659 research outputs found
An Extended Result on the Optimal Estimation under Minimum Error Entropy Criterion
The minimum error entropy (MEE) criterion has been successfully used in
fields such as parameter estimation, system identification and the supervised
machine learning. There is in general no explicit expression for the optimal
MEE estimate unless some constraints on the conditional distribution are
imposed. A recent paper has proved that if the conditional density is
conditionally symmetric and unimodal (CSUM), then the optimal MEE estimate
(with Shannon entropy) equals the conditional median. In this study, we extend
this result to the generalized MEE estimation where the optimality criterion is
the Renyi entropy or equivalently, the \alpha-order information potential (IP).Comment: 15 pages, no figures, submitted to Entrop
A Wang-Landau method for calculating Renyi entropies in finite-temperature quantum Monte Carlo simulations
We implement a Wang-Landau sampling technique in quantum Monte Carlo (QMC)
for the purpose of calculating the Renyi entanglement entropies and associated
mutual information. The algorithm converges an estimate for an analogue to the
density of states for Stochastic Series Expansion QMC allowing a direct
calculation of Renyi entropies without explicit thermodynamic integration. We
benchmark results for the mutual information on two-dimensional (2D) isotropic
and anisotropic Heisenberg models, 2D transverse field Ising model, and 3D
Heisenberg model, confirming a critical scaling of the mutual information in
cases with a finite-temperature transition. We discuss the benefits and
limitations of broad sampling techniques compared to standard importance
sampling methods.Comment: 9 pages, 7 figure
Thermal vs. Entanglement Entropy: A Measurement Protocol for Fermionic Atoms with a Quantum Gas Microscope
We show how to measure the order-two Renyi entropy of many-body states of
spinful fermionic atoms in an optical lattice in equilibrium and
non-equilibrium situations. The proposed scheme relies on the possibility to
produce and couple two copies of the state under investigation, and to measure
the occupation number in a site- and spin-resolved manner, e.g. with a quantum
gas microscope. Such a protocol opens the possibility to measure entanglement
and test a number of theoretical predictions, such as area laws and their
corrections. As an illustration we discuss the interplay between thermal and
entanglement entropy for a one dimensional Fermi-Hubbard model at finite
temperature, and its possible measurement in an experiment using the present
scheme
Renyi entropies for classical stringnet models
In quantum mechanics, stringnet condensed states - a family of prototypical
states exhibiting non-trivial topological order - can be classified via their
long-range entanglement properties, in particular topological corrections to
the prevalent area law of the entanglement entropy. Here we consider classical
analogs of such stringnet models whose partition function is given by an
equal-weight superposition of classical stringnet configurations. Our analysis
of the Shannon and Renyi entropies for a bipartition of a given system reveals
that the prevalent volume law for these classical entropies is augmented by
subleading topological corrections that are intimately linked to the anyonic
theories underlying the construction of the classical models. We determine the
universal values of these topological corrections for a number of underlying
anyonic theories including su(2)_k, su(N)_1, and su(N)_2 theories
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