Digital Signatures with Classical Shadows of Random Circuits

Classical cryptography relies on several foundational theoretical assumptions, and the invalidation of these conjectures could render many existing cryptographic protocols insecure. Quantum cryptography, however, offers resilience even in such scenarios, with digital signature schemes that utilize quantum communication as a notable example. In this work, we introduce a quantum digital signature scheme that operates without the need for quantum communication. We experimentally demonstrate a key building block of our protocol on a trapped-ion quantum processor, achieving fidelity beyond the required threshold.