Dynamic hierarchical quantum secret sharing based on the multiscale entanglement renormalization ansatz

Tensor networks offer a novel and powerful tool for solving a variety of problems in mathematics, data science, and engineering. One such network is the multiscale entanglement renormalization ansatz (MERA). The MERA exhibits a hierarchical structure of layers, where each layer corresponds to a particular length (or energy) scale. The structure can be easily constructed using isometric and disentangler transformations. The following question arises: Is it possible to use the MERA to build hierarchical quantum secret sharing (HQSS)? The paper answers the question in the affirmative. In particular, it shows how a hierarchy of participant trust and authority relates to a MERA structure. The structure consists of binary and ternary MERA modules, which generate secret shares for participants. Because a binary MERA can be replaced by its ternary sibling and vice versa, our HQSS scheme is dynamic, allowing promotion and demotion of participants from the different layers but also enrollment of new ones and disenrollment of old ones from the same layer. The correctness and security of our dynamic hierarchical quantum secret sharing scheme are discussed.

Figure 1

Hilbert space coarse graining with one block equal to two sites.

Figure 2

Flow chart of the real-space renormalization-group transformation for (a) the binary MERA and (b) the ternary MERA.

Figure 3

Illustration of our proposed DHQMBSS based on the binary and the ternary MERA.

Figure 4

Graphical presentation of how the isometry $W$ and the noninjectivity of $W^{†}$ would work in the binary and the ternary MERA.