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”.
Highlights
Quantum information and quantum computation have inspired new developments of some basic concepts of the quantum theoretic formalism, which for a long time had been regarded as mysterious and potentially paradoxical. In this framework the concept of quantum probability has been investigated according to new perspectives, giving rise to possible applications to fields that are far apart from microphysics
The basic idea of quantum computation theory is that information can be stored and transmitted by quantum physical objects
Pieces of quantum information can be identified with states of some special quantum systems that are storing the information in question
Summary
Quantum information and quantum computation have inspired new developments of some basic concepts of the quantum theoretic formalism, which for a long time had been regarded as mysterious and potentially paradoxical. A piece of quantum information corresponds to a complex knowledge that can be mathematically represented as a pure or mixed state of a composite quantum system: a density operator ρ of a finite-dimensional Hilbert space whose standard form is. The theory of quantum circuits has inspired a natural logical abstraction, giving rise to the development of new forms of quantum logic that have been termed quantum computational logics In these logics, formulas are supposed to denote pieces of quantum information, while logical connectives are interpreted as special examples of gates. A typical example is represented by teleportation-experiments, where an agent (say, Alice) transmits qubit-states to a far agent (say, Bob), by using some special quantum non-locality phenomena, which may appear prima facie strange and mysterious These puzzling (non-classical) situations have inspired new ideas in the field of epistemic logics. In this article we will investigate another epistemic concept: the operation “being probabilistically informed”, which plays a significant role in a number of interesting quantum situations (for instance, in the case of quantum teleportation-experiments)
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