4,018 research outputs found
A Study on Edge-Set Graphs of Certain Graphs
Let be a simple connected graph, with In this
paper, we define an edge-set graph constructed from the graph
such that any vertex of corresponds to the -th
-element subset of and any two vertices of
are adjacent if and only if there is at least one edge in the
edge-subset corresponding to which is adjacent to at least one edge
in the edge-subset corresponding to where are positive
integers. It can be noted that the edge-set graph of a graph
id dependent on both the structure of as well as the number of edges
We also discuss the characteristics and properties of the edge-set
graphs corresponding to certain standard graphs.Comment: 10 pages, 2 figure
Unifying parameter estimation and the Deutsch-Jozsa algorithm for continuous variables
We reveal a close relationship between quantum metrology and the Deutsch-Jozsa algorithm on continuous-variable quantum systems. We develop a general procedure, characterized by two parameters, that unifies parameter estimation and the Deutsch-Jozsa algorithm. Depending on which parameter we keep constant, the procedure implements either the parameter-estimation protocol or the Deutsch-Jozsa algorithm. The parameter-estimation part of the procedure attains the Heisenberg limit and is therefore optimal. Due to the use of approximate normalizable continuous-variable eigenstates, the Deutsch-Jozsa algorithm is probabilistic. The procedure estimates a value of an unknown parameter and solves the Deutsch-Jozsa problem without the use of any entanglement
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