Universal Control of Symmetric States Using Spin Squeezing

The manipulation of quantum many-body systems is a crucial goal in quantum science. Entangled quantum states that are symmetric under qubits permutation are of growing interest. Yet, the creation and control of symmetric states has remained a challenge. Here, we introduce a method to universally control symmetric states, proposing a scheme that relies solely on coherent rotations and spin squeezing. We present protocols for the creation of different symmetric states including Schrödinger's cat and Gottesman-Kitaev-Preskill states. The obtained symmetric states can be transferred to traveling photonic states via spontaneous emission, providing a powerful approach for engineering desired quantum photonic states.