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 all parties, and to send to 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 Quantum Private Broadcasting ($t$-QPB) and compare them in terms of key lengths. The first method is the independent encryption with the quantum one-time pad, which requires a key linear in the number of recipients, $t$. We show that the key length can be decreased to be logarithmic in $t$ by using unitary $t$-designs. Our main contribution is to show that this can be improved to a key length that is logarithmic in the dimension of the symmetric subspace, using a new concept that we define of symmetric unitary $t$-designs, that may be of independent interest.

References in corpus (9)

• Evenly distributed unitaries: on the structure of unitary designs
• Randomizing quantum states: Constructions and applications
• Optimizing quantum process tomography with unitary 2-designs
• Unitary designs and codes
• The Clifford group fails gracefully to be a unitary 4-design
• Computing the distance between quantum channels: Usefulness of the Fano representation
• Quantum circuits for exact unitary $t$-designs and applications to higher-order randomized benchmarking
• Randomized Benchmarking Using Unitary t-Design for Average Fidelity Estimation of Practical Quantum Circuit
• Private quantum channels for multi-photon pulses and unitary k-designs