Quantum spectral authentication: entity authentication and key derivation from a hidden eigenstate of a public unitary challenge

Abstract We introduce Quantum Spectral Authentication (QSA), a symmetric-key entity-authentication and key-derivation protocol in which a remote endpoint proves it still holds a hidden planted state, an eigenstate of the challenge it can prepare, without revealing it. Each round issues a fresh public unitary challenge with its own planted state, and the endpoint returns an eigenphase feature from which both parties derive transcript-bound session material. QSA runs in two provisioning modes with materially different security: a seed mode , storing a classical seed that regenerates the planted state, and a state mode , holding only the physical register carrying it, non-copyable and consumed on use. We give a formal security model in which QSA is an identification scheme, prove mutual authentication under a single label-hiding assumption, and prove unconditionally that the published spectrum is near-uniform at the readout resolution, leaving at least m-1 bits of min-entropy per instance; state mode satisfies the assumption by construction. We develop a symmetric verifier-driven compiler compatible with low-depth quantum phase estimation, which also admits a fast path that recovers the label by an inverse-compiler measurement. Simulations show it is more noise-tolerant than an asymmetric alternative, and experiments on IBM _ provide a hardware sanity check.