635 research outputs found
Contextuality with vanishing coherence and maximal robustness to dephasing
Generalized contextuality is a resource for a wide range of communication and
information processing protocols. However, contextuality is not possible
without coherence, and so can be destroyed by dephasing noise. Here, we explore
the robustness of contextuality to partially dephasing noise in a scenario
related to state discrimination (for which contextuality is a resource). We
find that a vanishing amount of coherence is sufficient to demonstrate the
failure of noncontextuality in this scenario, and we give a proof of
contextuality that is robust to arbitrary amounts of partially dephasing noise.
This is in stark contrast to partially depolarizing noise, which is always
sufficient to destroy contextuality.Comment: 13 pages, 7 figures. Comments are welcome
Contextual advantage for state discrimination
Finding quantitative aspects of quantum phenomena which cannot be explained
by any classical model has foundational importance for understanding the
boundary between classical and quantum theory. It also has practical
significance for identifying information processing tasks for which those
phenomena provide a quantum advantage. Using the framework of generalized
noncontextuality as our notion of classicality, we find one such nonclassical
feature within the phenomenology of quantum minimum error state discrimination.
Namely, we identify quantitative limits on the success probability for minimum
error state discrimination in any experiment described by a noncontextual
ontological model. These constraints constitute noncontextuality inequalities
that are violated by quantum theory, and this violation implies a quantum
advantage for state discrimination relative to noncontextual models.
Furthermore, our noncontextuality inequalities are robust to noise and are
operationally formulated, so that any experimental violation of the
inequalities is a witness of contextuality, independently of the validity of
quantum theory. Along the way, we introduce new methods for analyzing
noncontextuality scenarios, and demonstrate a tight connection between our
minimum error state discrimination scenario and a Bell scenario.Comment: 18 pages, 9 figure
Certified Quantum Measurement of Majorana Fermions
We present a quantum self-testing protocol to certify measurements of fermion
parity involving Majorana fermion modes. We show that observing a set of ideal
measurement statistics implies anti-commutativity of the implemented Majorana
fermion parity operators, a necessary prerequisite for Majorana detection. Our
protocol is robust to experimental errors. We obtain lower bounds on the
fidelities of the state and measurement operators that are linear in the
errors. We propose to analyze experimental outcomes in terms of a contextuality
witness , which satisfies for any classical
probabilistic model of the data. A violation of the inequality witnesses
quantum contextuality, and the closeness to the maximum ideal value indicates the degree of confidence in the detection of Majorana
fermions.Comment: 13 pages, 3 figure
Constraints on Macroscopic Realism Without Assuming Non-Invasive Measurability
Macroscopic realism is the thesis that macroscopically observable properties
must always have definite values. The idea was introduced by Leggett and Garg
(1985), who wished to show a conflict with the predictions of quantum theory.
However, their analysis required not just the assumption of macroscopic realism
per se, but also that the observable properties could be measured
non-invasively. In recent years there has been increasing interest in
experimental tests of the violation of the Leggett-Garg inequality, but it has
remained a matter of controversy whether this second assumption is a reasonable
requirement for a macroscopic realist view of quantum theory. In a recent
critical assessment Maroney and Timpson (2017) identified three different
categories of macroscopic realism, and argued that only the simplest category
could be ruled out by Leggett-Garg inequality violations. Allen, Maroney, and
Gogioso (2016) then showed that the second of these approaches was also
incompatible with quantum theory in Hilbert spaces of dimension 4 or higher.
However, we show that the distinction introduced by Maroney and Timpson between
the second and third approaches is not noise tolerant, so unfortunately Allen's
result, as given, is not directly empirically testable. In this paper we
replace Maroney and Timpson's three categories with a parameterization of
macroscopic realist models, which can be related to experimental observations
in a noise tolerant way, and recover the original definitions in the noise-free
limit. We show how this parameterization can be used to experimentally rule out
classes of macroscopic realism in Hilbert spaces of dimension 3 or higher,
including the category tested by the Leggett-Garg inequality, without any use
of the non-invasive measurability assumption.Comment: 20 pages, 10 figure
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