Marek Żukowski

Armin Tavakoli, Isabelle Herbauts, Marek Zukowski et al.

We give an example of a wide class of problems for which quantum information protocols based on multi-system entanglement can be mapped into much simpler ones involving one system. Secret sharing is a cryptographic primitive which plays a central role in various secure multiparty computation tasks and management of keys in cryptography. In secret sharing protocols, a classical message is divided into shares given to recipient parties in such a way that some number of parties need to collaborate in order to reconstruct the message. Quantum protocols for the task commonly rely on multi-partite GHZ entanglement. We present a multiparty secret sharing protocol which requires only sequential communication of a single quantum d-level system (for any prime d). It has huge advantages in scalabilility and can be realized with the state of the art technology. n be realized with the state of the art technology.

Ramij Rahaman, Marcin Wieśniak, Marek Żukowski

We present a device-independent quantum scheme for the {\em Byzantine Generals} problem. The protocol is for three parties. Party $C$ is to send two identical one bit messages to parties $A$ and $B$. The receivers $A$ and $B$ may exchange two one bit messages informing the other party on the message received from $C$. A bit flipping error in one of the transmissions, does not allow the receiving parties to establish what was the message of $C$. Our quantum scheme has the feature that if the messages of the Byzantine protocol are readable (that is give an unambiguous bit value for any of the receivers), then any error by $C$ (cheating by one of the commanding general) is impossible. $A$ and $B$ do not have to exchange protocol messages to be sure of this.