Quantum Information Processing, Vol. 6, No. 4, August 2007 (© 2007)
Groverian Entanglement Measure and Evolution
of Entanglement in Search Algorithm for
n(= 3, 5)-Qubit Systems with Real Coefﬁcients
and C. M. Bhandari
Received September 11, 2006; accepted May 19, 2007; Published online: July 18, 2007
Evolution of entanglement with the processing of quantum algorithms affects the
outcome of the algorithm. Particularly, the performance of Grover’s search algo-
rithm gets worsened if the initial state of the algorithm is an entangled one. The
success probability of search can be seen as an operational measure of entan-
glement. This paper demonstrates an entanglement measure based on the perfor-
mance of Grover’s search algorithm for three and ﬁve qubit systems. We also
show that although the overall pattern shows growth of entanglement, its rise to
a maximum and then consequent decay, the presence of local ﬂuctuation within
each iterative step is likely.
KEY WORDS: Groverian entanglement; Grover’s search algorithm; success prob-
ability; entanglement monotone; von Neumann entropy; three-way tangle.
PACS: 03.67.-a; 03.65.Ud.
are the pillars of quantum
computation and quantum information theory.
tion theory has reached the new arenas exploiting these two. Quantum
entanglement, inherently a non-classical phenomenon, signiﬁes correla-
tions between quantum systems even if they are space-like separated. In
recent times it has been reckoned as a physical resource and hence utilized
for various computational tasks including quantum information process-
Hence, quantiﬁcation of entanglement of quan-
tum states attains utmost importance. Various entanglement evaluating
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