285 research outputs found
Contextuality as a resource for models of quantum computation on qubits
A central question in quantum computation is to identify the resources that
are responsible for quantum speed-up. Quantum contextuality has been recently
shown to be a resource for quantum computation with magic states for odd-prime
dimensional qudits and two-dimensional systems with real wavefunctions. The
phenomenon of state-independent contextuality poses a priori an obstruction to
characterizing the case of regular qubits, the fundamental building block of
quantum computation. Here, we establish contextuality of magic states as a
necessary resource for a large class of quantum computation schemes on qubits.
We illustrate our result with a concrete scheme related to measurement-based
quantum computation.Comment: Published version. We have revised the title, introduction and
discussion, as well as slightly simplified the setting in this versio
Bell non-locality and Kochen-Specker contextuality: How are they connected?
Bell non-locality and Kochen-Specker (KS) contextuality are logically
independent concepts, fuel different protocols with quantum vs classical
advantage, and have distinct classical simulation costs. A natural question is
what are the relations between these concepts, advantages, and costs. To
address this question, it is useful to have a map that captures all the
connections between Bell non-locality and KS contextuality in quantum theory.
The aim of this work is to introduce such a map. After defining the
theory-independent notions of Bell non-locality and KS contextuality for ideal
measurements, we show that, in quantum theory, due to Neumark's dilation
theorem, every matrix of quantum Bell non-local correlations can be mapped to
an identical matrix of KS contextual correlations produced in a scenario with
identical relations of compatibility but where measurements are ideal and no
space-like separation is required. A more difficult problem is identifying
connections in the opposite direction. We show that there are "one-to-one" and
partial connections between KS contextual correlations and Bell non-local
correlations for some KS contextuality scenarios, but not for all of them.
However, there is also a method that transforms any matrix of KS contextual
correlations for quantum systems of dimension into a matrix of Bell
non-local correlations between two quantum subsystems each of them of dimension
. We collect all these connections in map and list some problems which can
benefit from this map.Comment: 13 pages, 2 figure
Wigner function negativity and contextuality in quantum computation on rebits
We describe a universal scheme of quantum computation by state injection on
rebits (states with real density matrices). For this scheme, we establish
contextuality and Wigner function negativity as computational resources,
extending results of [M. Howard et al., Nature 510, 351--355 (2014)] to
two-level systems. For this purpose, we define a Wigner function suited to
systems of rebits, and prove a corresponding discrete Hudson's theorem. We
introduce contextuality witnesses for rebit states, and discuss the
compatibility of our result with state-independent contextuality.Comment: 18 + 4 page
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