Multiple photon subtraction from Gaussian states cannot produce arbitrary non-Gaussian quantum states of light
Christos N. Gagatsos, Saikat Guha · arXiv (Cornell University) · 2019
Gaussian states and measurements collectively are not powerful-enough resources for quantum computing, as any Gaussian dynamics can be simulated efficiently, classically. Photon subtraction from squeezed vacuum---a single-mode Gaussian state in quantum optics---can produce an approximate cat state, a macroscopic superposition of two coherent states. Furthermore, it is known that any one non-Gaussian Hamiltonian, along with Gaussian unitaries, makes for universal quantum resources. Photon subtraction, a readily-realizable non-Gaussian operation, therefore, has been a popular tool to try and engineer non-Gaussian states for universal quantum processing. In this paper, we give a formula to calculate the fidelity between a non-Gaussian target state and the heralded state resulting from an $N$-mode Gaussian state subjected to multi-mode, multi-photon subtraction. We also derive an easy-to-calculate upper bound of said fidelity. Then, we consider an example of an $N$-mode coherent cat-basis cluster state (CCCS), a resource sufficient for universal quantum computing---and prove that the fidelity between the state produced by photon subtraction on any Gaussian state and the CCCS cannot be more than $1/2^N$. Further, we prove that photon subtraction can be used to prepare states whose fidelity with coherent GHZ states is very close to one.