Bounding Real Tensor Optimizations via the Numerical Range
arXiv:2212.12811 · doi:10.13001/ela.2023.7635
Abstract
We show how the numerical range of a matrix can be used to bound the optimal value of certain optimization problems over real tensor product vectors. Our bound is stronger than the trivial bounds based on eigenvalues, and can be computed significantly faster than bounds provided by semidefinite programming relaxations. We discuss numerous applications to other hard linear algebra problems, such as showing that a real subspace of matrices contains no rank-one matrix, and showing that a linear map acting on matrices is positive.
arXiv comment22 pages
References in corpus (11)
- Separability Criterion for Density Matrices
- Bell Inequalities and the Separability Criterion
- A complete family of separability criteria
- On the dimension of subspaces with bounded Schmidt rank
- A note on the optimality of decomposable entanglement witnesses and completely entangled subspaces
- An improved semidefinite programming hierarchy for testing entanglement
- Positive maps and entanglement in real Hilbert spaces
- Norms and Cones in the Theory of Quantum Entanglement
- Simple sufficient condition for subspace to be completely or genuinely entangled
- A Complete Hierarchy of Linear Systems for Certifying Quantum Entanglement of Subspaces
- Operation fidelity explored by numerical range of Kraus operators