Alladi Ramakrishnan Hall

Exploring contextuality and determining the parity of a permutation using an NMR qutrit

Shruti Dogra

IISER--Mohali

Quantum information processors exploit the intrinsic quantumness of quantum systems to perform
computational tasks more efficiently than their classical counterparts. This talk focuses on exploring
single-qutrit contextuality, which is an intrinsic feature providing speed up in quantum computational
tasks. Contextuality refers to the context of a measurement, which states that the measurement of an
observable may bear different outcomes when measured in different contexts. In this talk, I will discuss
the experimental demonstration of a single qutrit contextuality, based on nine observables [1], using a
set of four NMR experiments [2]. A single-shot test to reveal the contextuality of diagonal states of a
single qutrit is also performed [2]. The quantum features of the single-qutrit are further exploited by
implementing a black-box based algorithm, that determines the parity of a permutation among three
objects by a single oracle call whereas its classical counterpart requires two oracle calls [3, 4]. The NMR
experiments on a single-qutrit are carried out on a spin-1 oriented in a liquid crystalline matrix.

References:-

[1] P. Kurzynski and D. Kaszlikowski, ``Contextuality of almost all qutrit states can be revealed with nine
observables," Phys. Rev. A vol. 86, pp. 042125 (2012).

[2] S. Dogra, K. Dorai, and Arvind, ``Experimental demonstration of quantum contextuality on an NMR
qutrit," Phys. Lett. A vol. 380, pp. 1941 (2016).

[3] Z. Gedik, I. A. Silva, B. Cakmak, G. Karpat, E. L. G. Vidoto, D. O. Soares-Pinto, E. R. deAzevedo,
and F. F. Fanchini, ``Computational speed-up with a single qudit," Scientific Reports vol. 5, pp. 14671 (2015).

[4] S. Dogra, Arvind, and K. Dorai, ``Determining the parity of a permutation using an experimental NMR qutrit," Phys. Lett. A vol. 378, pp. 3452 (2014).
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