5,320 research outputs found
Classical and quantum fingerprinting with shared randomness and one-sided error
Within the simultaneous message passing model of communication complexity,
under a public-coin assumption, we derive the minimum achievable worst-case
error probability of a classical fingerprinting protocol with one-sided error.
We then present entanglement-assisted quantum fingerprinting protocols
attaining worst-case error probabilities that breach this bound.Comment: 10 pages, 1 figur
Quantum Communication Cannot Simulate a Public Coin
We study the simultaneous message passing model of communication complexity.
Building on the quantum fingerprinting protocol of Buhrman et al., Yao recently
showed that a large class of efficient classical public-coin protocols can be
turned into efficient quantum protocols without public coin. This raises the
question whether this can be done always, i.e. whether quantum communication
can always replace a public coin in the SMP model. We answer this question in
the negative, exhibiting a communication problem where classical communication
with public coin is exponentially more efficient than quantum communication.
Together with a separation in the other direction due to Bar-Yossef et al.,
this shows that the quantum SMP model is incomparable with the classical
public-coin SMP model.
In addition we give a characterization of the power of quantum fingerprinting
by means of a connection to geometrical tools from machine learning, a
quadratic improvement of Yao's simulation, and a nearly tight analysis of the
Hamming distance problem from Yao's paper.Comment: 12 pages LaTe
From Low-Distortion Norm Embeddings to Explicit Uncertainty Relations and Efficient Information Locking
The existence of quantum uncertainty relations is the essential reason that
some classically impossible cryptographic primitives become possible when
quantum communication is allowed. One direct operational manifestation of these
uncertainty relations is a purely quantum effect referred to as information
locking. A locking scheme can be viewed as a cryptographic protocol in which a
uniformly random n-bit message is encoded in a quantum system using a classical
key of size much smaller than n. Without the key, no measurement of this
quantum state can extract more than a negligible amount of information about
the message, in which case the message is said to be "locked". Furthermore,
knowing the key, it is possible to recover, that is "unlock", the message. In
this paper, we make the following contributions by exploiting a connection
between uncertainty relations and low-distortion embeddings of L2 into L1. We
introduce the notion of metric uncertainty relations and connect it to
low-distortion embeddings of L2 into L1. A metric uncertainty relation also
implies an entropic uncertainty relation. We prove that random bases satisfy
uncertainty relations with a stronger definition and better parameters than
previously known. Our proof is also considerably simpler than earlier proofs.
We apply this result to show the existence of locking schemes with key size
independent of the message length. We give efficient constructions of metric
uncertainty relations. The bases defining these metric uncertainty relations
are computable by quantum circuits of almost linear size. This leads to the
first explicit construction of a strong information locking scheme. Moreover,
we present a locking scheme that is close to being implementable with current
technology. We apply our metric uncertainty relations to exhibit communication
protocols that perform quantum equality testing.Comment: 60 pages, 5 figures. v4: published versio
Insightful classification of crystal structures using deep learning
Computational methods that automatically extract knowledge from data are
critical for enabling data-driven materials science. A reliable identification
of lattice symmetry is a crucial first step for materials characterization and
analytics. Current methods require a user-specified threshold, and are unable
to detect average symmetries for defective structures. Here, we propose a
machine-learning-based approach to automatically classify structures by crystal
symmetry. First, we represent crystals by calculating a diffraction image, then
construct a deep-learning neural-network model for classification. Our approach
is able to correctly classify a dataset comprising more than 100 000 simulated
crystal structures, including heavily defective ones. The internal operations
of the neural network are unraveled through attentive response maps,
demonstrating that it uses the same landmarks a materials scientist would use,
although never explicitly instructed to do so. Our study paves the way for
crystal-structure recognition of - possibly noisy and incomplete -
three-dimensional structural data in big-data materials science.Comment: Nature Communications, in press (2018
Hierarchical Visualization of Materials Space with Graph Convolutional Neural Networks
The combination of high throughput computation and machine learning has led
to a new paradigm in materials design by allowing for the direct screening of
vast portions of structural, chemical, and property space. The use of these
powerful techniques leads to the generation of enormous amounts of data, which
in turn calls for new techniques to efficiently explore and visualize the
materials space to help identify underlying patterns. In this work, we develop
a unified framework to hierarchically visualize the compositional and
structural similarities between materials in an arbitrary material space with
representations learned from different layers of graph convolutional neural
networks. We demonstrate the potential for such a visualization approach by
showing that patterns emerge automatically that reflect similarities at
different scales in three representative classes of materials: perovskites,
elemental boron, and general inorganic crystals, covering material spaces of
different compositions, structures, and both. For perovskites, elemental
similarities are learned that reflects multiple aspects of atom properties. For
elemental boron, structural motifs emerge automatically showing characteristic
boron local environments. For inorganic crystals, the similarity and stability
of local coordination environments are shown combining different center and
neighbor atoms. The method could help transition to a data-centered exploration
of materials space in automated materials design.Comment: 22 + 7 pages, 6 + 5 figure
Emergence of thermodynamic behavior within composite quantum systems
Entanglement within a given device provides a potential resource for quantum
information processing. Entanglement between system and environment leads to
decoherence (thus suppressing non-classical features within the system) but
also opens up a route to robust and universal control. The latter is related to
thermodynamic equilibrium, a generic behavior of bi-partite quantum systems.
Fingerprints of this equilibrium behavior (including relaxation and stability)
show up already far from the thermodynamic limit, where a complete solution of
the underlying Schroedinger dynamics of the total system is still feasible.Comment: 12 pages, 12 figures, accepted for publication in Physica
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