution based on measurement inputsAug 29 2013May 17 2015We provide an analysis of a new family of device independent quantum key distribution (QKD) protocols with several novel features: (a) The bits used for the secret key do not come from the results of the measurements on an entangled state but from the ... More

Connections Between Mutually Unbiased Bases and Quantum Random Access CodesSep 14 2017Mar 28 2018We present a new quantum communication complexity protocol, the promise--Quantum Random Access Code, which allows us to introduce a new measure of unbiasedness for bases of Hilbert spaces. The proposed measure possesses a clear operational meaning and ... More

Quantum nonlocality via local contextuality with qubit-qubit entanglementJul 30 2015Apr 30 2016Quantum nonlocality can be revealed "via local contextuality" in qudit-qudit entangled systems with $d > 2$, that is, through the violation of inequalities containing Alice-Bob correlations that admit a local description, and Alice-Alice correlations ... More

Device independent witness of arbitrary dimensional quantum systems employing binary outcome measurementsMar 14 2018Jan 04 2019Device independent dimension witnesses (DW) are a remarkable way to test the dimension of a quantum system in a prepare-and-measure scenario imposing minimal assumptions on the internal features of the devices. However, as the dimension increases, the ... More

A classical-quantum hybrid oracle architecture for Boolean oracle identification in the noisy intermediate-scale quantum eraMay 14 2019Quantum algorithms have the potential to be very powerful. However, to exploit quantum parallelism, some quantum algorithms require an embedding of large classical data into quantum states. This embedding can cost a lot of resources, for instance by implementing ... More

Electron spin rotations induced by oscillating Rashba interaction in a quantum wireSep 30 2015Dec 10 2015A novel method and nanodevice are introduced that allows to rotate the single electron spin confined in a gated electrostatic InSb nanowire quantum dot. Proposed method does not require application of any (oscillating or static) external magnetic fields. ... More

Quantum-mechanical machinery for rational decision-making in classical guessing gameAug 20 2015Nov 23 2015In quantum game theory, one of the most intriguing and important questions is, "Is it possible to get quantum advantages without any modification of the classical game?" The answer to this question so far has largely been negative. So far, it has usually ... More

One-Qubit and Two-Qubit Codes in Noisy State TransferMay 04 2009Quantum state transfer is a procedure, which allows to exchange quantum information between stationary qubit systems. It is anticipated that the transfer will find applications in solid-state quantum computing. In this contribution, we discuss the effects ... More

Finding Traps in Non-linear Spin ArraysNov 18 2009Precise knowledge of the Hamiltonian of a system is a key to many of its applications. Tasks such state transfer or quantum computation have been well studied with a linear chain, but hardly with systems, which do not possess a linear structure. While ... More

Semi-device independent random number expansion protocol with n to 1 quantum random access codesSep 24 2011Mar 13 2012We study random number expansion protocols based on the $n \to 1$ quantum random access codes (QRACs). We consider them in the semi-device independent scenario where the inner workings of the devices are unknown to us but we can certify the dimensions ... More

Free randomness amplification using bipartite chain correlationsMar 22 2013A direct analysis of the protocol of randomness amplification using Bell inequality violation is performed in terms of the convex combination of no-signaling boxes required to simulate quantum violation of the inequality. The probability distributions ... More

Entanglement storage by classical fixed points in the two-axis countertwisting modelNov 30 2015We analyze a scheme for storage of entanglement quantified by the quantum Fisher information in the two-axis countertwisting model. A characteristic feature of the two-axis countertwisting Hamiltonian is the existence of the four stable center and two ... More

Generation of spin-dependent coherent states in a quantum wireFeb 26 2016Jul 08 2016We propose an all-electrically controlled nanodevice - a gated semiconductor nanowire - capable of generating a coherent state of a single electron trapped in a harmonic oscillator or superposition of such coherent states - the Schr\"odinger cat state. ... More

Parameter estimation in the presence of the most general Gaussian dissipative reservoirSep 11 2016We analyze the performance of quantum parameter estimation in the presence of the most general Gaussian dissipative reservoir. We derive lower bounds on the precision of phase estimation and a closely related problem of frequency estimation. For both ... More

Electron spin separation without magnetic fieldSep 23 2013Feb 24 2014A nanodevice capable of separating spins of two electrons confined in a quantum dot formed in a gated semiconductor nanowire is proposed. Two electrons confined initially in a single quantum dot in the singlet state are transformed into the system of ... More

Generation of Schrödinger's cat states in a planar semiconductor heterostructureOct 20 2016We propose a nanodevice based on a typical planar semiconductor heterostructure with lateral confinement potential created by voltages applied to local electrodes. We show how to obtain near parabolical confinement along the nanodevice, and how to use ... More

Information and Interpretation of Quantum MechanicsNov 23 2010Feb 09 2012This work is a discussion on the concept of information. We define here information as an abstraction that is able to be copied. We consider the connection between the process of copying information in quantum systems and the emergence of the so-called ... More

Simple Model of First-Order Phase TransitionMar 12 2009Jul 29 2009One-dimensional model of a system where first-order phase transition occurs is examined in the present paper. It is shown that basic properties of the phenomenon, such as a well defined temperature of transition, are caused both by existence of a border ... More

Twisted acceleration-enlarged Newton-Hooke Hopf algebrasJul 27 2010Ten Abelian twist deformations of acceleration-enlarged Newton-Hooke Hopf algebra are considered. The corresponding quantum space-times are derived as well. It is demonstrate that their contraction limit $\tau \to \infty$ leads to the new twisted acceleration-enlarged ... More

On moduli spaces of semistable sheaves on Enriques surfacesMar 30 2010We describe some one-dimensional moduli spaces of rank 2 Gieseker semistable sheaves on an Enriques surface improving earlier results of H. Kim. In case of a nodal Enriques surface the obtained moduli spaces are reducible for general polarizations. For ... More

d-wave Superconductivity, Orbital Magnetism, and Unidirectional Charge Order in the t-J ModelMay 15 2008Recent scanning tunneling microscopy in the superconducting regime of two different cuprate families has revealed unidirectional bond-centered modulation in the local electronic density of states. Motivated by this result we investigate the emergence ... More

Canonical and Lie-algebraic twist deformations of $κ$-Poincare and contractions to $κ$-Galilei algebrasFeb 14 2008Jan 27 2009We propose canonical and Lie-algebraic twist deformations of $\kappa$-deformed Poincare Hopf algebra which leads to the generalized $\kappa$-Minkowski space-time relations. The corresponding deformed $\kappa$-Poincare quantum groups are also calculated. ... More

A General Scheme for Construction of Coherent States of Anharmonic OscillatorsJun 26 2007A mixed supersymmetric-algebraic approach to construction of the minimum uncertainty coherent states of anharmonic oscillators is presented. It permits generating not only the well-known coherent states of the harmonic and Morse oscillators but also the ... More

Comment on: Disproof of Bell's Theorem by Clifford Algebra Valued Local VariablesMar 23 2007Mar 25 2007We ''save'' Bell's Theorem by showing a flaw in Christian's argument.

Translations in Quantum Field Theory and the Poincaré Gauge Theory of GravitySep 29 2009In standard quantum field theory, the one-particle states are classified by the unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite-dimensional (non-unitary) representations of the (homogeneous) ... More

Phase spaces of twisted Lie-algebraically deformed relativistic and nonrelativistic symmetriesAug 27 2009The twisted Lie-algebraically deformed relativistic and nonrelativistic phase spaces are constructed with the use of Heisenberg double procedure. The corresponding Heisenberg uncertainty principles are discussed as well.

Einstein-Cartan gravity with Holst term and fermionsDec 06 2008Mar 25 2009We investigate the consequences of the ambiguity of minimal coupling procedure for Einstein-Cartan gravity with Holst term and fermions. A new insight is provided into the nature and physical relevance of coupling procedures considered hitherto in the ... More

$σ$-continuity and related forcingsJul 08 2008The Steprans forcing notion arises as a quotient of Borel sets modulo the ideal of $\sigma$-continuity of a certain Borel not $\sigma$-continuous function. We give a characterization of this forcing in the language of trees and using this characterization ... More

Canonical and Lie-algebraic twist deformations of Galilei algebraJan 08 2008Jan 27 2009We describe various nonrelativistic contractions of two classes of twisted Poincare algebra: canonical one ($\theta_{\mu\nu}$-deformation) and the one leading to Lie-algebraic models of noncommutative space-times. The cases of contraction-independent ... More

The topological obstructions to the existence of an irreducible SO(3) structure on a five manifoldJan 04 2006A nonstandard (maximal) inclusion SO(3) in SO(5) associated with the irreducible representation \rho_5 of SO(3) in R^5 is considered. The topological obstructions for admitting the SO(3) structure on the frame bundle over 5-manifold are investigated. ... More

The 1.6um Bump as a Photometric Redshift IndicatorSep 20 2002I describe the principle of using the 1.6um H- spectral feature as a photometric redshift indicator and demonstrate that the technique holds promise by successfully recovering the redshifts of a small sample of z=0-1 galaxies using only their infrared ... More

The build-up of mass in UV-selected sub-L* galaxies at z~2Feb 09 2011Broadband spectral energy distribution (SED) fitting is used to study a deep sample of UV-selected sub-L* galaxies at z~2. They are found to be less dusty than L* galaxies, and to contribute more mass to the cosmic mass budget at this epoch than is inferred ... More

A comment on "The Computational 2D Materials Database: high-throughput modeling and discovery of atomically thin crystals"Dec 13 2018Recently, Sten Haastrup, Mikkel Strange, Mohnish Pandey, Thorsten Deilmann, Per S Schmidt, Nicki F Hinsche, Morten N Gjerding, Daniele Torelli, Peter M Larsen, Anders C Riis-Jensen, Jakob Gath, Karsten W Jacobsen, Jens Jrgen Mortensen, Thomas Olsen and ... More

Twist deformations of Newtonian Schwarzschild-(Anti-)de Sitter classical systemApr 26 2019In this article we provide three new twist-deformed Newtonian Schwarzschild-(Anti-)de Sitter models. They are defined on the Lie-algebraically as well as on the canonically noncommutative space-times respectively. Particularly we find the corresponding ... More

Complexity of Ramsey null setsMar 31 2010We show that the set of codes for Ramsey positive analytic sets is $\mathbf{\Sigma}^1_2$-complete. This is a one projective-step higher analogue of the Hurewicz theorem saying that the set of codes for uncountable analytic sets is $\mathbf{\Sigma}^1_1$-complete. ... More

Extreme amenability of abelian $L_0$ groupsJan 03 2012We show that for any abelian topological group $G$ and arbitrary diffused submeasure $\mu$, every continuous action of $L_0(\mu,G)$ on a compact space has a fixed point. This generalizes earlier results of Herer and Christensen, Glasner, Furstenberg and ... More

Riesz transform characterization of H^1 spaces associated with certain Laguerre expansionsFeb 17 2010Nov 26 2011For alpha>0 we consider the system l_k^{(alpha-1)/2}(x) of the Laguerre functions which are eigenfunctions of the differential operator Lf =-\frac{d^2}{dx^2}f-\frac{alpha}{x}\frac{d}{dx}f+x^2 f. We define an atomic Hardy space H^1_{at}(X), which is a ... More

Regularity and non-emptyness of linear systems in $\mathbb P^n$Feb 07 2008The main goal of this paper is to present a new algorithm bounding the regularity and ``alpha'' (the lowest degree of existing hypersurface) of a linear system of hypersurfaces (in $\mathbb P^n$) passing through multiple points in general position. To ... More

Atomic decompositions for Hardy spaces related to Schrödinger operatorsSep 16 2014Let L_U = -Delta+U be a Schr\"odinger operator on R^d, where U\in L^1_{loc}(R^d) is a non-negative potential and d\geq 3. The Hardy space H^1(L_U) is defined in terms of the maximal function for the semigroup K_{t,U} = exp(-t L_U), namely H^1(L_U) = {f\in ... More

On spectra and affine strict polynomial functorsDec 31 2015We compare derived categories of the category of strict polynomial functors over a finite field and the category of ordinary endofunctors on the category of vector spaces. We introduce two intermediate categories: the category of $\infty$--affine strict ... More

Spectra of disc operator for twisted acceleration-enlarged Newton-Hooke space-timesJan 10 2011The time-dependent spectra of disc area operator for twisted acceleration-enlarged Newton-Hooke space-times are derived. It is demonstrated that the corresponding area quanta are expanding or oscillating in time.

Generalized Dirac bracket and the role of the Poincaré symmetry in the program of canonical quantization of fields 2Nov 12 2010In this article the methods of canonical analysis and quantization that were reviewed in the first part of the series are applied to the case of the Dirac field in the presence of electromagnetic interaction. It is shown that the quantization of electrodynamics, ... More

Deformation of nonrelativistic space-time and forces noticed by noninertial observerJul 27 2010We consider the nonrelativistic particle moving on noncommutative space-time in the presence of constant force $\vec{F}$. Further, following the paper M. Daszkiewicz, C.J. Walczyk, Phys. Rev. D 77, 105008 (2008); arXiv: 0802.3575 [math-ph], we recall ... More

Ellipsoids of U(3) modelNov 19 2009Nov 25 2009The Cartan model of SO(3)/SO(2) matrices is applied to reduce of rotational degrees of freedom on coadjoint orbits of u^*(3) Poisson algebra. The seven--dimensional Poisson algebra u_SO(3) obtained by SO(3) reduction of u^*(3) algebra is found and canonical ... More

Generalized Dirac bracket and the role of the Poincaré symmetry in the program of canonical quantization of fields 1Oct 27 2010Nov 12 2010An elementary presentation of the methods for the canonical quantization of constraint systems with Fermi variables is given. The emphasis is on the subtleties of the construction of an appropriate classical bracket that could be consistently replaced ... More

Local approximation of the solutions of algebraic equationsMar 27 2008A method of local approximation of holomorphic solutions of algebraic equations is discussed

Quantum Wire as Open SystemNov 15 2007May 02 2008The faithful exchange of quantum information will soon become one of the challenges of the emerging quantum information technology. One of the possible solutions is to transfer a superposition through a chain of properly coupled spins. Such a system is ... More

Quasi-Quantum Model of PotentizationNov 23 2009Analytical time-dependent functions describing the change of the concentration of the solvent S(t) and the homeopathic active substance A(t) during the decimal and centesimal dilution are derived. The function S(t) is a special case of the West-Brown-Enquist ... More

Investigation of astrophysical phenomena in short time scales with "Pi of the Sky" apparatusOct 07 2008In this thesis the data analysis designed by author for the "Pi of the Sky" experiment is presented. The data analysis consists of data reduction and specific algorithms for identification of short time scale astrophysical processes. The algorithms have ... More

Approximation of sets defined by polynomials with holomorphic coefficientsDec 18 2007Let X be an analytic set defined by polynomials whose coefficients a_1,...,a_s are holomorphic functions. We formulate conditions such that for all sequences {a_(1,n)},...,{a_(s,n)} of holomorphic functions converging locally uniformly to a_1,...,a_s ... More

Analysis of Implementation Hierocrypt-3 algorithm (and its comparison to Camellia algorithm) using ALTERA devicesDec 17 2003Alghoritms: HIEROCRYPT-3, CAMELLIA and ANUBIS, GRAND CRU, NOEKEON, NUSH, Q, RC6, SAFER++128, SC2000, SHACAL were requested for the submission of block ciphers (high level block cipher) to NESSIE (New European Schemes for Signatures, Integrity, and Encryption) ... More

Error correction in quantum cryptography based on artificial neural networksOct 01 2018Intensive work on quantum computing has increased interest in quantum cryptography in recent years. Although this technique is characterized by a very high level of security, there are still challenges that limit the widespread use of quantum key distribution. ... More

Classical conformal blocks from TBA for the elliptic Calogero-Moser systemFeb 26 2011Jun 22 2011The so-called Poghossian identities connecting the toric and spherical blocks, the AGT relation on the torus and the Nekrasov-Shatashvili formula for the elliptic Calogero-Moser Yang's (eCMY) functional are used to derive certain expressions for the classical ... More

Analysis of experimental uncertainties in the R-correlation measurement in the decay of free neutronsJun 29 2004Sep 07 2004The experiment aiming at the simultaneous determination of the two transversal polarisation components of electrons emitted in the decay of free, polarised neutrons is in progress at the Paul Scherrer Institute (Villigen, Switzerland). The non-zero value ... More

Completeness of the isomorphism problem for separable C*-algebrasJun 05 2013Jul 13 2013We prove that the isomorphism problem for separable nuclear C*-algebras is complete in the class of orbit equivalence relations. In fact, already the isomorphism of simple, separable AI C*-algebras is a complete orbit equivalence relation. This means ... More

Symbolic powers of ideals of generic points in P^3May 02 2011B. Harbourne and C. Huneke conjectured that for any ideal $I$ of fat points in $P^N$ its $r$-th symbolic power $I^{(r)}$ should be contained in $M^{(N-1)r}I^r$, where $M$ denotes the homogeneous maximal ideal in the ring of coordinates of $P^N$. We show ... More

The fermionic observable in the Ising model and the inverse Kac-Ward operatorMar 12 2013Apr 30 2015We show that the critical Kac-Ward operator on isoradial graphs acts in a certain sense as the operator of s-holomorphicity, and we identify the fermionic observable for the spin Ising model as the inverse of this operator. This result is partially a ... More

Circle patterns and critical Ising modelsDec 23 2017A circle pattern is an embedding of a planar graph in which each face is inscribed in a circle. We define and prove magnetic criticality of a new family of Ising models on planar graphs whose dual is a circle pattern. Our construction includes as a special ... More

Square-free graphs are multiplicativeJan 18 2016Aug 23 2016A graph K is square-free if it contains no four-cycle as a subgraph. A graph K is multiplicative if GxH -> K implies G -> K or H -> K, for all graphs G,H. Here GxH is the tensor (or categorical) graph product and G -> K denotes the existence of a graph ... More

On Serre functor in the category of strict polynomial functorsMar 19 2016We introduce and study a Serre functor in the category ${\cal P}_d$ of strict polynomial functors over a field of positive characteristic. By using it we obtain the Poincar\'e duality formula for Ext--groups from [C3] in elementary way. We also show that ... More

Derived Kan extension for strict polynomial functorsJun 16 2011Nov 08 2014We investigate fundamental properties of adjoint functors to the precomposition functor in the category of strict polynomial functors.

On inverse powers of graphs and topological implications of Hedetniemi's conjectureDec 08 2017We consider a natural graph operation $\Omega_k$ that is a certain inverse (formally: the right adjoint) to taking the k-th power of a graph. We show that it preserves the topology (the $\mathbb{Z}_2$-homotopy type) of the box complex, a basic tool in ... More

Galois theory for H-extensionsApr 29 2013We show that there exists a Galois correspondence between subalgebras of an H-comodule algebra A over a base ring R and generalised quotients of a Hopf algebra H if both A and H are flat Mittag--Leffler modules. We also provide new criteria for subalgebras ... More

The $C^0$ estimate for the quaternionic Calabi conjectureJun 11 2019We prove the $C^0$ estimate for the quaternionic Monge-Amp\`ere equation on compact hyperK\"ahler with torsion manifolds. Our goal is to provide a simpler proof than the one presented by Alesker and Shelukhin.

Well-posedness and asymptotic behavior of a multidimensional model of morphogen transportDec 26 2011Morphogen transport is a biological process, occurring in the tissue of living organisms, which is a determining step in cell differentiation. We present rigorous analysis of a simple model of this process, which is a system coupling parabolic PDE with ... More

On inverse powers of graphs and topological implications of Hedetniemi's conjectureDec 08 2017May 13 2019We consider a natural graph operation $\Omega_k$ that is a certain inverse (formally: the right adjoint) to taking the k-th power of a graph. We show that it preserves the topology (the $\mathbb{Z}_2$-homotopy type) of the box complex, a basic tool in ... More

A model of morphogen transport in the presence of glypicans IIINov 28 2014Apr 07 2015We analyse a stationary problem for the two dimensional model of morphogen transport introduced by Hufnagel et al. The model consists of one linear elliptic PDE posed on $(-1,1)\times(0,h)$ which is coupled via a nonlinear boundary condition with a nonlinear ... More

Experimental quantum randomness generation invulnerable to the detection loopholeOct 13 2014Oct 28 2014Random numbers are essential for multiple applications, including cryptography, financial security, digital rights management and scientific simulations. However, producing random numbers from a finite state machine, such as a classical computer, is impossible. ... More

Separable Hilbert space for loop quantizationMar 12 2014Sep 16 2014We discuss, within the simplified context provided by the polymeric harmonic oscillator, a construction leading to a separable Hilbert space that preserves some of the most important features of the spectrum of the Hamiltonian operator. This construction ... More

Casimir effect for tachyonic fieldsJul 04 2003Aug 29 2003In this paper we examine Casimir effect in the case of tachyonic field, which is connected with particles with negative four-momentum square. We consider here only the case of one dimensional, scalar field. In order to describe tachyonic field, we use ... More

Algebraic approximation of analytic sets and mappingsDec 19 2007Let {X_n} be a sequence of analytic sets converging to some analytic set X in the sense of holomorphic chains. We introduce a condition which implies that every irreducible component of X is the limit of a sequence of irreducible components of the sets ... More

The relation between the quantum games, communication complexity problems and Bell inequalitiesOct 22 2007We study the relation between the quantum games, communication complexity problems and Bell inequalities. In particular we are interested in answering the question whether for every element of one of these groups there is a corresponding element in the ... More

Casimir effect in external magnetic fieldApr 13 2005Dec 19 2005In this paper we examine the Casimir effect for charged fields in presence of external magnetic field. We consider scalar field (connected with spinless particles) and the Dirac field (connected with 1/2-spin particles). In both cases we describe quantum ... More

The Ultraviolet-Far Infrared Energy Budget of the Gravitationally Lensed Lyman Break Galaxy MS1512-cB58Feb 12 2001A 2-hour service-mode SCUBA observation of the gravitationally-lensed Lyman break galaxy MS1512-cB58 resulted in a 3 sigma upper limit of 3.9 mJy at 850um. A comparison of this upper limit with values expected from rest-UV/optical measurements of extiction ... More

Remarks on normal basesOct 13 1997We prove that any Galois extension of commutative rings with normal basis and abelian Galois group of odd order has a self dual normal basis. Also we show that if S/R is an unramified extension of number rings with Galois group of odd order and $R$ is ... More

Nontrivial realization of the space-time translations in the theory of quantum fieldsSep 15 2010In standard quantum field theory, the one-particle states are classified by unitary representations of the Poincar\'e group, whereas the causal fields' classification employs the finite dimensional (non-unitary) representations of the (homogeneous) Lorentz ... More

Modified coupling procedure for the Poincaré gauge theory of gravityJun 18 2009The minimal coupling procedure, which is employed in standard Yang-Mills theories, appears to be ambiguous in the case of gravity. We propose a slight modification of this procedure, which removes the ambiguity. Our modification justifies some earlier ... More

Generalized twist deformations of Poincare and Galilei Hopf algebrasDec 09 2008The three new deformed Poincare Hopf algebras are constructed with use of twist procedure. The corresponding relativistic space-times providing the sum of canonical and Lie-algebraic type of noncommutativity are proposed. Finally, the nonrelativistic ... More

The Poincaré Gauge Theory of Gravty and the Immirzi parameterOct 27 2010The minimal coupling method proved to yield definite and correct physical predictions when applied to fundamental fermions within the framework of Yang--Mills theories of Standard Model. Similarly, the possibility of formulating gravity as the Poincar\'e ... More

F-term uplifted racetrack inflationMay 30 2010It is shown that two classes of racetrack inflation models, saddle point and inflection point ones, can be constructed in a fully supersymmetric framework with the matter field F-term as a source of supersymmetry (SUSY) breaking and uplifting. Two models ... More

Canonical, Lie-algebraic and quadratic twist deformations of Galilei groupJul 01 2008Jan 27 2009New Galilei quantum groups dual to the Hopf algebras proposed in [1] are obtained by the nonrelativistic contraction procedures. The corresponding Lie-algebraic and quadratic quantum space-times are identified with the translation sectors of considered ... More

How not to discard half of the cases in QKDAug 07 2007Aug 24 2007All known QKD protocols require the parties to discard the results when they have chosen differen bases. In this paper we show that it is not necessary. We give examples of QKD protocols that are as safe as standard ones but do not involve the discarding ... More

Twist deformations of Newton-Hooke Hopf algebrasApr 02 2009We construct five new quantum Newton-Hooke Hopf algebras with the use of Abelian twist procedure. Further we demonstrate that the corresponding deformed space-times with quantum space and classical time are periodic or expanding in time.

Quantum Information Processing with Continuous Variables and Atomic EnsemblesFeb 09 2011This thesis presents three different results in quantum information theory. The first result addresses the theoretical foundations of quantum metrology. The Heisenberg limit considered as the ultimate limit in quantum metrology sets a lower bound on how ... More

Low-dimensional quantum systemsOct 17 2018We study low-dimensional quantum systems with analytical and computational methods. Firstly, the one-dimensional extended $t$-$V$ model of fermions with interactions of a finite range is investigated. The model exhibits a phase transition between liquid ... More

Decoherence through Spin Chains: Toy ModelAug 22 2011Aug 29 2011The description of the dynamics of closed quantum systems, governed by the Schroedinger equation at first sight seems incompatible with the Lindblad equation describing open ones. By analyzing closed dynamics of a spin-1/2 chain we reconstruct exponential ... More