Quantum learning can scale with reflected states, bypassing size limits

The work reveals that learning bosonic quantum states with protocols avoiding entanglement requires sample complexity that grows exponentially with the number of modes in the system. However, researchers found combining reflected states with entangled measurements bypasses this limitation, achieving a sample complexity independent of system size. These results identify when efficient learning of continuous-variable states requires full quantum resources, and when simpler strategies suffice. This limitation, however, is not absolute, as scientists have demonstrated a pathway to circumvent these size constraints by strategically combining reflected states with entangled measurements. The work establishes conditions under which efficient learning of continuous-variable states necessitates the full use of quantum resources. The research team proved that any entanglement-free learning scheme requires an exponentially increasing number of samples as the…