Optimizing local Hamiltonians for the best metrological performance
- URL: http://arxiv.org/abs/2206.02820v1
- Date: Mon, 6 Jun 2022 18:01:03 GMT
- Title: Optimizing local Hamiltonians for the best metrological performance
- Authors: \'Arp\'ad Luk\'acs, R\'obert Tr\'enyi, Tam\'as V\'ertesi, G\'eza
T\'oth
- Abstract summary: We discuss efficient methods to optimize the metrological performance over local Hamiltonians in a bipartite quantum system.
We present the quantum Fisher information in a bilinear form and maximize it by iterating a see-saw.
We consider a number of other problems in quantum information theory that can be solved in a similar manner.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We discuss efficient methods to optimize the metrological performance over
local Hamiltonians in a bipartite quantum system. For a given quantum state,
our methods find the best local Hamiltonian for which the state outperforms
separable states the most from the point of view of quantum metrology. We show
that this problem can be reduced to maximize the quantum Fisher information
over a certain set of Hamiltonians. We present the quantum Fisher information
in a bilinear form and maximize it by iterating a see-saw, in which each step
is based on semidefinite programming. We also solve the problem with the method
of moments that works very well for smaller systems. We consider a number of
other problems in quantum information theory that can be solved in a similar
manner. For instance, we determine the bound entangled quantum states that
maximally violate the Computable Cross Norm-Realignment (CNNR) criterion.
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