Implementing Parrondo s paradox with two-coin quantum walks
#MMPMID29515873
Rajendran J
; Benjamin C
R Soc Open Sci
2018[Feb]; 5
(2
): 171599
PMID29515873
show ga
Parrondo's paradox is ubiquitous in games, ratchets and random walks. The
apparent paradox, devised by J. M. R. Parrondo, that two losing games A and B can
produce a winning outcome has been adapted in many physical and biological
systems to explain their working. However, proposals on demonstrating Parrondo's
paradox using quantum walks failed for a large number of steps. In this work, we
show that instead of a single coin if we consider a two-coin initial state which
may or may not be entangled, we can observe a genuine Parrondo's paradox with
quantum walks. Furthermore, we focus on reasons for this and pin down the
asymmetry in initial two-coin state or asymmetry in shift operator, either of
which is necessary for observing a genuine Parrondo's paradox. We extend our work
to a three-coin initial state too with similar results. The implications of our
work for observing quantum ratchet-like behaviour using quantum walks are also
discussed.
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