A number of classical algorithms are based on random walks on graphs. It is hoped that recently defined quantum walks can serve as the basis for quantum algorithms that will faster than the… (More)

We show how to construct discrete-time quantum walks on directed, Eulerian graphs. These graphs have tails on which the particle making the walk propagates freely, and this makes it possible to… (More)

We show how to optimally unambiguously discriminate between two subspaces of a Hilbert space. In particular we suppose that we are given a quantum system in either the state |ψ1〉, where |ψ1〉 can be… (More)

This article explores Japanese attitudes about brain death and organ transplantation. First, ancient burial customs and death-related rituals associated with Shinto and Buddhism are examined. Next,… (More)

We discuss sequential unambiguous state-discrimination measurements performed on the same qubit. Alice prepares a qubit in one of two possible states. The qubit is first sent to Bob, who measures it,… (More)

Our “jungle gyms” are 2–dimensional differentiable manifolds M , with preferred Riemannian metrics, associated to graphs. Our interest is in proving that the validity of the Neumann–Cheeger… (More)

The inequality (1) is usually referred to as λ–transience of M. See [5]; also see [3]. We add that in [3] it is shown that, in general, eλtp always has a limit when t ↑ +∞, which either is… (More)

We solve the long-standing problem of making n perfect clones from m copies of one of two known pure states with minimum failure probability in the general case where the known states have arbitrary… (More)

A complete geometric view is presented for the optimal unambiguous discrimination among N > 2 pure states. A single intuitive picture contains all aspects of the problem: linear independence of the… (More)