Quantum private broadcasting

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 classical, straightforward solution encrypt with key shared among all parties, and send copy of ciphertext. Surprisingly, analogous method insufficient case where quantum (i.e. Quantum Broadcasting (QPB)). this work, we give three solutions $t$-recipient ($t$-QPB) compare them terms lengths. The first independent encryption one-time pad, which requires linear number recipients, $t$. We show length be decreased logarithmic $t$ by using unitary $t$-designs. Our main contribution improved dimension symmetric subspace, new concept define $t$-designs, may interest.