1,434 research outputs found
A note on the noncommutative correction to gravity
An apparent contradiction in the leading order correction to noncommutative
(NC) gravity reported in the literature has been pointed out. We show by direct
computation that actually there is no such controvarsy and all perturbative NC
corrections start from the second order in the NC parameter. The role of
symmetries in the vanishing of the first order correction is manifest in our
calculation.Comment: Revtex, 3 pages, transferred from PRC to PRD, references added, this
version to be published in Phys. Rev.
On the origin of nonclassicality in single systems
In the framework of certain general probability theories of single systems,
we identify various nonclassical features such as incompatibility, multiple
pure-state decomposability, measurement disturbance, no-cloning and the
impossibility of certain universal operations, with the non-simpliciality of
the state space. This is shown to naturally suggest an underlying simplex as an
ontological model. Contextuality turns out to be an independent nonclassical
feature, arising from the intransitivity of compatibility.Comment: Close to the published versio
Orthogonal-state-based cryptography in quantum mechanics and local post-quantum theories
We introduce the concept of cryptographic reduction, in analogy with a
similar concept in computational complexity theory. In this framework, class
of crypto-protocols reduces to protocol class in a scenario , if for
every instance of , there is an instance of and a secure
transformation that reproduces given , such that the security of
guarantees the security of . Here we employ this reductive framework to
study the relationship between security in quantum key distribution (QKD) and
quantum secure direct communication (QSDC). We show that replacing the
streaming of independent qubits in a QKD scheme by block encoding and
transmission (permuting the order of particles block by block) of qubits, we
can construct a QSDC scheme. This forms the basis for the \textit{block
reduction} from a QSDC class of protocols to a QKD class of protocols, whereby
if the latter is secure, then so is the former. Conversely, given a secure QSDC
protocol, we can of course construct a secure QKD scheme by transmitting a
random key as the direct message. Then the QKD class of protocols is secure,
assuming the security of the QSDC class which it is built from. We refer to
this method of deduction of security for this class of QKD protocols, as
\textit{key reduction}. Finally, we propose an orthogonal-state-based
deterministic key distribution (KD) protocol which is secure in some local
post-quantum theories. Its security arises neither from geographic splitting of
a code state nor from Heisenberg uncertainty, but from post-measurement
disturbance.Comment: 12 pages, no figure, this is a modified version of a talk delivered
by Anirban Pathak at Quantum 2014, INRIM, Turin, Italy. This version is
published in Int. J. Quantum. Info
Posterior contraction in sparse Bayesian factor models for massive covariance matrices
Sparse Bayesian factor models are routinely implemented for parsimonious
dependence modeling and dimensionality reduction in high-dimensional
applications. We provide theoretical understanding of such Bayesian procedures
in terms of posterior convergence rates in inferring high-dimensional
covariance matrices where the dimension can be larger than the sample size.
Under relevant sparsity assumptions on the true covariance matrix, we show that
commonly-used point mass mixture priors on the factor loadings lead to
consistent estimation in the operator norm even when . One of our major
contributions is to develop a new class of continuous shrinkage priors and
provide insights into their concentration around sparse vectors. Using such
priors for the factor loadings, we obtain similar rate of convergence as
obtained with point mass mixture priors. To obtain the convergence rates, we
construct test functions to separate points in the space of high-dimensional
covariance matrices using insights from random matrix theory; the tools
developed may be of independent interest. We also derive minimax rates and show
that the Bayesian posterior rates of convergence coincide with the minimax
rates upto a term.Comment: Published in at http://dx.doi.org/10.1214/14-AOS1215 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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