Showing papers on "Quantum channel published in 1994"

Deformed oscillator algebras for two-dimensional quantum superintegrable systems.

Abstract: Quantum superintegrable systems in two dimensions are obtained from their classical counterparts, the quantum integrals of motion being obtained from the corresponding classical integrals by a symmetrization procedure. For each quantum superintegrable systema deformed oscillator algebra, characterized by a structure function specific for each system, is constructed, the generators of the algebra being functions of the quantum integrals of motion. The energy eigenvalues corresponding to a state with finite dimensional degeneracy can then be obtained in an economical way from solving a system of two equations satisfied by the structure function, the results being in agreement to the ones obtained from the solution of the relevant Schrodinger equation. The method shows how quantum algebraic techniques can simplify the study of quantum superintegrable systems, especially in two dimensions.

Key distribution in a multiple access network using quantum cryptography

Abstract: In a method of quantum cryptography, a transmitter (T) communicates on a quantum channel with several receivers (R1-R3). The receivers are located on different branches of a common communications network. The method establishes a different respective secret key for each receiver. A timing pulse may be transmitted from the transmitter to the receivers to synchronise the receivers prior to a transmission on a quantum channel. The quantum channel may be multiplexed and transmitted concurrently with classical multi-photon transmissions on the network.

System and method for quantum cryptography

Abstract: In a method of communication using quantum cryptography an encryption alphabet is used for coding signals for transmission on a quantum channel. The encryption alphabet comprises pairs of operators applied successively to single-photon signals transmitted onto the quantum channel with a pre-determined delay between them. When the signals are detected, the different signals of each pair are split according to their encoded state and directed to different detectors via paths giving a differential delay. The delay is substantially complementary to the original pre-determined delay. Coincidence detection is employed at the detectors to eliminate spurious detection counts.

Quantum, classical and intermediate: An illustrative example

Abstract: We present a model that allows one to build structures that evolve continuously from classical to quantum, and we study the intermediate situations, giving rise to structures that are neither classical nor quantum. We construct the closure structure corresponding to the collection of eigenstate sets of these intermediate situations, and demonstrate how the superposition principle disappears during the transition from quantum to classical. We investigate the validity of the axioms of quantum mechanics for the intermediate situations.

Quantum homogeneous spaces, duality, and quantum 2-spheres

Abstract: For a quantum groupG the notion of quantum homogeneousG-space is defined. Two methods to construct such spaces are discussed. The first one makes use of quantum subgroups, the second more general one is based upon the notion of infinitesimal invariance with respect to certain two-sided coideals in the Hopf algebra dual to the Hopf algebra ofG. These methods are applied to the quantum group SU(2). As two-sided coideals we take the subspaces spanned by twisted primitive elements in the sl(2) quantized universal enveloping algebra. A one-parameter series of mutually non-isomorphic quantum 2-spheres is obtained, together with the spectral decomposition of the corresponding right regular representation of quantum SU(2). The link with the quantum spheres defined by Podleś is established.

Ensemble-dependent bounds for accessible information in quantum mechanics.

Abstract: We simplify the derivation of the Holevo upper bound on the maximum information extractable from a quantum communication channel. This simplification leads to upper and lower bounds for binary channels, both of which depend explicitly on the message ensemble.

Fundamental limits upon the measurement of state vectors.

Abstract: Using the Shannon information theory and the Bayesian methodology for inverting quantum data [K. R. W. Jones, Ann. Phys. (N.Y.) 207, 140 (1991)] we prove a fundamental bound upon the measurability of finite-dimensional quantum states. To do so we imagine a thought experiment for the quantum communication of a pure state , known to one experimenter, to his colleague via the transmission of N identical copies of it in the limit of zero temperature. Initial information available to the second experimenter is merely that of the allowed manifold of superpositions upon which the chosen may lie. Her efforts to determine it, in an optimal way, subject to the fundamental constraints imposed by quantum noise, define a statistical uncertainty principle. This limits the accuracy with which can be measured according to the number N of transmitted copies. The general result is illustrated in the physically realizable case of polarized photons.

Quantum Diffusion, Measurement and Filtering I

Abstract: A brief presentation is given of the basic concepts in quantum probability theory in analogy to the classical ones, as well as the necessary information about noncommutative stochastic integration and its explicit representation in the Fock space.Algebraic differential relations that define quantum diffusion motion with nondemolition observation are derived. In the Markov case we obtain the stochastic equation of quantum diffusion filtering which is analogous to the Zakai equation of classical nonlinear filtering.A quantum linear stochastic model with continuous observation is given for which this equation is reduced to a linear stochastic quantum filtering equation of Kalman-Busi type and to the operator Riccati equation. We also consider an example of observing the coordinate of a free quantum particle, for which the solution of a stationary quantum filtering problem is obtained.

Reduction of Quantum Entropy by Reversible Extraction of Classical Information

Abstract: We inquire under what conditions some of the information in a quantum signal source, namely a set of pure states ψa emitted with probabilities p a, can be extracted in classical form by a measurement leaving the quantum system with less entropy than it had before, but retaining the ability to regenerate the source state exactly from the classical measurement result and the after-measurement state of the quantum system. We show that this can be done if and only if the source states ψa fall into two or more mutually orthogonal subsets.

Quantum transmitting boundary method in a magnetic field

Abstract: A numerical algorithm for the solution of the two‐dimensional effective‐mass Schrodinger equation for current‐carrying states, the quantum transmitting boundary method, is extended to magnetotransport problems where a magnetic field is applied Boundary conditions appropriate for such states are developed and a solution algorithm based on the finite‐element method is constructed The algorithm is valid for general device shapes, general potential profiles, and multiple leads of general orientations The technique is applied to a quantum channel with a single scatterer, an antidot, in the channel Magnetic quasibound states (MQBS) are formed around the scatterer and MQBS‐induced resonant reflection is observed

On the relation between classical and quantum cosmology in a two-dimensional dilaton-gravity model

Abstract: We analyse the classical and quantum theory of a scalar field interacting with gravitation in two dimensions. We describe a class of analytic solutions to the Wheeler--DeWitt equation from which we are able to synthesize states that give prominence to a set of classical cosmologies. These states relate in a remarkable way to the general solution of the classical field equations. We express these relations, without approximation, in terms of a metric and a closed form on the domain of quantum states.

Electron scattering in an arbitrarily bent planar quantum channel

Abstract: The bend region of a two-dimensional quantum channel of constant width is shown to generate a well-type effective potential in the problem of electron wave scattering. For narrow channels the longitudinal modes of electron propagation should be considered as approximately independent. In the one-mode approximation the coefficient of electron reflection is calculated and its non-monotonic dependence on the incident electron momentum and the channel bend angle is determined. The local maxima in the reflection coefficient decrease exponentially with increasing electron momentum and increase with increasing channel bend.

Communication Using Quantum States

Abstract: Standard information theory deals with alphabets and their transmission over communication channels. Here we examine the novel features introduced by allowing the alphabet symbols to be quantum states. A simple device for communication of one bit of information is discussed and the transition between quantum and classical behaviour is highlighted. A further level of complexity is introduced when we allow the communication to take place with quantum-correlated states. We show, by the simple expedient of constructing a suitable local hidden variable theory, that many of the novel features of such communication are compatible with the concept of local realism. We introduce a convenient parameter for characterizing the contribution of the quantum entanglement to the communication.

Q-deformed quantum cryptography

Abstract: In this paper we present an application of the q-deformed quantum mechanics on quantum cryptography and possibility for a new eavesdropping strategy

The nonlinear structure on the general quantum hyperplanes: the quantum hypersurfaces and the nonlinear realizations of the quantum groups

Abstract: In this paper we prove that by the use of an extended algebra the nonlinear transformations of the general quantum hyperplanes can be obtained. The images of this transformation and its linear part, which are two quantum hyperspaces, can be interpreted as a quantum hypersurface and its quantum tangent hyperplane, respectively. The quantum group concerned is nonlinearly realized on this quantum hypersurface. The concrete results of GLq(N), as an example, are calculated.

Conditional quantum channel and its certain construction

Abstract: This paper presents a sophisticated concept and a construction method of conditional linear isometric operators which represent optical information channels belonging to a kind of non-unitary process -- the conditional quantum channel. The conditional linear isometric representations of quantum channel are studied as an example in quantum optics. It is shown that the concept of conditional linear isometry is very natural.

Infinite Abelian Subalgebras in Quantum W-Algebras: An Elementary Proof

Abstract: An elementary proof is given for the existence of infinite dimensional abelian subalgebras in quantum W-algebras. In suitable realizations these subalgebras define the conserved charges of various quantum integrable systems. We consider all principle W-algebras associated with the simple Lie algebras. The proof is based on the more general result that for a class of vertex operators the quantum operators are related to their classical counterparts by an equivalence transformation.

Quantum 1/f Noise in High Technology Applications Including Ultrasmall Structures and Devices

Abstract: : The present report brings a final answer to the question on the nature of fundamental i/f noise and its ubiquity. A sufficient criterion for a 1/f spectrum in arbitrary chaotic nonlinear systems is derived for the first time. This criterion guarantees a 1/f spectrum for nonlinear systems which also satisfy a condition of mathematical homogeneity. Briefly stated, nonlinearity + homogeneity = 1/f noise. The criterion results because the 1/f spectrum reproduces itself in a self-convolution. Among the five examples to which the criterion is applied is also quantum electrodynamics (QED). resulting in quantum 1/f noise as a fundamental form of quantum chaos. Nonlinearity of the system of a charged particle and its field, plus the basic homogeneity of physical equations causes the criterion to predict the quantum 1/f effect. The simple universal quantum 1/f formula is applied to infrared detectors and yields quantum 1/f noise in the dark current, but not in the photogenerated current. The fractal dimension of quantum 1/f noise is determined on the basis of its quantum chaos definition and is obtained theoretically as a function of bandwidth in a simple model by applying the Grassberger- Procaccia-Takens algorithm to the quantum 1/f theory. The quantum 1/f effect is successfully applied to quartz resonators and bipolar junction transistors. Finally, the quantum 1/f mobility fluctuations are calculated in silicon and the coherent quantum 1/f effect is derived for the first time from a new QED propagator with branch-point singularity. This opens the way to better bridging the gap between coherent and conventional quantum 1/f noise in small and ultrasmall devices.

$Q$-Meromorphic Functions, Quantums sets and Homomorphisms of the Quantum Plane

Abstract: In this paper which is the completion of [1], we construct the $A_0(q)$-algebra of $Q$-meromorphic functions on the quantum plane. This is the largest non-commutative, associative, $A_0(q)$-algebra of functions constructed on the quantum plane. We also define the notion of quantum subsets of R$^2$ which is a generalization of the notion of quantum disc and charactrize some of their properties. In the end we study the $Q$-homomorphisms of the quantum plane.

Classical r-matrices and construction of quantum groups

Abstract: A problem of constructing quantum groups from classical r-matrices is discussed.

Quantum matrices inN dimensions

Abstract: We obtain the commutation relation between rows and columns ofN ×N quantum matrices. We derive the quantum determinant and discuss its property in terms of the q-deformed Levi-Civita symbol. We find the inverse and trace ofN×N quantum matrices. Finally we discuss the q-deformed complexification of the quantum matrices.