Given a ciphertext, is it possible to prove the deletion of the underlying plaintext? Since classical ciphertexts can be copied, clearly such a feat is impossible using classical information alone... In stark contrast to this, we show that quantum encodings enable certified deletion. More precisely, we show that it is possible to encrypt classical data into a quantum ciphertext such that the recipient of the ciphertext can produce a classical string which proves to the originator that the recipient has relinquished any chance of recovering the plaintext should the decryption key be revealed. Our scheme is feasible with current quantum technology: the honest parties only require quantum devices for single-qubit preparation and measurements; the scheme is also robust against noise in these devices. Furthermore, we provide an analysis that is suitable in the finite-key regime. (read more)