## 1 Introduction
Similarly, researchers are exploring quantum-secure blockchain technologies to preserve the integrity of decentralized systems in a post-quantum world [9]. This dual-edge nature of quantum computing--its capacity to solve complex problems and its potential to disrupt established security paradigms--has fueled extensive investigation and development. Researchers and technologists are striving to balance these opportunities and challenges, emphasizing the need for innovative approaches to integrate quantum computing into existing digital ecosystems while mitigating its risks. The transition into the NISQ (Noisy Intermediate-Scale Quantum) era, characterized by limited quantum computational capabilities, underscores the urgency of addressing these challenges [10]. The security of the blockchain is built on mathematical challenges that are extremely difficult for even the most powerful conventional computers to solve. In these two distinct scenarios, starting from the works [11; 12; 13], the authors proposed an intrinsically quantum blockchain called MUREQUA, which is an acronym for Multiscale Relativistic Quantum Chain. In [13], the focus of the work was centered on two fundamental aspects of blockchain technologies. The first aspect regards the construction of keys resistant to quantum attacks, thanks to a specific computational infrastructure. It is intrinsically quantum from a conceptual point of view. The second aspect is the generation of consensus. It is based on a negotiation mechanism. In this paper, the attention will be moved to another relevant component of MUREQUA infrastructure, i.e., the decentralized storage component, with its capability to protect data and information. The solutions cited above as useful bibliographic references regarding the current state of the art highlight the importance and growing interest in storage and decentralized storage, as will also be discussed in the following section, dedicated to the topic of storage and its decentralization. Such storage is used as the main alternative to localized storage, such as servers, computational clusters, or the cloud. Regarding this aspect, the present work aims to address the topic of decentralization at a finer and more challenging level of granularity, where not the entire content is decentralized but rather its distribution pertains to its fragments. As we will see, this approach, along with other functional requirements that have been satisfied, provides the technological solution with a level of data security and protection far superior to current standards. Even conceptually, it requires a potential attacker to possess the capability to simultaneously attack multiple nodes of the infrastructure just to reconstruct a single file or piece of content. At the same time, it represents a significant challenge, as methodologies are required that allow the reconstruction of the original content after multiple encryption steps and after the fragments have been rendered dynamic. At the conclusion of the following section, after providing further details on the topic of storage and decentralized storage infrastructures, we will emphasize the fundamental issues that this solution seeks to address, in addition to what has already been described here regarding finer-grained decentralization. The present article is organized as follows. While Section 1 provides an introduction to the specific context of interest, Section 2 summarizes the main results in data storage to better highlight the novelty of the present work. Section 3 is dedicated to the scientific foundations of the work and all methodological aspects. Additionally, that section briefly presents the general architecture of the solution and its deployment for storage, in terms of both data upload and download.