Generation of entanglement via single-qubit rotation in torn Hilbert space

We present an efficient and simple protocol for generating arbitrary symmetric entangled states in a torn Hilbert space using only global single-qubit rotations.

The system is based on spin 1/2 qubits in resonators, such as atoms in optical cavities or superconducting qubits coupled to metallic microwave resonators. By sending light or microwaves into the resonator, it induces an AC Stark shift in the qubit's specific angular momentum eigenstate (Dick state). We can then generate barriers that impede transitions between adjacent Dick states,<br _istranslated="1" _mstmutation="1" /> And tear the original Hilbert space into pieces. Therefore, a simple global single-qubit rotation becomes very non-trivial, creating entanglement between many-body systems.

By optimally controlling the energy shift of the Dick state, we can generate any symmetric entangled state. We also illustrate that in just one or a few steps we can create a variety of useful states with near-uniform fidelity, including W states, spin-squeezed states (SSS), and Greenberger-Horne-Zeilinger (GHZ) states. In particular, SSS can only be created in one step with a compression parameter $\xi_R^2\sim1/N^{0.843}$ close to the Heisenberg limit (HL). Our findings establish a method for universal entanglement generation using only single-qubit actuation, where all multi-qubit control is integrated into a simple on/off microwave. It has direct applications in variational quantum optimizers available with existing technology.