22,653 research outputs found
On the tailoring of CAST-32A certification guidance to real COTS multicore architectures
The use of Commercial Off-The-Shelf (COTS) multicores in real-time industry is on the rise due to multicores' potential performance increase and energy reduction. Yet, the unpredictable impact on timing of contention in shared hardware resources challenges certification. Furthermore, most safety certification standards target single-core architectures and do not provide explicit guidance for multicore processors. Recently, however, CAST-32A has been presented providing guidance for software planning, development and verification in multicores. In this paper, from a theoretical level, we provide a detailed review of CAST-32A objectives and the difficulty of reaching them under current COTS multicore design trends; at experimental level, we assess the difficulties of the application of CAST-32A to a real multicore processor, the NXP P4080.This work has been partially supported by the Spanish Ministry of Economy and Competitiveness (MINECO) under grant
TIN2015-65316-P and the HiPEAC Network of Excellence.
Jaume Abella has been partially supported by the MINECO under Ramon y Cajal grant RYC-2013-14717.Peer ReviewedPostprint (author's final draft
Entanglement, quantum randomness, and complexity beyond scrambling
Scrambling is a process by which the state of a quantum system is effectively
randomized due to the global entanglement that "hides" initially localized
quantum information. In this work, we lay the mathematical foundations of
studying randomness complexities beyond scrambling by entanglement properties.
We do so by analyzing the generalized (in particular R\'enyi) entanglement
entropies of designs, i.e. ensembles of unitary channels or pure states that
mimic the uniformly random distribution (given by the Haar measure) up to
certain moments. A main collective conclusion is that the R\'enyi entanglement
entropies averaged over designs of the same order are almost maximal. This
links the orders of entropy and design, and therefore suggests R\'enyi
entanglement entropies as diagnostics of the randomness complexity of
corresponding designs. Such complexities form a hierarchy between information
scrambling and Haar randomness. As a strong separation result, we prove the
existence of (state) 2-designs such that the R\'enyi entanglement entropies of
higher orders can be bounded away from the maximum. However, we also show that
the min entanglement entropy is maximized by designs of order only logarithmic
in the dimension of the system. In other words, logarithmic-designs already
achieve the complexity of Haar in terms of entanglement, which we also call
max-scrambling. This result leads to a generalization of the fast scrambling
conjecture, that max-scrambling can be achieved by physical dynamics in time
roughly linear in the number of degrees of freedom.Comment: 72 pages, 4 figures. Rewritten version with new title. v3: published
versio
Absolutely Maximally Entangled states, combinatorial designs and multi-unitary matrices
Absolutely Maximally Entangled (AME) states are those multipartite quantum
states that carry absolute maximum entanglement in all possible partitions. AME
states are known to play a relevant role in multipartite teleportation, in
quantum secret sharing and they provide the basis novel tensor networks related
to holography. We present alternative constructions of AME states and show
their link with combinatorial designs. We also analyze a key property of AME,
namely their relation to tensors that can be understood as unitary
transformations in every of its bi-partitions. We call this property
multi-unitarity.Comment: 18 pages, 2 figures. Comments are very welcom
The Perfect Binary One-Error-Correcting Codes of Length 15: Part II--Properties
A complete classification of the perfect binary one-error-correcting codes of
length 15 as well as their extensions of length 16 was recently carried out in
[P. R. J. \"Osterg{\aa}rd and O. Pottonen, "The perfect binary
one-error-correcting codes of length 15: Part I--Classification," IEEE Trans.
Inform. Theory vol. 55, pp. 4657--4660, 2009]. In the current accompanying
work, the classified codes are studied in great detail, and their main
properties are tabulated. The results include the fact that 33 of the 80
Steiner triple systems of order 15 occur in such codes. Further understanding
is gained on full-rank codes via switching, as it turns out that all but two
full-rank codes can be obtained through a series of such transformations from
the Hamming code. Other topics studied include (non)systematic codes, embedded
one-error-correcting codes, and defining sets of codes. A classification of
certain mixed perfect codes is also obtained.Comment: v2: fixed two errors (extension of nonsystematic codes, table of
coordinates fixed by symmetries of codes), added and extended many other
result
Upper bounds for partial spreads
A partial -spread in is a collection of -dimensional
subspaces with trivial intersection such that each non-zero vector is covered
at most once. We present some improved upper bounds on the maximum sizes.Comment: 4 page
Unitary -designs via random quenches in atomic Hubbard and Spin models: Application to the measurement of R\'enyi entropies
We present a general framework for the generation of random unitaries based
on random quenches in atomic Hubbard and spin models, forming approximate
unitary -designs, and their application to the measurement of R\'enyi
entropies. We generalize our protocol presented in [Elben2017:
arXiv:1709.05060, to appear in Phys. Rev. Lett.] to a broad class of atomic and
spin lattice models. We further present an in-depth numerical and analytical
study of experimental imperfections, including the effect of decoherence and
statistical errors, and discuss connections of our approach with many-body
quantum chaos.Comment: This is a new and extended version of the Supplementary material
presented in arXiv:1709.05060v1, rewritten as a companion paper. Version
accepted to Phys. Rev. A. Minus sign corrected in Eq (5
Classification of large partial plane spreads in and related combinatorial objects
In this article, the partial plane spreads in of maximum possible
size and of size are classified. Based on this result, we obtain the
classification of the following closely related combinatorial objects: Vector
space partitions of of type , binary MRD
codes of minimum rank distance , and subspace codes with parameters
and .Comment: 31 pages, 9 table
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