Quantum State Transfer in Engineered Spin Chain under Influence of Spatially Distributed Environment

It has been shown that a quantum state could be perfectly transferred via a spin chain with engineered ``always-on interaction". In this paper, we study a more realistic problem for such a quantum state transfer (QST) protocol, how the efficacy of QST is reduced by the quantum decoherence induced by a spatially distributed environment. Here, the environment is universally modeled as a bath of fermions located in different positions. By making use of the irreducible tensor method in angular momentum theory, we investigate the effect of environment on the efficiency of QST for both cases at zero and finite temperatures. We not onlyshow the generic exponential decay of QST efficiency as the number of sites increase, but also find some counterintuitive effect, the QST can be enhanced as temperature increases in some cases.     

The Tensors of the Averaged Relative Energy–Momentum and Angular Momentum in General Relativity and Some of Their Applications

There exist different kinds of averaging of the differences of the energy–momentum and angular momentum in normal coordinates NC(P) which give tensorial quantities. The obtained averaged quantities are equivalent mathematically because they differ only by constant scalar dimensional factors. One of these averaging was used in our papers [J. Garecki, Rep. Math. Phys. 33, 57 (1993); Int. J. Theor. Phys. 35, 2195 (1996); Rep. Math. Phys. 40, 485 (1997); J. Math. Phys. 40, 4035 (1999); Rep. Math. Phys. 43, 397 (1999); Rep. Math. Phys. 44, 95 (1999); Ann. Phys. (Leipzig) 11, 441 (2002); M.P. Dabrowski and J. Garecki, Class. Quantum. Grar. 19, 1 (2002)] giving the canonical superenergy and angular supermomentum tensors. In this paper we present another averaging of the differences of the energy–momentum and angular momentum which gives tensorial quantities with proper dimensions of the energy–momentum and angular momentum densities. We have called these tensorial quantities “the averaged relative energy–momentum and angular momentum tensors”. These tensors are very closely related to the canonical superenergy and angular supermomentum tensors and they depend on some fundamental length L > 0. The averaged relative energy–momentum and angular momentum tensors of the gravitational field obtained in the paper can be applied, like the canonical superenergy and angular supermomentum tensors, to coordinate independent analysis (local and in special cases also global) of this field. Up to now we have applied the averaged relative energy–momentum tensors to analyze vacuum gravitational energy and momentum and to analyze energy and momentum of the Friedman (and also more general, only homogeneous) universes. The obtained results are interesting, e.g., the averaged relative energy density is positive definite for the all Friedman and other universes which have been considered in this paper.      

Fractional Spin of System with Chern–Simons Term Coupled to Polaron

The fractional spin of a system with Chern–Simons (CS) term coupled to a polaron at the quantum level is studied. The Faddeev–Senjanovic (FS) scheme for path-integral quantization of constrained Hamiltonian systems is applied. The quantal conserved angular momentum and the fractional spin at the quantum level of this system are presented based on the quantal Noether theorem. The fractional spin is also presented for the system with Maxwell kinetic term.     

Would-Be Local Fields

General quantum field theory is formulated for the case when the Wightman distributions can grow in momentum space as the exponential of a covariant polynomial. Appropriate spaces of test functions are introduced, and it is shown that the vacuumexpectation values can be written in terms of various associated tempered distributions, which enjoy some of the properties of ordinary Wightman distributions; in particular, they can be represented as boundary values of functions holomorphic in the usual extended tubes. Notions of locality for the tempered distributions can be introduced, which are sufficient to imply the PCT theorem and theorems on the connection between spin and statistic for the non-tempered fields. It is shown how a Haag-Ruelle theory of asymptotic states and fields may be set up. A possible line of generalisation is illustrated by the special example of fields of the type χ (□) A (x), where A is a tempered field, and χ an entire analytic function of finite exponential order.     

Some remarks concerning Nambu mechanics

The quantum probability flux of a particle integrated over time and a distant surface gives the probability for the particle crossing that surface at some time. We prove the free flux-across-surfaces theorem, which was conjectured by Combes, Newton and Shtokhamer (Phys. Rev. D. 11 (1975), 366), and which relates the integrated quantum flux to the usual quantum mechanical formula for the cross-section. The integrated quantum flux is equal to the probability of outward crossings of surfaces by Bohmian trajectories in the scattering regime.     

Quantum Symmetry of a Chern–Simons System Coupled to a Polaron

The property of fractional spin of the system with Chern–Simons (CS) term coupled to polaron at the quantum level is studied. According to the rule of path integral quantization for constrained Hamiltonian system in Faddeev–Senjanovic (FS) scheme, this system is quantized. Based on the quantal Noether theorem, the quantal conserved angular momentum and the fractional spin at the quantum level of this system is presented. The fractional spin is also presented in the system including Maxwell kinetic term.     

Investigation of continuous-time quantum walk by using Krylov subspace-Lanczos algorithm

In papers [Jafarizadehn and Salimi, Ann. Phys. 322, 1005 (2007) and J. Phys. A: Math. Gen. 39, 13295 (2006)], the amplitudes of continuous-time quantum walk (CTQW) on graphs possessing quantum decomposition (QD graphs) have been calculated by a new method based on spectral distribution associated with their adjacency matrix. Here in this paper, it is shown that the CTQW on any arbitrary graph can be investigated by spectral analysis method, simply by using Krylov subspace-Lanczos algorithm to generate orthonormal bases of Hilbert space of quantum walk isomorphic to orthogonal polynomials. Also new type of graphs possessing generalized quantum decomposition (GQD) have been introduced, where this is achieved simply by relaxing some of the constrains imposed on QD graphs and it is shown that both in QD and GQD graphs, the unit vectors of strata are identical with the orthonormal basis produced by Lanczos algorithm. Moreover, it is shown that probability amplitude of observing the walk at a given vertex is proportional to its coefficient in the corresponding unit vector of its stratum, and it can be written in terms of the amplitude of its stratum. The capability of Lanczos-based algorithm for evaluation of CTQW on graphs (GQD or non-QD types), has been tested by calculating the probability amplitudes of quantum walk on some interesting finite (infinite) graph of GQD type and finite (infinite) path graph of non-GQD type, where the asymptotic behavior of the probability amplitudes at the limit of the large number of vertices, are in agreement with those of central limit theorem of [Phys. Rev. E 72, 026113 (2005)]. At the end, some applications of the method such as implementation of quantum search algorithms, calculating the resistance between two nodes in regular networks and applications in solid state and condensed matter physics, have been discussed, where in all of them, the Lanczos algorithm, reduces the Hilbert space to some smaller subspaces and the problem is investigated in the subspace with maximal dimension.     

Quantum Hypothesis Testing for Gaussian States: Quantum Analogues of χ2, t-, and F-Tests

We consider quantum counterparts of testing problems for which the optimal tests are the χ², t-, and F-tests. These quantum counterparts are formulated as quantum hypothesis testing problems concerning Gaussian state families, and they contain nuisance parameters, which have group symmetry. The quantum Hunt-Stein theorem removes some of these nuisance parameters, but other difficulties remain. In order to remove them, we combine the quantum Hunt-Stein theorem and other reduction methods to establish a general reduction theorem that reduces a complicated quantum hypothesis testing problem to a fundamental quantum hypothesis testing problem. Using these methods, we derive quantum counterparts of the χ², t-, and F-tests as optimal tests in the respective settings.     

Magnetoexcitons in type-II quantum dots

The ground state of a spatially indirect exciton in type-II quantum dots with a short-range potential acquires nonzero angular momentum in the presence of a magnetic field oriented perpendicular to the plane of the system. The critical magnetic field of the transition to a ground state with nonzero angular momentum depends on the radius of the quantum dot. Such a transition can be observed as quenching of luminescence by a magnetic field in quantum dots of the GaSb/GaAs system, for example. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 8, 634–637 (25 October 1998)     

Quantum regime for dielectric Cherenkov radiation and graphene surface plasmons

In this article, we propose a quantum regime for Cherenkov free-electron laser (CFEL) and surface plasmon polaritons (SPPs) excited in dielectric and multilayer graphene waveguides, respectively. This quantum regime is realized when the momentum spread induced in the interaction is smaller than the photon recoil. The discrete momentum exchange characterizing this interaction yields a significantly narrow single emission line. To determine the condition of the quantum regime, we derive an expression for the gain in the Cherenkov effect using a quantum mechanical treatment. It is assumed that the effective spread in momentum is due to the finite interaction length L (or the propagation length in the case of SPPs). For both cases, CFEL and SPPs, the effects of electron beam and waveguide parameters on the possibility of the quantum regime are studied. We conclude that the quantum regime can be basically verified at low electron beam energy (<40 keV) and at emission wavelengths in the near infrared range (<5 μm) when L is in the order of millimeters. In the case of SPPs, we also show that the feasibility to realize quantum SPPs is enhanced by increasing the chemical potential and number of graphene layers.     

Exact calculation,using angular momentum,of combined Zeeman and quadrupolar interactions in NMR

The NMR of nuclei with spins greater than ½ is often strongly influenced by the quadrupole interaction. This combination of Zeeman and quadrupole terms can usually be treated using perturbation theory, but an exact calculation is also needed. We explain an exact approach that eliminates the evaluation of commutators of complicated operators. Instead, the calculation is based on matrix elements of the Liouvillian, the commutator with the Hamiltonian. The spectrum can then be calculated directly from the eigenvectors and eigenvalues of the Liouvillian. With the aid of angular momentum methods, it can be shown that the quadupole interaction for spin I is fully determined by only (2I ?1) reduced matrix elements—for spin 3/2, this means only two quantities. The exact nature of the various basis operators is not needed, since the calculation only needs the angular momentum quantum numbers. The full Liouvillian matrix can be calculated from selection rules and the Wigner-Eckart theorem. Furthermore, we present an expression for these reduced matrix elements which is valid for any spin. This theory covers the whole range from quadrupole-perturbed NMR spectra to Zeeman-perturbed nuclear quadrupole resonance.     

Analytical study of bound states in graphene nanoribbons and carbon nanotubes: The variable phase method and the relativistic Levinson theorem

The problem of localized states in 1D systems with a relativistic spectrum, namely, graphene stripes and carbon nanotubes, is studied analytically. The bound state as a superposition of two chiral states is completely described by their relative phase, which is the foundation of the variable phase method (VPM) developed herein. Based on our VPM, we formulate and prove the relativistic Levinson theorem. The problem of bound states can be reduced to the analysis of closed trajectories of some vector field. Remarkably, the Levinson theorem appears as the Poincaré index theorem for these closed trajectories. The VPM equation is also reduced to the nonrelativistic and semiclassical limits. The limit of a small momentum p_y of transverse quantization is applicable to an arbitrary integrable potential. In this case, a single confined mode is predicted.     

非Abel Chern-Simons理论中量子水平的分数自旋性质

与经典水平下的研究不同，研究了（2＋1）维含非Abel Chern-Simons 项的非线性σ模 型量子水平的分数自旋性质.根据约束Hamilton系统的Faddeev-Senjanovic(FS)路径积分量 子化方案,对该系统进行量子化，由量子Noether定理给出了量子守恒角动量，说明了在量子 水平上该系统仍具有分数自旋的性质. 关键词： 约束Hamilton系统 分数自旋 O(3)非线性σ模型     

Ultradistributions and quantum fields: Fourier-Laplace transforms and boundary values of analytic functions

The distribution theory is the mathematical framework of the axiomatic quantum field theory of A.S. Wightman. The axioms are satisfied in the case of the free field and in some non-trivial models studied in the constructive quantum field theory introduced by J. Glimm and A. Jaffe (two and three dimensions). No non-trivial example in four dimensions is known. The vacuum expectation values in the Wightman theory can have at most polynomial increase in momentum space. A. Jaffe has extended the axioms in order to allow non-polynomial increase in momentum space. In this paper we discuss the ultradistribution framework which is the most general framework for Jaffe fields (strictly localizable fields). The ultradistributions have been introduced by A. Beurling, G. Björck and independently by C. Roumieu. Ultradistribution theory is a natural generalization of the distribution theory. We study the Fourier-Laplace transform of ultradistributions, extenting results of A. Jaffe [8,9] in several directions. A Bochner-Schwartz theorem for ultradistributions is also shown to be valid. We expect ultradistribution theory to play a role in constructive quantum field theory.     

Quantum Communication Complexity

Can quantum communication be more efficient than its classical counterpart? Holevo's theorem rules out the possibility of communicating more than n bits of classical information by the transmission of n quantum bits—unless the two parties are entangled, in which case twice as many classical bits can be communicated but no more. In apparent contradiction, there are distributed computational tasks for which quantum communication cannot be simulated efficiently by classical means. In some cases, the effect of transmitting quantum bits cannot be achieved classically short of transmitting an exponentially larger number of bits. In a similar vein, can entanglement be used to save on classical communication? It is well known that entanglement on its own is useless for the transmission of information. Yet, there are distributed tasks that cannot be accomplished at all in a classical world when communication is not allowed, but that become possible if the non-communicating parties share prior entanglement. This leads to the question of how expensive it is, in terms of classical communication, to provide an exact simulation of the spooky power of entanglement.     

Logical Pre- and Post-Selection Paradoxes,Measurement-Disturbance and Contextuality

Many seemingly paradoxical effects are known in the predictions for outcomes of measurements made on pre- and post-selected quantum systems. A class of such effects, which we call ‘`logical pre- and post-selection paradoxes,’' bear a striking resemblance to proofs of the Bell-Kochen-Specker theorem, which suggests that they demonstrate the contextuality of quantum mechanics. Despite the apparent similarity, we show that such effects can occur in noncontextual hidden variable theories, provided measurements are allowed to disturb the values of the hidden variables. PACS: 03.65.Ta.     

Testing the validity of the Ehrenfest theorem beyond simple static systems: Caldirola–Kanai oscillator driven by a time-dependent force

The relationship between quantum mechanics and classical mechanics is investigated by taking a Gaussian-type wave packet as a solution of the Schr o¨dinger equation for the Caldirola–Kanai oscillator driven by a sinusoidal force. For this time-dependent system, quantum properties are studied by using the invariant theory of Lewis and Riesenfeld. In particular,we analyze time behaviors of quantum expectation values of position and momentum variables and compare them to those of the counterpart classical ones. Based on this, we check whether the Ehrenfest theorem which was originally developed in static quantum systems can be extended to such time-varying systems without problems.     

Environmental recording of the angular momentum in quantum mechanics

We discuss the coupling of a quantum system through the angular momentum to the reservoir of quantum harmonic oscillators. In classical mechanics an observation of the oscillator trajectories allows one to determine the system's angular momentum. We discuss the quantum dynamics of the model. We show that the model of an observation of environmental coordinates can be related to some models of angular momentum measurement based on a stochastic Schrödinger equation.     

Interpretations of Quantum Mechanics in Terms of Beable Algebras

In terms of beable algebras Halvorson and Clifton [International Journal of Theoretical Physics 38 (1999) 2441–2484] generalized the uniqueness theorem (Studies in History and Philosophy of Modern Physics 27 (1996) 181–219] which characterizes interpretations of quantum mechanics by preferred observables. We examine whether dispersion-free states on beable algebras in the generalized uniqueness theorem can be regarded as truth-value assignments in the case where a preferred observable is the set of all spectral projections of a density operator, and in the case where a preferred observable is the set of all spectral projections of the position operator as well.