Dynamic and compressed quantum many-body state secret sharing based on site-independent matrix product states

Tensor network states, in which tensor networks are used to encode the coefficients of a state wavefunction, have been proposed for the study of quantum many-body systems. The most common tensor network state is matrix product state (MPS). Furthermore, we can change the tensor in an MPS but not the quantum state it represents (that is, we only change its mathematical representation, not its actual physical quantity). Most importantly, MPS can be faithfully compressed. However, a dynamic and compressed quantum many-body state secret sharing scheme has yet to be proposed, which is important in practical settings. Therefore, based on the characteristics of site-independent matrix product states, we focus our attention in this paper on the scenario where the shared quantum state is large, but quantum storage resources are limited, and the number of participants can be dynamically adjusted to fill this gap and develop a dynamic and compressed quantum many-body state secret sharing scheme. The notable features of our scheme are that (i) the quantum secret state is faithfully compressed, (ii) the dynamic property is achieved by tensor contraction, tensor addition, and tensor subtraction of MPS form corresponding to the change in the number of quantum participants and the shared quantum many-body state update or quantum participant’s replacement, (iii) our scheme allows for the sharing of a large volume of quantum data in an inherently multipartite way, and (iv) the amount of quantum storage required by participants can be reduced exponentially.