Simulating quantum operations with mixed environments

We study the physical resources required to implement general quantum operations, and provide new bounds on the minimum possible size which an environment must be in order to perform certain quantum operations. We prove that contrary to a previous conjecture, not all quantum operations on a single-qubit can be implemented with a single-qubit environment, even if that environment is initially prepared in a mixed state. We show that a mixed single-qutrit environment is sufficient to implement a special class of operations, the generalized depolarizing channels.Comment: 4 pages Revtex + 1 fig, pictures at http://stout.physics.ucla.edu/~smolin/tetrahedron .Several small correction

Hudson's Theorem for finite-dimensional quantum systems

We show that, on a Hilbert space of odd dimension, the only pure states to possess a non-negative Wigner function are stabilizer states. The Clifford group is identified as the set of unitary operations which preserve positivity. The result can be seen as a discrete version of Hudson's Theorem. Hudson established that for continuous variable systems, the Wigner function of a pure state has no negative values if and only if the state is Gaussian. Turning to mixed states, it might be surmised that only convex combinations of stabilizer states give rise to non-negative Wigner distributions. We refute this conjecture by means of a counter-example. Further, we give an axiomatic characterization which completely fixes the definition of the Wigner function and compare two approaches to stabilizer states for Hilbert spaces of prime-power dimensions. In the course of the discussion, we derive explicit formulas for the number of stabilizer codes defined on such systems.Comment: 17 pages, 3 figures; References updated. Title changed to match published version. See also quant-ph/070200

Block synchronization for quantum information

Locating the boundaries of consecutive blocks of quantum information is a fundamental building block for advanced quantum computation and quantum communication systems. We develop a coding theoretic method for properly locating boundaries of quantum information without relying on external synchronization when block synchronization is lost. The method also protects qubits from decoherence in a manner similar to conventional quantum error-correcting codes, seamlessly achieving synchronization recovery and error correction. A family of quantum codes that are simultaneously synchronizable and error-correcting is given through this approach.Comment: 7 pages, no figures, final accepted version for publication in Physical Review

Hydrophobically associating polyacrylamides and their partially hydrolyzed derivatives prepared by post-modification. 2. Properties of non-hydrolyzed polymers in pure water and brine

cited By 104International audienceDilute and semi-dilute solution properties of polyacrylamide (PAM) and its hydrophobically modified analogues (HAPAMs) in both pure water and brine were compared by means of viscometry, light scattering and fluorescence spectrometry. In dilute solution, large differences in reduced viscosity and apparent molecular weight M̄wapp of HAPAMs were found between pure water and 0.1 M NaCl solutions, while no significant differences were observed for PAM. In addition, in pure water, intrinsic viscosity and M̄wapp of HAPAMs are higher than those of PAM. In semi dilute regime, with increasing salinity, the reduced viscosity of PAM remains almost unchanged, whereas enhanced viscosity was observed for the HAPAM polymers in both monovalent and divalent cation aqueous environment. HAPAM solutions behave as classical shear-thinning fluid in pure water, whereas addition of NaCl induces shear-thickening response for these polymers. The experimental results are interpreted in terms of the hydrophobe distribution and its influence on the formation of intra- and intermolecular associations. The differences between the behaviors described in this paper and those usually obtained with HAPAMs characterized by a blocky hydrophobe distribution are discussed. © 2005 Elsevier Ltd. All rights reserved