No-go theorems for quantum information theory and computational logic for variable lenght quantum registers

In this dissertation we take in account the possibility to face the notion of quantum information from two different points of view: meanwhile in the first part we develop a concrete approach to the notion of quantum information, in the second part we proceed to a more abstract approach. The firts part explores what quantum mechanics forbids to do with information encoded in states of quantum systems. Many of the results of researches about what we can and what we can t do with the information encoded in quantum states are known as no-go theorems; in this dissertation we explore new limitations on the possibility to manipulate quantum information revealing that many easy tasks for classical information are impossible when the information is encoded in quantum states. As result of our analysis it arises that the nature of information encoded in quantum states restricts in a very structured way the possible manipulations or exact behaviour of the operations on the information itself. In the second part of dissertation we concentrate on logic-algebraich approach to quantum information. We relax the condition of a quantum circuit constitued by a fixed number of particles and we take in account a quantum system of variable and undeterminate number of particles. This approach is developed in the mathematical framework of Fock space which allows a more flexible treatment of information encoded in quantum register of variable lenght. As consequence, we proceed towards a possible logic-algebraic formalization of the behaviour of quantum information encoded in variable lenght registers during a computational process.