Quantum secret sharing with multilevel mutually (un)biased bases

We construct general schemes for multipartite quantum secret sharing using multilevel systems, and find that the consistency conditions for valid measurements can be summarized in two simple algebraic conditions. The scheme using very high-dimensional mutually unbiased bases can in principle achieve perfect security against intercept-resend attack; and for the scheme using mutually biased bases, it reaches the optimal but nonperfect security at the four-level system. We also address the security issue against general attacks in the context of our multilevel schemes. In particular, we propose a protocol to enhance both the efficiency and the security against an entanglement-assisted participant's attack by incorporating quantum-key-distribution and measurement-basis-encrypted schemes so that its security is as robust as quantum-key distribution.