Generating qudits with d=3,4 encoded on two-photon states

We present an experimental method to engineer arbitrary pure states of qudits with d=3,4 using linear optics and a single nonlinear crystal.Comment: 4 pages, 1 eps figure. Minor changes. The title has been changed for publication on Physical Review

Write Channel Model for Bit-Patterned Media Recording

We propose a new write channel model for bit-patterned media recording that reflects the data dependence of write synchronization errors. It is shown that this model accommodates both substitution-like errors and insertion-deletion errors whose statistics are determined by an underlying channel state process. We study information theoretic properties of the write channel model, including the capacity, symmetric information rate, Markov-1 rate and the zero-error capacity.Comment: 11 pages, 12 figures, journa

Qubits in phase space: Wigner function approach to quantum error correction and the mean king problem

We analyze and further develop a new method to represent the quantum state of a system of $n$ qubits in a phase space grid of $N\times N$ points (where $N=2^n$). The method, which was recently proposed by Wootters and co--workers (Gibbons {\it et al.}, quant-ph/0401155), is based on the use of the elements of the finite field $GF(2^n)$ to label the phase space axes. We present a self--contained overview of the method, we give new insights on some of its features and we apply it to investigate problems which are of interest for quantum information theory: We analyze the phase space representation of stabilizer states and quantum error correction codes and present a phase space solution to the so--called ``mean king problem''.Comment: 18 pages, 16 figures; typos fixed, some minor corrections, figures of the circuits were change

Mutually Unbiased Bases and Trinary Operator Sets for N Qutrits

A complete orthonormal basis of N-qutrit unitary operators drawn from the Pauli Group consists of the identity and 9^N-1 traceless operators. The traceless ones partition into 3^N+1 maximally commuting subsets (MCS's) of 3^N-1 operators each, whose joint eigenbases are mutually unbiased. We prove that Pauli factor groups of order 3^N are isomorphic to all MCS's, and show how this result applies in specific cases. For two qutrits, the 80 traceless operators partition into 10 MCS's. We prove that 4 of the corresponding basis sets must be separable, while 6 must be totally entangled (and Bell-like). For three qutrits, 728 operators partition into 28 MCS's with less rigid structure allowing for the coexistence of separable, partially-entangled, and totally entangled (GHZ-like) bases. However, a minimum of 16 GHZ-like bases must occur. Every basis state is described by an N-digit trinary number consisting of the eigenvalues of N observables constructed from the corresponding MCS.Comment: LaTeX, 10 pages, 2 references adde