How to mix

How to Mix a Density Matrix

A given density matrix may be represented in many ways as a mixture of pure states. We show how any density matrix may be realized as a uniform ensemble. It has been conjectured that one may realize all probability distributions that are majorized by the vector of eigenvalues of the density matrix. We show that if the states in the ensemble are assumed to be distinct then it is not true, but a ...

How Many Shuffles to Mix a Deck?

A simple probabilistic model is devised to determine the number of shuffles required for the bottom card of a deck to become uniformly distributed with a specified tolerance. This number is a lower bound on the number of shuffles needed for the entire deck to be randomly mixed. We wish to find a lower bound on the number of riffle shuffles required to mix a deck of k cards. In such a shuffle, t...

The Vector Space of Convex Curves: How to Mix Shapes

We present a novel, log-radius profile representation for convex curves and define a new operation for combining the shape features of curves. Unlike the standard, angle profile-based methods, this operation accurately combines the shape features in a visually intuitive manner. This method have implications in shape analysis as well as in investigating how the brain perceives and generates curv...

How to Break , Fix , and Optimize \ Optimisti Mix

How to break a practical MIX anddesign a new

A MIX net takes a list of ciphertexts (c1; ; cN) and outputs a permuted list of the plaintexts (m1; ; mN) without revealing the relationship between (c1; ; cN) and (m1; ; mN). This paper rst shows that the Jakobsson's MIX net of Eurocrypt'98, which was believed to be resilient and very eecient, is broken. We next propose an eecient t-resilient MIX net with O(t 2) servers in which the cost of ea...