Quantum Private Broadcasting

Abstract

In Private Broadcasting, a single plaintext is broadcast to multiple recipients in an encrypted form, such that each recipient can decrypt locally. When the message is classical, a straightforward solution is to encrypt the plaintext with a single key shared among the parties, and to send each recipient a copy of the ciphertext. Surprisingly, the analogous method is insufficient in the case where the message is quantum (i.e. in Quantum Private Broadcasting (QPB)). In this work, we give three solutions to t-recipient QPB and compare them in terms of encryption key length. We examine independent encryption with the quantum one-time pad, unitary t-designs, and a new concept we define as symmetric unitary t-designs. Of these three, symmetric t-designs are the best choice when t is large, and these symmetric designs may be of independent interest beyond QPB.