arXiv subjects

Roberto Leporini

Publications and source records attributed to Roberto Leporini.

11 recordsLinked to original sources

arXiv2025

An Operational Quantum Information Framework for Experimental Studies on Color Perception

Starting from the foundational axiomatization of the perceptual color space initiated by Schr\"odinger in 1920 and eventually refined by Resnikoff in 1974, Berthier, Provenzi and their collaborators have recently proposed a reformulation of perceptual color attributes within the framework of quantum information. Their work is based on the Jordan algebra formalism of quantum theories and, more specifically, on a quantum system described by a spin factor over the field of real numbers. This theoretical framework is not that of ordinary quantum mechanics, mainly because it requires dealing with rebits, whereas the latter uses qubits. The aim of this paper is to show that this difference in no way hinders the implementation of experimental protocols for testing the validity of the predictions of the color perception model. In particular, we show how to compute the quantum information based perceptual attributes of perceived colors in terms of qubit density matrices.

q-bio.NC↗

arXiv2025

Identifying Quantum Structure in AI Language: Evidence for Evolutionary Convergence of Human and Artificial Cognition

We present the results of cognitive tests on conceptual combinations, performed using specific Large Language Models (LLMs) as test subjects. In the first test, performed with ChatGPT and Gemini, we show that Bell's inequalities are significantly violated, which indicates the presence of a 'non-classical probability model' with probabilities that do not satisfy Kolmogorov's axioms. In the second test, also performed using ChatGPT and Gemini, we identify the presence of 'Bose-Einstein statistics', rather than the intuitively expected 'Maxwell-Boltzmann statistics', in the distribution of the words contained in large-size texts. Interestingly, these findings mirror the results previously obtained in both cognitive tests with human participants and information retrieval tests on large corpora. Taken together, they point to the 'systematic emergence of non-classical quantum-like structures in conceptual-linguistic domains', regardless of whether the cognitive agent is human or artificial. Although LLMs are classified as neural networks for historical reasons, we believe that a more essential form of knowledge organization takes place in the distributive semantic structure of vector spaces built on top of the neural network. It is this meaning-bearing structure that lends itself to a phenomenon of evolutionary convergence between human cognition and language, slowly established through biological evolution, and LLM cognition and language, emerging much more rapidly as a result of self-learning and training. We analyze various aspects and examples that contain evidence supporting the above hypothesis. We also advance a unifying framework that explains the pervasive quantum organization of meaning that we identify.

cs.CL↗

arXiv2025

Bell's Inequalities and Entanglement in Corpora of Italian Language

We analyze the results of three information retrieval tests on conceptual combinations that we have recently performed using corpora of Italian language. The tests have the form of a 'Bell-type test' and were aimed at identifying 'quantum entanglement' in the combination, or composition, of two concepts. In the first two tests, we studied the Italian translation of the combination 'The Animal Acts', while in the third test, we studied the Italian translation of the combination 'The Animal eats the Food'. We found a significant violation of Bell's inequalities in all tests. Empirical patterns confirm the results obtained with corpora of English language, which indicates the existence of deep structures in concept formation that are language-independent. The systematic violation of Bell's inequalities suggests the presence of entanglement and, indeed, we elaborate here a 'quantum model in Hilbert space' for the collected data. This investigation supports our theoretical hypothesis about entanglement as a phenomenon of 'contextual updating', independently of the nature, micro-physical or conceptual linguistic, of the entities involved. Finally, these findings allow us to further clarify the mutual relationships between entanglement, Cirel'son's bound, and no-signaling in Bell-type situations.

q-bio.NC↗

arXiv2024

Turing Video-based Cognitive Tests to Handle Entangled Concepts

We have proved in both human-based and computer-based tests that natural concepts generally 'entangle' when they combine to form complex sentences, violating the rules of classical compositional semantics. In this article, we present the results of an innovative video-based cognitive test on a specific conceptual combination, which significantly violates the Clauser-Horne-Shimony-Holt version of Bell's inequalities ('CHSH inequality'). We also show that collected data can be faithfully modeled within a quantum-theoretic framework elaborated by ourselves and a 'strong form of entanglement' occurs between the component concepts. While the video-based test confirms previous empirical results on entanglement in human cognition, our empirical approach surpasses language barriers and eliminates the need for prior knowledge, enabling universal accessibility. Finally, this transformative methodology allows one to unravel the underlying connections that drive our perception of reality. As a matter of fact, we provide a novel explanation for the appearance of entanglement in both physics and cognitive realms.

q-bio.NC↗

arXiv2017

A discussion about LNG Experiment: Irreversible or Reversible Generation of the OR Logic Gate?

In a recent paper M. Lopez-Suarez, I. Neri, and L. Gammaitoni (LNG) present a concrete realization of the Boolean OR irreversible gate, but contrary to the standard Landauer principle, with an arbitrary small dissipation of energy. A Popperian good falsification! In this paper we discuss a theoretical description of the LNG device which is indeed a 3in/3out self--reversible realization of the involved OR gate, satisfying in this way the Landauer principle of no dispersion of energy, contrary to the LNG conclusions. The different point of view is due to a different interpretation of the two outputs corresponding to the inputs 10 and 01, which are considered by LNG indistinguishable so producing a non reversible realization of the standard 2in/1out gate. On the contrary, always considering these two outputs indistinguishable, by a suitable normalization function of the cantilever angles, the experimental results obtained by the LNG device coincide with the OR connective obtained from the third output of the self-reversible 3in/3out CL gate by the Inputs-Ancilla->Garbage-Output procedure. Thus, by the self-reversibility this realization is without dissipation of energy according to the Landauer principle. Furthermore, using the self-reversible Toffoli gate it is possible to obtain from the LNG device the realization of the connective AND adopting another normalization function on the cantilever angles. Finally, by other suitable normalization procedures on cantilever angles it is possible to obtain also the other logic NOR and NAND connectives, and in a more sophisticated way the XOR and NXOR connectives in a self-reversible way. All this leads to introduce a universal logic machine consisting of the LNG device plus a memory containing all the necessary angle normalization functions to produce in a self-reversible way, by choosing one of these latter, the logic connectives now listed.

cs.ET↗

arXiv2016

A Quantum Computational Semantics for Epistemic Logical Operators. Part I: Epistemic Structures

Some critical open problems of epistemic logics can be investigated in the framework of a quantum computational approach. The basic idea is to interpret sentences - like Alice knows that Bob does not understand that Pi is irrational - as pieces of quantum information (generally represented by density operators of convenient Hilbert spaces). Logical epistemic operators (to understand, to know ...) are dealt with as (generally irreversible) quantum operations, which are, in a sense, similar to measurement-procedures. This approach permits us to model some characteristic epistemic processes, that concern both human and artificial intelligence. For instance, the operation of \memorizing and retrieving information" can be formally represented, in this framework, by using a quantum teleportation phenomenon.

quant-ph↗

arXiv2016

A Quantum Computational Semantics for Epistemic Logical Operators. Part II: Semantics

By using the abstract structures investigated in the first Part of this article, we develop a semantics for an epistemic language, which expresses sentences like "Alice knows that Bob does not understand that PI is irrational". One is dealing with a holistic form of quantum computational semantics, where entanglement plays a fundamental role, thus, the meaning of a global expression determines the contextual meanings of its parts, but generally not the other way around. The epistemic situations represented in this semantics seem to reflect some characteristic limitations of the real processes of acquiring information. Since knowledge is not generally closed under logical consequence, the unpleasant phenomenon of logical omniscience is here avoided.

quant-ph↗

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.

quant-ph↗

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.

quant-ph↗

arXiv2003

Towards a Theory of Conservative Computing

We extend the notion of conservativeness, given by Fredkin and Toffoli in 1982, to generic gates whose input and output lines may assume a finite number d of truth values. A physical interpretation of conservativeness in terms of conservation of the energy associated to the data used during the computation is given. Moreover, we define conservative computations, and we show that they naturally induce a new NP-complete decision problem. Finally, we present a framework that can be used to explicit the movement of energy occurring during a computation, and we provide a quantum implementation of the primitives of such framework using creation and annihilation operators on the Hilbert space C^d, where d is the number of energy levels considered in the framework.

quant-ph↗

arXiv2002

Fredkin Gates for Finite-valued Reversible and Conservative Logics

The basic principles and results of Conservative Logic introduced by Fredkin and Toffoli on the basis of a seminal paper of Landauer are extended to d-valued logics, with a special attention to three-valued logics. Different approaches to d-valued logics are examined in order to determine some possible universal sets of logic primitives. In particular, we consider the typical connectives of Lukasiewicz and Godel logics, as well as Chang's MV-algebras. As a result, some possible three-valued and d-valued universal gates are described which realize a functionally complete set of fundamental connectives.

quant-ph↗