arXiv subjects

Flavio Del Santo

Publications and source records attributed to Flavio Del Santo.

At least 19 recordsLinked to original sources

arXiv2026

Entanglement without Quantum Mechanics: Operational Constraints on the Quantum Signature

Quantum entanglement is defined as nonseparability of density operators, yet experimental phase-space statistics alone cannot distinguish classical from quantum sources, so classical data can be used to violate en- tanglement inequalities. Imposing uncertainty bounds, or full tomography, can map the same data onto positive, entangled density operators, yielding a hybrid regime in which classical and quantum models coincide. Thus, certifying genuine quantum entanglement requires additional tests, such as Wigner negativity, incompatibility beyond phase-space measurements, or nonlinear dynamics.

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arXiv2026

Reply to the Comment on "The Axiom of Choice and the No-Signalling Principle"

We clarify the meaning of a probabilistic no-signalling strategy in Ref [Proc. R. Soc. A 481, 20240601]. For every fixed input, the deterministic strategy constructed using the Axiom of Choice can indeed be represented by a Dirac probability distribution over the outputs. The relevant distinction arises when one considers the complete process from input to output, with the input itself sampled according to a probability distribution. In this case, the input and output spaces must be measurable and the dependence of the conditional output distribution on the input must also be measurable. Equivalently, the conditional distributions must form a Markov kernel. The Axiom-of-Choice strategy fails precisely this measurability requirement.

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arXiv2026

Was Schrödinger ever a determinist?

Erwin Schrödinger is often portrayed as a reactionary who resisted the indeterminism introduced by quantum mechanics, but on closer inspection his views on determinism prove to be more complex and more radical.

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arXiv2026

Classical and quantum mechanics across representations: an operational reading of the Wigner Weyl correspondence

The physical content of a theory is not intrinsically tied to any single mathematical formalism. Both classical and quantum mechanics admit equivalent representations, notably in phase space and in Hilbert space, related by the Wigner-Weyl correspondence. While this correspondence has long been studied in mathematical physics, its foundational and operational implications are often left implicit. Here we give a systematic account of what changes, and what does not, when classical and quantum theories are expressed in each other's native language. This representational viewpoint separates artifacts (such as the appearance of non-positivity or negativity under certain maps) from robust structural distinctions that persist across representations, in particular noncommutativity and its $\hbar$-dependent $\star$-deformation of the classical algebra. We develop the comparison at the level of states, kinematics, and dynamics, and extend it to measurement by formulating both outcome statistics and state-update rules within the same framework.

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arXiv2026

Superluminal Transformations and Indeterminism

Quantum theory is widely regarded as fundamentally indeterministic, yet classical frameworks can also exhibit indeterminism once infinite information is abandoned. At the same time, relativity is usually taken to forbid superluminal signalling, although Lorentz symmetry formally admits superluminal transformations (SpTs). Dragan and Ekert have argued that SpTs entail a form of indeterminism analogous to that encountered in quantum theory. Here, we derive a theory-independent no-go theorem from a set of natural assumptions: any framework admitting non-order-preserving SpTs must either abandon finite information, relinquish time-symmetric informational content, deny that the past stores memory, or abandon the notion that time determines a preferred causal ordering. In particular, one possible implication is that any theory accommodating SpTs suggests an ontology with unbounded informational content, akin to deterministic classical theories formulated over the real numbers. Consequently, any ontic indeterminacy associated with superluminal transformations cannot originate from finite information.

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arXiv2026

Creative and geometric times in physics, mathematics, logic, and philosophy

We distinguish two different concepts of time that play a role in physics: \textit{geometric time} and \textit{creative time}. The former is the time of deterministic physics and merely parametrizes a given evolution. The latter is instead characterized by real change, i.e. novel information that gets created when a non-necessary event becomes determinate in a fundamentally indeterministic physics. This allows one to give a naturalistic characterization of the present as the moment that separates the potential future from the determinate past. We discuss how these two concepts find natural applications in classical and intuitionistic mathematics, respectively, and in classical and intuitionistic logic, as well as how they relate to the well-known A- and B-theories in the philosophy of time. We acknowledge that we do not offer here a unified concept or a new philosophy of time. However, we contend that none of the existing philosophical accounts fully integrate both the geometric and creative concepts of time.

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arXiv2025

Classification of joint quantum measurements based on entanglement cost of localization

Despite their importance in quantum theory, joint quantum measurements remain poorly understood. An intriguing conceptual and practical question is whether joint quantum measurements on separated systems can be performed without bringing them together. Remarkably, by using shared entanglement, this can be achieved perfectly when disregarding the post-measurement state. However, existing localization protocols typically require unbounded entanglement. In this work, we address the fundamental question: "Which joint measurements can be localized with a finite amount of entanglement?" We develop finite-resource versions of teleportation-based schemes and analytically classify all two-qubit measurements that can be localized in the first steps of these hierarchies. These include several measurements with exceptional properties and symmetries, such as the Bell state measurement and the elegant joint measurement. This leads us to propose a systematic classification of joint measurements based on entanglement cost, which we argue directly connects to the complexity of implementing those measurements. We illustrate how to numerically explore higher levels and construct generalizations to higher dimensions and multipartite settings.

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arXiv2025

Naturalistic intuitionism for physics

Recently, a novel intuitionistic reconstruction of the foundations of physics has been primarily developed by Nicolas Gisin and Flavio Del Santo drawing on naturalism. Our goal in this paper is to examine and develop the philosophical background of their naturalistic intuitionism for physics in contrast with Brouwer's defense of his intuitionistic mathematics. To be exact, we propose a systematic rearticulation of Brouwer's so-called two acts of intuitionism to serve as the self-contained philosophical framework justifying naturalistic intuitionism in physics. This revision is accompanied by an investigation of the distinctive naturalistic treatment of some central intuitionistic topics, including logic, language, time, ontology, meaning, and truth.

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arXiv2025

Wigner's friend scenarios: on what to condition and how to verify the predictions

Wigner's friend experiment and its modern extensions display the ambiguity of the quantum mechanical description regarding the assignment of quantum states. While the friend applies the state-update rule to the system upon observing an outcome of her measurement in a quantum system, Wigner describes the friend's measurement as a unitary evolution, resulting in an entangled state for the composite system of the friend and the system. In this respect, Wigner is often referred to as a "superobserver" who has the supreme technological ability to keep the friend's laboratory coherent. As such, it is often argued that he has the "correct" description of the state. Here we show that the situation is more symmetrical than is usually thought: there are different types of information that each of the observers has that the other fundamentally cannot have - they reside in different "bubbles" (in Calvalcanti's terminology). While this can explain why the objectivity of the state assignment is only relative to the bubble, we consider more elaborated situations in the form of a game in which the players can switch between bubbles. We find that, in certain circumstances, observers may be entitled to adopt and verify the state assignment from another bubble if they condition their predictions on \textit{all} information that is in principle available to them.

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arXiv2025

Which features of quantum physics are not fundamentally quantum but are due to indeterminism?

What is fundamentally quantum? We argue that most of the features, problems, and paradoxes -- such as the measurement problem, the Wigner's friend paradox and its proposed solutions, single particle nonlocality, and no-cloning -- allegedly attributed to quantum physics have a classical analogue if one is to interpret classical physics as fundamentally indeterministic. What really characterizes non-classical effects are incompatible physical quantities, which, in quantum quantum theory are associated to the fundamental constant $\hbar$.

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arXiv2024

Quantum coherence in networks

From a quantum information perspective, verifying quantum coherence in a quantum experiment typically requires adjusting measurement settings or changing inputs. A paradigmatic example is that of a double-slit experiment, where observing the interference pattern on the screen in a series of experimental settings where one, the other, and both slits are open unambiguously proves quantum coherence. Here we show that this is not necessary by verifying quantum coherence in a network scenario without the need for inputs. We show that there exist probability distributions for joint outcomes of three parties in a triangular network with independent sources that cannot be replicated using classical resources. Furthermore, we generalize our results to $n$-party networks and show that the discrepancy between correlations in classical and quantum networks increases with the number of parties. To this end, we derive nonlinear inequalities that are satisfied by classical correlations and find quantum states that violate them.

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arXiv2024

Towards a measurement theory in QFT: "Impossible" quantum measurements are possible but not ideal

Naive attempts to put together relativity and quantum measurements lead to signaling between space-like separated regions. In QFT, these are known as impossible measurements. We show that the same problem arises in non-relativistic quantum physics, where joint nonlocal measurements (i.e., between systems kept spatially separated) in general lead to signaling, while one would expect no-signaling (based for instance on the principle of no-nonphysical communication). This raises the question: Which nonlocal quantum measurements are physically possible? We review and develop further a non-relativistic quantum information approach developed independently of the impossible measurements in QFT, and show that these two have been addressing virtually the same problem. The non-relativistic solution shows that all nonlocal measurements are localizable (i.e., they can be carried out at a distance without violating no-signaling) but they (i) may require arbitrarily large entangled resources and (ii) cannot in general be ideal, i.e., are not immediately reproducible. These considerations could help guide the development of a complete theory of measurement in QFT.

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arXiv2023

Potentiality realism: A realistic and indeterministic physics based on propensities

We propose an interpretation of physics named potentiality realism. This view, which can be applied to classical as well as to quantum physics, regards potentialities (i.e. intrinsic, objective propensities for individual events to obtain) as elements of reality, thereby complementing the actual properties taken by physical variables. This allows one to naturally reconcile realism and fundamental indeterminism in any theoretical framework. We discuss our specific interpretation of propensities, that require them to depart from being probabilities at the formal level, though allowing for statistics and the law of large numbers. This view helps reconcile classical and quantum physics by showing that most of the conceptual problems that are customarily taken to be unique issues of the latter -- such as the measurement problem -- are actually in common to all indeterministic physical theories.

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arXiv2023

On playing gods: The fallacy of the many-worlds interpretation

We present a methodological argument to refute the so-called many-worlds interpretation (MWI) of quantum theory. Several known criticisms in the literature have already pointed out problematic aspects of this interpretation, such as the lack of a satisfactory account of probabilities, or the huge ontological cost of MWI. Our criticism, however, does not go into the technical details of any version of MWI, but is at the same time more general and more radical. We show, in fact, that a whole class of theories--of which MWI is a prime example--fails to satisfy some basic tenets of science which we call facts about natural science. The problem of approaches the likes of MWI is that, in order to reproduce the observed empirical evidence about any concrete quantum measurement outcome, they require as a tacit assumption that the theory does in fact apply to an arbitrarily large range of phenomena, and ultimately to all phenomena. We call this fallacy the holistic inference loop, and we show that this is incompatible with the facts about natural science, rendering MWI untenable and dooming it to be refuted.

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arXiv2023

Between understanding and control: Science as a cultural product

Since the early days of humankind, people have been asking questions about Nature of two kinds: why did that happen? And how can that be used? In a broad sense, science was born that day. We show indeed that science has two complementary and interdependent souls that aim, respectively, to how to understand and how to control Nature. Through a broad historical analysis, this essay aims to (1) give an account of the development of science as an oscillation and an interplay between its two intrinsic natures, (2) demonstrate that this happened already in ancient times starting from the 6th century BC, and (3) the fact that in different periods one of the two natures was largely favored over the other is a consequence of science being a cultural product of the different social-historical contexts.

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arXiv2023

Iso-entangled bases and joint measurements

While entanglement between distant parties has been extensively studied, entangled measurements have received relatively little attention despite their significance in understanding non-locality and their central role in quantum computation and networks. We present a systematic study of entangled measurements, providing a complete classification of all equivalence classes of iso-entangled bases for projective joint measurements on 2 qubits. The application of this classification to the triangular network reveals that the Elegant Joint Measurement, along with white noise, is the only measurement resulting in output permutation invariant probability distributions when the nodes are connected by Werner states. The paper concludes with a discussion of partial results in higher dimensions.

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arXiv2023

Against the "nightmare of a mechanically determined universe": Why Bohm was never a Bohmian

David Bohm has put forward the first deterministic interpretation of quantum physics, and for this he seems to be regarded as a champion of determinism by physicists (both his contemporaries and the supporters of his interpretation, the so-called "Bohmians") as well as by historians of physics. The standard narrative is that he underwent a "conversion" from being a supporter of Bohr to being a staunch determinist, due to his interaction with Einstein and his commitment to Marxism. Here we show that Bohm actually upheld with continuity throughout his career some philosophical tenets that included a strong rejection of mechanistic determinism. As such, we conclude that Bohm was never a Bohmian and that his philosophical views have been largely misinterpreted.

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arXiv2023

Indeterminism, causality and information: Has physics ever been deterministic?

A tradition handed down among physicists maintains that classical physics is a perfectly deterministic theory capable of predicting the future with absolute certainty, independently of any interpretations. It also tells that it was quantum mechanics that introduced fundamental indeterminacy into physics. We show that there exist alternative stories to be told in which classical mechanics, too, can be interpreted as a fundamentally indeterministic theory. On the one hand, this leaves room for the many possibilities of an open future, yet, on the other, it brings into classical physics some of the conceptual issues typical of quantum mechanics, such as the measurement problem. We discuss here some of the issues of an alternative, indeterministic classical physics and their relation to the theory of information and the notion of causality.

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