Physics – Quantum Physics
Scientific paper
2006-11-10
J.Phys.Conf.Ser.67:012045,2007
Physics
Quantum Physics
10 pages, 1 figure,LaTeX. Shorter version for proceedings requirements. Contributed paper at DICE2006, Piombino, Italy
Scientific paper
10.1088/1742-6596/67/1/012045
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.
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