294 research outputs found
Explicit reconstruction of the entanglement wedge
The problem of how the boundary encodes the bulk in AdS/CFT is still a
subject of study today. One of the major issues that needs more elucidation is
the problem of subregion duality; what information of the bulk a given boundary
subregion encodes. Although the proof given by Dong, Harlow, and Wall states
that the entanglement wedge of the bulk should be encoded in boundary
subregions, no explicit procedure for reconstructing the entanglement wedge was
given so far. In this paper, mode sum approach to obtaining smearing functions
for a single bulk scalar is generalised to include bulk reconstruction in the
entanglement wedge of boundary subregions. It is generally expectated that
solutions to the wave equation on a complicated coordinate patch are needed,
but this hard problem has been transferred to a less hard but tractable problem
of matrix inversion.Comment: version accepted by JHEP; added references and discussions on
covarianc
Quantization and Compressive Sensing
Quantization is an essential step in digitizing signals, and, therefore, an
indispensable component of any modern acquisition system. This book chapter
explores the interaction of quantization and compressive sensing and examines
practical quantization strategies for compressive acquisition systems.
Specifically, we first provide a brief overview of quantization and examine
fundamental performance bounds applicable to any quantization approach. Next,
we consider several forms of scalar quantizers, namely uniform, non-uniform,
and 1-bit. We provide performance bounds and fundamental analysis, as well as
practical quantizer designs and reconstruction algorithms that account for
quantization. Furthermore, we provide an overview of Sigma-Delta
() quantization in the compressed sensing context, and also
discuss implementation issues, recovery algorithms and performance bounds. As
we demonstrate, proper accounting for quantization and careful quantizer design
has significant impact in the performance of a compressive acquisition system.Comment: 35 pages, 20 figures, to appear in Springer book "Compressed Sensing
and Its Applications", 201
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