37,984 research outputs found
Semidefinite relaxations for semi-infinite polynomial programming
This paper studies how to solve semi-infinite polynomial programming (SIPP)
problems by semidefinite relaxation method. We first introduce two SDP
relaxation methods for solving polynomial optimization problems with finitely
many constraints. Then we propose an exchange algorithm with SDP relaxations to
solve SIPP problems with compact index set. At last, we extend the proposed
method to SIPP problems with noncompact index set via homogenization. Numerical
results show that the algorithm is efficient in practice.Comment: 23 pages, 4 figure
Quantum measurement in two-dimensional conformal field theories: Application to quantum energy teleportation
We construct a set of quasi-local measurement operators in 2D CFT, and then
use them to proceed the quantum energy teleportation (QET) protocol and show it
is viable. These measurement operators are constructed out of the projectors
constructed from shadow operators, but further acting on the product of two
spatially separated primary fields. They are equivalently the OPE blocks in the
large central charge limit up to some UV-cutoff dependent normalization but the
associated probabilities of outcomes are UV-cutoff independent. We then adopt
these quantum measurement operators to show that the QET protocol is viable in
general. We also check the CHSH inequality a la OPE blocks.Comment: match the version published on PLB, the main conclusion didn't
change, some techincal details can be found in the previous versio
Thermal entanglement in a two-spin-qutrit system under a nonuniform external magnetic field
The thermal entanglement in a two-spin-qutrit system with two spins coupled
by exchange interaction under a magnetic field in an arbitrary direction is
investigated. Negativity, the measurement of entanglement, is calculated. We
find that for any temperature the evolvement of negativity is symmetric with
respect to magnetic field. The behavior of negativity is presented for four
different cases. The results show that for different temperature, different
magnetic field give maximum entanglement. Both the parallel and antiparallel
magnetic field cases are investigated qualitatively (not quantitatively) in
detail, we find that the entanglement may be enhanced under an antiparallel
magnetic field.Comment: 2 eps figure
Minimizing Rational Functions by Exact Jacobian SDP Relaxation Applicable to Finite Singularities
This paper considers the optimization problem of minimizing a rational
function. We reformulate this problem as polynomial optimization by the
technique of homogenization. These two problems are shown to be equivalent
under some generic conditions. The exact Jacobian SDP relaxation method
proposed by Nie is used to solve the resulting polynomial optimization. We also
prove that the assumption of nonsingularity in Nie's method can be weakened as
the finiteness of singularities. Some numerical examples are given to
illustrate the efficiency of our method.Comment: 23 page
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