Alternative robust ways of witnessing nonclassicality in the simplest
scenario
- URL: http://arxiv.org/abs/2311.13474v2
- Date: Tue, 12 Mar 2024 12:31:53 GMT
- Title: Alternative robust ways of witnessing nonclassicality in the simplest
scenario
- Authors: Massy Khoshbin, Lorenzo Catani, Matthew Leifer
- Abstract summary: We relate notions of nonclassicality in the simplest nontrivial scenario.
We use an approach based on the notion of bounded ontological distinctness for preparations.
As an application of our findings, we treat the case of two-bit parity-oblivious multiplexing in the presence of noise.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: In this paper we relate notions of nonclassicality in the simplest nontrivial
scenario (a prepare and measure scenario composed of four preparations and two
binary-outcome tomographically complete measurements). Specifically, we relate
the established method developed in [Pusey, PRA 98,022112(2018)] to witness a
violation of preparation noncontextuality, that is not suitable in experiments
where the operational equivalences to be tested are specified in advance, with
an approach based on the notion of bounded ontological distinctness for
preparations, defined in [Chaturvedi and Saha, Quantum 4, 345 (2020)]. In our
approach, we test bounded ontological distinctness for two particular
preparations that are relevant in certain information processing tasks in that
they are associated with the even- and odd-parity of the bits to communicate.
When there exists an ontological model where this distance is preserved we talk
of parity preservation. Our main result provides a noise threshold under which
violating parity preservation (and so bounded ontological distinctness) agrees
with the established method for witnessing preparation contextuality in the
simplest nontrivial scenario. This is achieved by first relating the violation
of parity preservation to the quantification of contextuality in terms of
inaccessible information as developed in [Marvian, arXiv:2003.05984(2020)],
that we also show, given the way we quantify noise, to be more robust in
witnessing contextuality than Pusey's noncontextuality inequality. As an
application of our findings, we treat the case of two-bit parity-oblivious
multiplexing in the presence of noise. In particular, we provide a condition
for which the result establishing preparation contextuality as a resource for
the quantum advantage of the protocol in the noiseless case still holds in the
noisy case.
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