Basic Logic and Quantum Computing: Logical Judgements by an Insider Observer

Logical Interpretation of a Reversible Measurement in Quantum Computing

We give the logical description of a new kind of quantum measurement that is a reversible operation performed by an hypothetical insider observer, or, which is the same, a quantum measurement made in a quantum space background, like the fuzzy sphere. The result is that the non-contradiction and the excluded middle principles are both invalidated, leading to a paraconsistent, symmetric logic. Our conjecture is that, in this setting, one can develop the adequate logic of quantum computing. The role of standard quantum logic is then confined to describe the projective measurement scheme.