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

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

SIC~POVMs and Clifford groups in prime dimensions

We show that in prime dimensions not equal to three, each group covariant symmetric informationally complete positive operator valued measure (SIC~POVM) is covariant with respect to a unique Heisenberg--Weyl (HW) group. Moreover, the symmetry group of the SIC~POVM is a subgroup of the Clifford group. Hence, two SIC~POVMs covariant with respect to the HW group are unitarily or antiunitarily equivalent if and only if they are on the same orbit of the extended Clifford group. In dimension three, each group covariant SIC~POVM may be covariant with respect to three or nine HW groups, and the symmetry group of the SIC~POVM is a subgroup of at least one of the Clifford groups of these HW groups respectively. There may exist two or three orbits of equivalent SIC~POVMs for each group covariant SIC~POVM, depending on the order of its symmetry group. We then establish a complete equivalence relation among group covariant SIC~POVMs in dimension three, and classify inequivalent ones according to the geometric phases associated with fiducial vectors. Finally, we uncover additional SIC~POVMs by regrouping of the fiducial vectors from different SIC~POVMs which may or may not be on the same orbit of the extended Clifford group.Comment: 30 pages, 1 figure, section 4 revised and extended, published in J. Phys. A: Math. Theor. 43, 305305 (2010

A small-angle neutron scattering study of sodium dodecyl sulfate-poly(propylene oxide) methacrylate mixed micelles

cited By 3International audienceMixed micelle of protonated or deuterated sodium dodecyl sulfate (SDS and SDSd25, respectively) and poly(propylene oxide) methacrylate (PPOMA) are studied by small-angle neutron scattering (SANS). In all the cases the scattering curves exhibit a peak whose position changes with the composition of the system. The main parameters which characterize mixed micelles, i.e., aggregation numbers of SDS and PPOMA, geometrical dimensions of the micelles and degree of ionisation are evaluated from the analysis of the SANS curves. The position qmax of the correlation peak can be related to the average aggregation numbers of SDS-PPOMA and SDSd25-PPOMA mixed micelles. It is found that the aggregation number of SDS decreases upon increasing the weight ratio PPOMA/SDS (or SDSd25). The isotopic combination, which uses the "contrast effect" between the two micellar systems, has allowed us to determine the mixed micelle composition. Finally, the SANS curves were adjusted using the RMSA for the structure factor S(q) of charged spherical particles and the form factor P(q) of spherical core-shell particle. This analysis confirms the particular core-shell structure of the SDS-PPOMA mixed micelle, i.e., a SDS "core" micelle surrounded by the shell formed by PPOMA macromonomers. The structural parameters of mixed micelles obtained from the analysis of the SANS data are in good agreement with those determined previously by conductimetry and fluorescence studies. © 2005 Elsevier Inc. All rights reserved