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Giuseppe Sergioli

Publications and source records attributed to Giuseppe Sergioli.

23 records · Page 2Linked to original sources
arXiv2016

Holistic logical arguments in quantum computation

Quantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters), while logical connectives correspond to (quantum logical) gates that transform quantum information in a reversible way. The characteristic holistic features of the quantum theoretic formalism (which play an essential role in entanglement-phenomena) can be used in order to develop a holistic version of the quantum computational semantics. In contrast with the compositional character of most standard semantic approaches, meanings of formulas are here dealt with as global abstract objects that determine the contextual meanings of the formulas' components (from the whole to the parts). We present a survey of the most significant logical arguments that are valid or that are possibly violated in the framework of this semantics. Some logical features that may appear prima facie strange seem to reflect pretty well informal arguments that are currently used in our rational activity.

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arXiv2016

Quantum Approach to Epistemic Semantics

Quantum information has suggested new forms of quantum logic, called quantum computational logics, where meanings of sentences are represented by pieces of quantum information (generally, density operators of some Hilbert spaces), which can be stored and transmitted by means of quantum particles. This approach can be applied to a semantic characterization of epistemic logical operations, which may occur in sentences like "At time t0 Bob knows that at time t Alice knows that the spin-value is up". Each epistemic agent (say, Alice, Bob,...) has a characteristic truth-perspective, corresponding to a particular orthonormal basis of the Hilbert space C^2. From a physical point of view, a truth-perspective can be associated to an apparatus that allows one to measure a given observable. An important feature that characterizes the knowledge of any agent is the amount of information that is accessible to him/her (technically, a special set of density operators, which also represents the internal memory of the agent in question). One can prove that interesting epistemic operations are special examples of quantum channels, which generally are not unitary. The act of knowing may involve some intrinsic irreversibility due to possible measurement procedures or to a loss of information about the environment. We also illustrate some relativistic-like effects that arise in the behavior of epistemic agents.

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arXiv2016

A note on many valued quantum computational logics

The standard theory of quantum computation relies on the idea that the basic information quantity is represented by a superposition of elements of the canonical basis and the notion of probability naturally follows from the Born rule. In this work we consider three valued quantum computational logics. More specifically, we will focus on the Hilbert space C^3, we discuss extensions of several gates to this space and, using the notion of effect probability, we provide a characterization of its states.

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arXiv2013

Counting Steps: A New Approach to Objective Probability in Physics

We propose a new interpretation of objective deterministic chances in statistical physics based on physical computational complexity. This notion applies to a single physical system (be it an experimental set--up in the lab, or a subsystem of the universe), and quantifies (1) the difficulty to realize a physical state given another, (2) the `distance' (in terms of physical resources) of a physical state from another, and (3) the size of the set of time--complexity functions that are compatible with the physical resources required to reach a physical state from another. This view (a) exorcises "ignorance" from statistical physics, and (b) underlies a new interpretation to non--relativistic quantum mechanics.

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