Quantum Random Walks and Piecewise Deterministic EvolutionsBlanchard, Ph
doi: 10.1103/PhysRevLett.92.120601pmid: 15089658
In the continuous space and time limit, we show that the probability density to find the quantum random walk (QRW) driven by the Hadamard “coin” solves a hyperbolic evolution equation similar to the one obtained for a random two-velocity evolution with spatially inhomogeneous transition rates between the velocity states. In spite of the presence of a nonlinear drift term, it is remarkable that the QRW position can easily be described in simple analytical terms. This allows us to derive the quadratic time dependence of the variance typical for the QRW.
Determining a Quantum State by Means of a Single ApparatusAllahverdyan, A. E; Balian, R. E; Nieuwenhuizen, Th. M
doi: 10.1103/PhysRevLett.92.120402pmid: 15089654
The unknown state ρ ^ of a quantum system S is determined by letting it interact with an auxiliary system A , the initial state of which is known. A one-to-one mapping can thus be realized between the density matrix ρ ^ and the probabilities of the occurrence of the eigenvalues of a single and factorized observable of S + A , so that ρ ^ can be determined by repeated measurements using a single apparatus. If S and A are spins, it suffices to measure simultaneously their z components after a controlled interaction. The most robust setups are determined in this case for an initially pure or a completely disordered state of A . They involve an Ising or anisotropic Heisenberg coupling and an external field.