139 research outputs found
Optimal design and quantum benchmarks for coherent state amplifiers
We establish the ultimate quantum limits to the amplification of an unknown
coherent state, both in the deterministic and probabilistic case, investigating
the realistic scenario where the expected photon number is finite. In addition,
we provide the benchmark that experimental realizations have to surpass in
order to beat all classical amplification strategies and to demonstrate genuine
quantum amplification. Our result guarantees that a successful demonstration is
in principle possible for every finite value of the expected photon number.Comment: 5 + 8 pages, published versio
H2TF for Hyperspectral Image Denoising: Where Hierarchical Nonlinear Transform Meets Hierarchical Matrix Factorization
Recently, tensor singular value decomposition (t-SVD) has emerged as a
promising tool for hyperspectral image (HSI) processing. In the t-SVD, there
are two key building blocks: (i) the low-rank enhanced transform and (ii) the
accompanying low-rank characterization of transformed frontal slices. Previous
t-SVD methods mainly focus on the developments of (i), while neglecting the
other important aspect, i.e., the exact characterization of transformed frontal
slices. In this letter, we exploit the potentiality in both building blocks by
leveraging the \underline{\bf H}ierarchical nonlinear transform and the
\underline{\bf H}ierarchical matrix factorization to establish a new
\underline{\bf T}ensor \underline{\bf F}actorization (termed as H2TF). Compared
to shallow counter partners, e.g., low-rank matrix factorization or its convex
surrogates, H2TF can better capture complex structures of transformed frontal
slices due to its hierarchical modeling abilities. We then suggest the
H2TF-based HSI denoising model and develop an alternating direction method of
multipliers-based algorithm to address the resultant model. Extensive
experiments validate the superiority of our method over state-of-the-art HSI
denoising methods
Settling the Query Complexity of Non-Adaptive Junta Testing
We prove that any non-adaptive algorithm that tests whether an unknown Boolean function f is a k-junta or epsilon-far from every k-junta must make ~Omega(k^{3/2}/ epsilon) many queries for a wide range of parameters k and epsilon. Our result dramatically improves previous lower bounds from [BGSMdW13,STW15], and is essentially optimal given Blais\u27s non-adaptive junta tester from [Blais08], which makes ~O(k^{3/2})/epsilon queries. Combined with the adaptive tester of [Blais09] which makes O(k log k + k / epsilon) queries, our result shows that adaptivity enables polynomial savings in query complexity for junta testing
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