1,450 research outputs found
Tsirelson's problem and Kirchberg's conjecture
Tsirelson's problem asks whether the set of nonlocal quantum correlations
with a tensor product structure for the Hilbert space coincides with the one
where only commutativity between observables located at different sites is
assumed. Here it is shown that Kirchberg's QWEP conjecture on tensor products
of C*-algebras would imply a positive answer to this question for all bipartite
scenarios. This remains true also if one considers not only spatial
correlations, but also spatiotemporal correlations, where each party is allowed
to apply their measurements in temporal succession; we provide an example of a
state together with observables such that ordinary spatial correlations are
local, while the spatiotemporal correlations reveal nonlocality. Moreover, we
find an extended version of Tsirelson's problem which, for each nontrivial Bell
scenario, is equivalent to the QWEP conjecture. This extended version can be
conveniently formulated in terms of steering the system of a third party.
Finally, a comprehensive mathematical appendix offers background material on
complete positivity, tensor products of C*-algebras, group C*-algebras, and
some simple reformulations of the QWEP conjecture.Comment: 57 pages, to appear in Rev. Math. Phy
Transparency in Complex Computational Systems
Scientists depend on complex computational systems that are often ineliminably opaque, to the detriment of our ability to give scientific explanations and detect artifacts. Some philosophers have s..
Novel Area-Efficient and Flexible Architectures for Optimal Ate Pairing on FPGA
While FPGA is a suitable platform for implementing cryptographic algorithms,
there are several challenges associated with implementing Optimal Ate pairing
on FPGA, such as security, limited computing resources, and high power
consumption. To overcome these issues, this study introduces three approaches
that can execute the optimal Ate pairing on Barreto-Naehrig curves using
Jacobean coordinates with the goal of reaching 128-bit security on the Genesys
board. The first approach is a pure software implementation utilizing the
MicroBlaze processor. The second involves a combination of software and
hardware, with key operations in and being transformed into
IP cores for the MicroBlaze. The third approach builds on the second by
incorporating parallelism to improve the pairing process. The utilization of
multiple MicroBlaze processors within a single system offers both versatility
and parallelism to speed up pairing calculations. A variety of methods and
parameters are used to optimize the pairing computation, including Montgomery
modular multiplication, the Karatsuba method, Jacobean coordinates, the Complex
squaring method, sparse multiplication, squaring in , and
the addition chain method. The proposed systems are designed to efficiently
utilize limited resources in restricted environments, while still completing
tasks in a timely manner.Comment: 13 pages, 8 figures, and 5 table
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