International Iberian Nanotechnology Laboratory (INL), Portugal, ernesto.galvao@inl.int
(joint work with Daniel J. Brod and Rui Soares Barbosa)
A SWAP test is a quantum circuit that measures the overlaps rρσ = Tr(ρσ) between two states ρ,σ. If we consider a set of n quantum states, different bounds on two-state overlaps result when we consider either i) diagonal, coherence-free states, or ii) general quantum states. The difference between i) and ii) allowed us to propose novel basis-independent coherence witnesses [1]. I will show that the inequalities for overlaps of coherence-free states correspond to noncontextuality and locality inequalities, which suggests a unified framework for resource theories of coherence, contextuality and nonlocality.
[1] E. F. Galvão and D. J. Brod. Quantum and classical bounds for two-state overlaps. Phys. Rev. A 101, 062110 (2020). https://arxiv.org/abs/1902.11039