Two qubit copying machine for economical quantum eavesdropping

We study the mapping which occurs when a single qubit in an arbitrary state interacts with another qubit in a given, fixed state resulting in some unitary transformation on the two qubit system which, in effect, makes two copies of the first qubit. The general problem of the quality of the resulting copies is discussed using a special representation, a generalization of the usual Schmidt decomposition, of an arbitrary two-dimensional subspace of a tensor product of two 2-dimensional Hilbert spaces. We exhibit quantum circuits which can reproduce the results of any two qubit copying machine of this type. A simple stochastic generalization (using a ``classical'' random signal) of the copying machine is also considered. These copying machines provide simple embodiments of previously proposed optimal eavesdropping schemes for the BB84 and B92 quantum cryptography protocols.Comment: Minor changes. 26 pages RevTex including 7 PS figure

Non--Newtonian viscosity of interacting Brownian particles: comparison of theory and data

A recent first-principles approach to the non-linear rheology of dense colloidal suspensions is evaluated and compared to simulation results of sheared systems close to their glass transitions. The predicted scenario of a universal transition of the structural dynamics between yielding of glasses and non-Newtonian (shear-thinning) fluid flow appears well obeyed, and calculations within simplified models rationalize the data over variations in shear rate and viscosity of up to 3 decades.Comment: 6 pages, 2 figures; J. Phys. Condens. Matter to be published (Jan. 2003

Flow curves of colloidal dispersions close to the glass transition: Asymptotic scaling laws in a schematic model of mode coupling theory

The flow curves, viz. the curves of stationary stress under steady shearing, are obtained close to the glass transition in dense colloidal dispersions using asymptotic expansions in a schematic model of mode coupling theory. The shear thinning of the viscosity in fluid states and the yielding of glassy states is discussed. At the transition between fluid and shear-molten glass, simple and generalized Herschel-Bulkley laws are derived with power law exponents that can be computed for different particle interactions from the equilibrium structure factor.Comment: 14 pages, 14 figures, 4 tables, Eur. Phys. J. E (submitted

Quantum State Disturbance vs. Information Gain: Uncertainty Relations for Quantum Information

When an observer wants to identify a quantum state, which is known to be one of a given set of non-orthogonal states, the act of observation causes a disturbance to that state. We investigate the tradeoff between the information gain and that disturbance. This issue has important applications in quantum cryptography. The optimal detection method, for a given tolerated disturbance, is explicitly found in the case of two equiprobable non-orthogonal pure states.Comment: 20 pages, standard LaTeX, four png figures (also available from the authors: [email protected] and [email protected]

Pooling quantum states obtained by indirect measurements

We consider the pooling of quantum states when Alice and Bob both have one part of a tripartite system and, on the basis of measurements on their respective parts, each infers a quantum state for the third part S. We denote the conditioned states which Alice and Bob assign to S by alpha and beta respectively, while the unconditioned state of S is rho. The state assigned by an overseer, who has all the data available to Alice and Bob, is omega. The pooler is told only alpha, beta, and rho. We show that for certain classes of tripartite states, this information is enough for her to reconstruct omega by the formula omega \propto alpha rho^{-1} beta. Specifically, we identify two classes of states for which this pooling formula works: (i) all pure states for which the rank of rho is equal to the product of the ranks of the states of Alice's and Bob's subsystems; (ii) all mixtures of tripartite product states that are mutually orthogonal on S.Comment: Corrected a mistake regarding the scope of our original result. This version to be published in Phys. Rev. A. 6 pages, 1 figur

Influence of the pion-nucleon interaction on the collective pion flow in heavy ion reactions

We investigate the influence of the real part of the in-medium pion optical potential on the pion dynamics in intermediate energy heavy ion reactions at 1 GeV/A. For different models, i.e. a phenomenological model and the $\Delta$--hole model, a pionic potential is extracted from the dispersion relation and used in Quantum Molecular Dynamics calculations. In addition with the inelastic scattering processes we thus take care of both, real and imaginary part of the pion optical potential. A strong influence of the real pionic potential on the pion in-plane flow is observed. In general such a potential has the tendency to reduce the anticorrelation of pion and nucleon flow in non-central collisions.Comment: 12 pages Latex, 4 PS-figure

Information Tradeoff Relations for Finite-Strength Quantum Measurements

In this paper we give a new way to quantify the folklore notion that quantum measurements bring a disturbance to the system being measured. We consider two observers who initially assign identical mixed-state density operators to a two-state quantum system. The question we address is to what extent one observer can, by measurement, increase the purity of his density operator without affecting the purity of the other observer's. If there were no restrictions on the first observer's measurements, then he could carry this out trivially by measuring the initial density operator's eigenbasis. If, however, the allowed measurements are those of finite strength---i.e., those measurements strictly within the interior of the convex set of all measurements---then the issue becomes significantly more complex. We find that for a large class of such measurements the first observer's purity increases the most precisely when there is some loss of purity for the second observer. More generally the tradeoff between the two purities, when it exists, forms a monotonic relation. This tradeoff has potential application to quantum state control and feedback.Comment: 15 pages, revtex3, 3 eps figure

Optimal Universal and State-Dependent Quantum Cloning

We establish the best possible approximation to a perfect quantum cloning machine which produces two clones out of a single input. We analyze both universal and state-dependent cloners. The maximal fidelity of cloning is shown to be 5/6 for universal cloners. It can be achieved either by a special unitary evolution or by a novel teleportation scheme. We construct the optimal state-dependent cloners operating on any prescribed two non-orthogonal states, discuss their fidelities and the use of auxiliary physical resources in the process of cloning. The optimal universal cloners permit us to derive a new upper bound on the quantum capacity of the depolarizing quantum channel.Comment: 30 pages (RevTeX), 2 figures (epsf), further results and further authors added, to appear in Physical Review

Comparative simulation study of colloidal gels and glasses

Using computer simulations, we identify the mechanisms causing aggregation and structural arrest of colloidal suspensions interacting with a short-ranged attraction at moderate and high densities. Two different non-ergodicity transitions are observed. As the density is increased, a glass transition takes place, driven by excluded volume effects. In contrast, at moderate densities, gelation is approached as the strength of the attraction increases. At high density and interaction strength, both transitions merge, and a logarithmic decay in the correlation function is observed. All of these features are correctly predicted by mode coupling theory

Jamming transitions in a schematic model of suspension rheology

We study the steady-state response to applied stress in a simple scalar model of sheared colloids. Our model is based on a schematic (F2) model of the glass transition, with a memory term that depends on both stress and shear rate. For suitable parameters, we find transitions from a fluid to a nonergodic, jammed state, showing zero flow rate in an interval of applied stress. Although the jammed state is a glass, we predict that jamming transitions have an analytical structure distinct from that of the conventional mode coupling glass transition. The static jamming transition we discuss is also distinct from hydrodynamic shear thickening.Comment: 7 pages; 3 figures; improved version with added references. Accepted for publication in Europhysics Letter