Paola Zizzi

QUBITS AND QUANTUM SPACES

We consider the quantum computational process as viewed by an insider observer: this is equivalent to an isomorphism between the quantum computer and a quantum space, namely the fuzzy sphere. The result is the formulation of a reversible quantum measurement scheme, with no hidden information.

Basic logic and quantum entanglement

As it is well known, quantum entanglement is one of the most important features of quantum computing, as it leads to massive quantum parallelism, hence to exponential computational speed-up. In a sense, quantum entanglement is considered as an implicit property of quantum computation itself. But... can it be made explicit? In other words, is it possible to find the connective entanglement in a logical sequent calculus for the machine language? And also, is it possible to teach the quantum computer to mimic the EPR paradox? The answer is in the affirmative, if the logical sequent calculus is that of the weakest possible logic, namely Basic logic. - A weak logic has few structural rules. But in logic, a weak structure leaves more room for connectives (for example the connective entanglement). Furthermore, the absence in Basic logic of the two structural rules of contraction and weakening corresponds to the validity of the no-cloning and no-erase theorems, respectively, in quantum computing.