Probabilities and Epistemic Operations in the Logics of Quantum Computation

Abstract

Quantum computation theory has inspired new forms of quantum logic, called quantum computational logics, where formulas are supposed to denote pieces of quantum information, while logical connectives are interpreted as special examples of quantum logical gates. The most natural semantics for these logics is a form of holistic semantics, where meanings behave in a contextual way. In this framework, the concept of quantum probability can assume different forms. We distinguish an absolute concept of probability, based on the idea of quantum truth, from a relative concept of probability (a form of transition-probability, connected with the notion of fidelity between quantum states). Quantum information has brought about some intriguing epistemic situations. A typical example is represented by teleportation-experiments. In some previous works we have studied a quantum version of the epistemic operations “to know”, “to believe”, “to understand”. In this article, we investigate another epistemic operation (which is informally used in a number of interesting quantum situations): the operation “being probabilistically informed”.

Quantum Probability and Randomness

“…The connection between quantum logic and quantum probability is highlighted by Dalla Chiara et al [ 25 ] in the paper entitled Probabilities and Epistemic Operations in the Logics of Quantum Computation. The authors stress that quantum computation theory has inspired new forms of quantum logic, called quantum computational logics.…”