A Multisection Broadband Impedance Transforming Branch-Line Hybrid

Measurements and design equations for a two section impedance transforming hybrid suitable for MMIC applications and a new method of synthesis for multisection branch-line hybrids are reported. The synthesis method allows the response to be specified either of Butterworth or Chebyshev type. Both symmetric (with equal input and output impedances) and non-symmetric (impedance transforming) designs are feasible. Starting from a given number of sections, type of response, and impedance transformation ratio and for a specified midband coupling, power division ratio, isolation or directivity ripple bandwidth, the set of constants needed for the evaluation of the reflection coefficient response is first calculated. The latter is used to define a driving point impedance of the circuit, synthesize it and obtain the branch line immittances with the use of the concept of double length unit elements (DLUE). The experimental results obtained with microstrip hybrids constructed to test the validity of the brute force optimization and the synthesized designs show very close agreement with the computed responses.Comment: 6 pages and 14 figures. Published in IEEE Transactions on Microwave Theory and Technique

NMR investigation of contextuality in a quantum harmonic oscillator via pseudospin mapping

Physical potentials are routinely approximated to harmonic potentials so as to analytically solve the system dynamics. Often it is important to know when a quantum harmonic oscillator (QHO) behaves quantum mechanically and when classically. Recently Su et. al. [Phys. Rev. A {\bf 85}, 052126 (2012)] have theoretically shown that QHO exhibits quantum contextuality (QC) for a certain set of pseudospin observables. In this work, we encode the four eigenstates of a QHO onto four Zeeman product states of a pair of spin-1/2 nuclei. Using the techniques of NMR quantum information processing, we then demonstrate the violation of a state-dependent inequality arising from the noncontextual hidden variable model, under specific experimental arrangements. We also experimentally demonstrate the violation of a state-independent inequality by thermal equilibrium states of nuclear spins, thereby assessing their quantumness.Comment: 5 Pages, 3 Figures, context dependency illustrated, error below eq. 5 correcte

Efficient Quantum State Tomography for Quantum Information Processing using a two-dimensional Fourier Transform Technique

A new method of quantum state tomography for quantum information processing is described. The method based on two-dimensional Fourier transform technique involves detection of all the off-diagonal elements of the density matrix in a two-dimensional experiment. All the diagonal elements are detected in another one-dimensional experiment. The method is efficient and applicable to a wide range of spin systems. The proposed method is explained using a 2 qubit system and demonstrated by tomographing arbitrary complex density matrices of 2 and 4 qubit systems using simulations.Comment: 11 pages and 2 figure

A Channel Coding Perspective of Collaborative Filtering

We consider the problem of collaborative filtering from a channel coding perspective. We model the underlying rating matrix as a finite alphabet matrix with block constant structure. The observations are obtained from this underlying matrix through a discrete memoryless channel with a noisy part representing noisy user behavior and an erasure part representing missing data. Moreover, the clusters over which the underlying matrix is constant are {\it unknown}. We establish a sharp threshold result for this model: if the largest cluster size is smaller than $C_1 \log(mn)$ (where the rating matrix is of size $m \times n$), then the underlying matrix cannot be recovered with any estimator, but if the smallest cluster size is larger than $C_2 \log(mn)$, then we show a polynomial time estimator with diminishing probability of error. In the case of uniform cluster size, not only the order of the threshold, but also the constant is identified.Comment: 32 pages, 1 figure, Submitted to IEEE Transactions on Information Theor