Mach-Zehnder interferometer is a common device in quantum phase estimation and the photon losses in it are an important issue for achieving a high phase accuracy. Here we thoroughly discuss the precision limit of the phase in the Mach-Zehnder interfe
rometer with a coherent state and a superposition of coherent states as input states. By providing a general analytical expression of quantum Fisher information, the phase-matching condition and optimal initial parity are given. Especially, in the photon loss scenario, the sensitivity behaviors are analyzed and specific strategies are provided to restore the phase accuracies for symmetric and asymmetric losses.
Top-k query processing finds a list of k results that have largest scores w.r.t the user given query, with the assumption that all the k results are independent to each other. In practice, some of the top-k results returned can be very similar to eac
h other. As a result some of the top-k results returned are redundant. In the literature, diversified top-k search has been studied to return k results that take both score and diversity into consideration. Most existing solutions on diversified top-k search assume that scores of all the search results are given, and some works solve the diversity problem on a specific problem and can hardly be extended to general cases. In this paper, we study the diversified top-k search problem. We define a general diversified top-k search problem that only considers the similarity of the search results themselves. We propose a framework, such that most existing solutions for top-k query processing can be extended easily to handle diversified top-k search, by simply applying three new functions, a sufficient stop condition sufficient(), a necessary stop condition necessary(), and an algorithm for diversified top-k search on the current set of generated results, div-search-current(). We propose three new algorithms, namely, div-astar, div-dp, and div-cut to solve the div-search-current() problem. div-astar is an A* based algorithm, div-dp is an algorithm that decomposes the results into components which are searched using div-astar independently and combined using dynamic programming. div-cut further decomposes the current set of generated results using cut points and combines the results using sophisticated operations. We conducted extensive performance studies using two real datasets, enwiki and reuters. Our div-cut algorithm finds the optimal solution for diversified top-k search problem in seconds even for k as large as 2,000.
We report the first temperature dependent phonon transport measurements in suspended Cu-CVD single layer graphene (SLG) from 15K to 380K using microfabricated suspended devices. The thermal conductance per unit cross section $sigma$/A increases with
temperature and exhibits a peak near T~280K ($pm$10K) due to the Umklapp process. At low temperatures (T<140K), the temperature dependent thermal conductivity scales as ~T^{1.5}, suggesting that the main contribution to thermal conductance arises from flexural acoustic (ZA) phonons in suspended SLG. The $sigma$/A reaches a high value of 1.7$times10^5 T^{1.5}$ W/m^2K, which is approaching the expected ballistic phonon thermal conductance for two-dimensional graphene sheets. Our results not only clarify the ambiguity in the thermal conductance, but also demonstrate the potential of Cu-CVD graphene for heat related applications.
