Quantum Multi-Proxy Signature Scheme Based on W State

With the in-depth study of quantum signatures, people pay more attention to and use entangled states such as Bell states and GHZ states, but pay less attention to other entangled states such as <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$W$</tex> states. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$W$</tex> state and GHZ state are both one of the main three-particle entangled states. In terms of the degree of entanglement, although the GHZ state is the maximum entangled state of three particles, if one of the particles is lost, the other particles will completely lose their entanglement correlation. Although the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\mathbf{W}$</tex> state is not in the maximum entangled state like the GHZ state, it is more robust and the entanglement is more difficult to eliminate. In the case of losing one particle, it will not affect the entangled state of the other two particles. We can infer that applying the W state to quantum signatures can produce better results. Therefore, this chapter proposes a quantum multiproxy signature scheme based on the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$W$</tex> state.