Experimental SWAP test of infinite dimensional quantum states

Understand

Efficient overlap estimation of high-dimensional quantum states is an important task in quantum information and a core element in computational speedups of quantum machine learning.

• Here we experimentally demonstrate the SWAP test that measures the overlap of two motional states in a system of trapped $^{171}\mathrm{Yb}^+$ ions.
• To illustrate the versatility of our implementation, we report the overlap measurement of a variety of quantum states: Fock states, coherent states, squeezed vacuum states, and cat states.
• We highlight applications of the SWAP test by measuring the purity of mixed states.