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and the similarly named, but different, quantum secret sharing protocol pro-
posed by Hillery et al. [2]. In Section 8.4 we discuss how to implement exper-
imentally and characterize a (2,3) threshold quantum state sharing protocol.
Section 8.5 shows the first experimental demonstration of a nontrivial thresh-
old quantum state sharing scheme. Finally, Section 8.6 presents an outlook on
the applications of this protocol.
8.2 Classical Secret Sharing
The first formal allusion to secret sharing (though not using this nomencla-
ture) was made by Liu [3] through a simple combinatorial problem in the
late 1960s. Liu's problem is illustrated in Figure 8.2. Suppose a group of 11
Figure 8.2 The problem of Liu's vault. How many locks on the vault, and how many
keys do the scientists (Felix Bloch, Satyendranath Bose, Erwin Schr odinger, Marie
Curie, Albert Einstein, David Hilbert, Hendrick Lorentz, Max Planck, Louis de Broglie,
Paul Dirac, and Wolfgang Pauli) need to have so that any permutation of six or more
of them will be able to open the vault?
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