Witness expansion: A unified framework for detecting quantum resources in mixed states

Quantum information science aims to harness different kinds of quantum resources to accomplish specific information-processing tasks.

We propose witness expansion, a unified framework for constructing nonlinear criteria for detecting quantum resources that are associated with a well-defined group of free unitaries.

These criteria apply to both pure and mixed quantum states and are based on polynomial functions of the target state, which can be estimated experimentally using multiple copies of the state and evaluated analytically in certain physical models.

We show how several well-known resource-detection quantities naturally emerge from our framework, including the $l_2$ norm of coherence, partial-transpose moments for entanglement, stabilizer entropy for nonstabilizerness (quantum magic), and fermionic antiflatness for fermionic non-Gaussianity.

It gives, to the best of our knowledge, the first analytical criterion for detecting mixed-state fermionic non-Gaussianity with respect to the convex hull of pure fermionic Gaussian states that remains nontrivial for arbitrary numbers of qubits.