Entanglement negativity bounds for fermionic Gaussian states

Understand

The entanglement negativity is a versatile measure of entanglement that has numerous applications in quantum information and in condensed matter theory.

• It can not only efficiently be computed in the Hilbert space dimension, but for non-interacting bosonic systems, one can compute the negativity efficiently in the number of modes.
• However, such an efficient computation does not carry over to the fermionic realm, the ultimate reason for this being that the partial transpose of a fermionic Gaussian state is no longer Gaussian.
• To provide a remedy for this state of affairs, in this work we introduce efficiently computable and rigorous upper and lower bounds to the negativity, making use of techniques of semi-definite programming, building upon the Lagrangian formulation of fermionic linear optics, and exploiting suitable products of Gaussian operators.