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Quantum State Preparation Representation
Quantum Simulation
Entanglement Theory Quantum Correlations
Bosonic Continuous Variable Quantum Computing
Nonnegativity for hafnians of certain matrices
arXiv
Authors: Kamil Bradler, Shmuel Friedland, Robert Israel
Year
2018
Paper ID
23119
Status
Preprint
Abstract Read
~2 min
Abstract Words
80
Citations
N/A
Abstract
We show that a complex symmetric matrix of the form A(Y,B) = begin{bmatrix}Y & B\\ B^→p & overline{Y} end{bmatrix}, where B is Hermitian positive semidefinite, has a nonnegative hafnian. These are positive scalar multiples of matrices A(Y,B) that are encodable in a Gaussian boson sampler. Further, the hafnian of this matrix is non-decreasing in B in the sense that hafA(Y,L) ge hafA(Y,B) if L succeq B.
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- We show that a complex symmetric matrix of the form A(Y,B) = beginbmatrixY & B B^ -> p & overlineY endbmatrix, where B is Hermitian positive semidefinite, has a nonnegative...
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