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

Nonorthogonal Quantum States Maximize Classical Information Capacity

I demonstrate that, rather unexpectedly, there exist noisy quantum channels for which the optimal classical information transmission rate is achieved only by signaling alphabets consisting of nonorthogonal quantum states.Comment: 5 pages, REVTeX, mild extension of results, much improved presentation, to appear in Physical Review Letter

From non-semisimple Hopf algebras to correlation functions for logarithmic CFT

We use factorizable finite tensor categories, and specifically the representation categories of factorizable ribbon Hopf algebras H, as a laboratory for exploring bulk correlation functions in local logarithmic conformal field theories. For any ribbon Hopf algebra automorphism omega of H we present a candidate for the space of bulk fields and endow it with a natural structure of a commutative symmetric Frobenius algebra. We derive an expression for the corresponding bulk partition functions as bilinear combinations of irreducible characters; as a crucial ingredient this involves the Cartan matrix of the category. We also show how for any candidate bulk state space of the type we consider, correlation functions of bulk fields for closed oriented world sheets of any genus can be constructed that are invariant under the natural action of the relevant mapping class group.Comment: 41 pages, several figures. version 2: typos corrected, bibliography updated, introduction extended, a few minor clarifications adde

Comparable Worth in a General Equilibrium Model of the U.S. Economy

This paper presents a computable general equilibrium model that simulates the effects on employment, output, wages, and economic efficiency of introducing comparable worth into the U.S. economy. The model calculates economy-wide aggregate impacts and disaggregated results for individuals grouped by sex, marital status, and education. The effects depend on the hiring rules that would accompany comparable worth, the source of existing male-female wage differentials, the extent of coverage of comparable worth, the intra-household behavior of married couples, and demand and supply elasticities. If, after comparable worth is introduced, employers are constrained to employ men and women in historical proportions, the adverse effects on aggregate employment, output, and efficiency would be much larger than if the employment constraint is based on applicant proportions. If existing wage gaps are the result of sex differences in productivity, the adverse of facts of comparable worth are relatively large; but if they are the result of discrimination, the efficiency losses are much smaller. If only part of the economy is subject to comparable worth, the efficiency loss is reduced under the productivity gap assumption, but increased if the wage gap is the result of discrimination. The redistributive effects of comparable worth on married men and women are sensitive to assumptions about intra-household behavior and the size of the gains from marriage. By contrast, unmarried women appear to benefit from comparable worth under most sets of assumptions while unmarried men lose.