Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming
We present randomized approximation algorithms for the maximum cut (MAX CUT) and
maximum 2-satisfiability (MAX 2SAT) problems that always deliver solutions of expected …
maximum 2-satisfiability (MAX 2SAT) problems that always deliver solutions of expected …
[BOOK][B] Geometry of cuts and metrics
Cuts and metrics are well-known objects that arise-independently, but with many deep and
fascinating connections-in diverse fields: in graph theory, combinatorial optimization …
fascinating connections-in diverse fields: in graph theory, combinatorial optimization …
On a positive semidefinite relaxation of the cut polytope
M Laurent, S Poljak - Linear Algebra and its Applications, 1995 - Elsevier
We study the convex set L n defined by L nZ≔{X| X=(xij) a positive semidefinite n× n matrix,
xii= 1 for all i}. We describe several geometric properties of L n. In particular, we show that L …
xii= 1 for all i}. We describe several geometric properties of L n. In particular, we show that L …
Nonasymptotic assisted distillation of quantum coherence
We characterize the operational task of environment-assisted distillation of quantum
coherence under different sets of free operations when only a finite supply of copies of a …
coherence under different sets of free operations when only a finite supply of copies of a …
On the facial structure of the set of correlation matrices
M Laurent, S Poljak - SIAM Journal on Matrix Analysis and Applications, 1996 - SIAM
We study the facial structure of the set E_n*n of correlation matrices (ie, the positive
semidefinite matrices with diagonal entries equal to 1). In particular, we determine the …
semidefinite matrices with diagonal entries equal to 1). In particular, we determine the …
A tight degree 4 sum-of-squares lower bound for the Sherrington–Kirkpatrick Hamiltonian
We show that, if WW is an N * NN× N matrix drawn from the gaussian orthogonal ensemble,
then with high probability the degree 4 sum-of-squares relaxation cannot certify an upper …
then with high probability the degree 4 sum-of-squares relaxation cannot certify an upper …
Inverting quantum decoherence by classical feedback from the environment
We show that for qubits and qutrits it is always possible to perfectly recover quantum
coherence by performing a measurement only on the environment, whereas for dimension …
coherence by performing a measurement only on the environment, whereas for dimension …
Diagonal unitary and orthogonal symmetries in quantum theory
We analyze bipartite matrices and linear maps between matrix algebras, which are
respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' …
respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' …
On the mixed-unitary rank of quantum channels
In the theory of quantum information, the mixed-unitary quantum channels, for any positive
integer dimension n, are those linear maps that can be expressed as a convex combination …
integer dimension n, are those linear maps that can be expressed as a convex combination …
[HTML][HTML] Positive semidefinite matrix completion, universal rigidity and the strong Arnold property
This paper addresses the following three topics: positive semidefinite (psd) matrix
completions, universal rigidity of frameworks, and the Strong Arnold Property (SAP). We …
completions, universal rigidity of frameworks, and the Strong Arnold Property (SAP). We …