arXiv subjects

Charles Alexandre Bédard

Publications and source records attributed to Charles Alexandre Bédard.

11 recordsLinked to original sources

arXiv2026

Realism and the Inequivalence of the Two Quantum Pictures

The standard claim that the Schrödinger and Heisenberg pictures of quantum mechanics are equivalent rests on the fact that they yield identical empirical predictions. This equivalence therefore assumes the instrumentalist worldview in which theories serve only as tools for prediction. Under scientific realism, by contrast, theories aim to describe reality. Whereas the Schrödinger picture posits a time-evolving wave function, the Heisenberg picture posits so-called descriptors, time-evolving generators of the algebra of observables. These two structures are non-isomorphic: descriptors surject onto but do not reduce to the Schrödinger state. Hence, under realism, the pictures are inequivalent. I argue that this inequivalence marks an opening toward a richer, separable ontology for quantum theory. On explanatory grounds, descriptors provide genuinely local accounts of superdense coding, teleportation, branching, and Bell inequality violations -- phenomena that the Schrödinger framework does not explain fully locally.

quant-ph↗

arXiv2026

Another Triumph of Locality: Colliding Histories Skew Handshakes

From gravity to electromagnetism, apparent action at a distance has always been resolved by deeper, local explanations. Yet today, Bell's theorem is widely interpreted as the death knell for local reality. In this chapter, I present the theorem in accessible terms, examine the three main strategies that attempt to preserve hidden variables, and argue that they share a common defect: the attempt to explain the quantum from the classical rather than the other way around. When quantum mechanics is applied universally, classicality itself is given a quantum account; and when the Bell scenario is formulated in the Heisenberg picture, a strictly local explanation emerges. This chapter serves as a non-technical front-end to Explaining Bell Locally (Proc. R. Soc. A).

quant-ph↗

arXiv2025

Explaining Bell Locally

In the Heisenberg picture of unitary quantum theory, Bell inequalities are violated with local elements of reality interacting locally. Here is how: Upon measuring her particle of the entangled pair, Alice -- like other coupled systems -- smoothly and locally evolves into two non-interacting versions of herself, each of which records a different outcome: she foliates. Everything that suitably interacts with the Alices foliates in turn, generating worlds which, for all practical purposes, remain distinct and autonomous. At spacelike separation, an analogous yet independent process occurs to Bob when he measures his particle, locally differentiating him and his surroundings into two non-interacting instances. To confirm the violation of Bell inequalities, Alice and Bob must further interact to produce a record of the joint outcomes. The record arises from the two local worlds of Alice, and those of Bob, and foliates into four instances: '00', '01', '10' and '11'. The outcomes that win the Clauser--Horne--Shimony--Holt (CHSH) game sum to a measure of $\cos^2(π/8)$.

quant-ph↗

arXiv2025

Lecture Notes on Algorithmic Information Theory

Algorithmic information theory roots the concept of information in computation rather than probability. These lecture notes were constructed in conjunction with the graduate course I taught at Università della Svizzera italiana in the spring of 2023. The course is intended for graduate students and researchers seeking a self-contained journey from the foundations of computability theory to prefix complexity and the information-theoretic limits of formal systems. My exposition ignores boundaries between computer science, mathematics, physics, and philosophy -- an approach I consider essential when explaining inherently multidisciplinary fields. Lecture recordings are available online. Among other topics, the notes cover bit strings, codes, Shannon information theory, computability theory, the universal Turing machine, the Halting Problem, Rice's Theorem, plain algorithmic complexity, the Invariance Theorem, incompressibility, Solomonoff's induction, self-delimiting Turing machines, prefix algorithmic complexity, the halting probability Omega, Chaitin's Incompleteness Theorem, The Coding Theorem, lower semi-computable semi-measures, and the chain rule for algorithmic complexity.

cs.IT↗

arXiv2025

On the Alleged Locality in the Schrödinger Picture

Vedral claims that the Schrödinger picture can describe quantum systems as locally as the Heisenberg picture, relying on a product notation for the density matrix. Here, I refute that claim. I show that the so-called `local factors' in the product notation do not correspond to individual systems and therefore fail to satisfy Einsteinian locality. Furthermore, the product notation does not track where local gates are applied. Finally, I expose internal inconsistencies in the argument: if, as is also stated, Schrödinger-picture locality ultimately depends on explicit bookkeeping of all operations, then the explanatory power of the product notation is de facto undermined.

quant-ph↗

arXiv2025

Temperature as Joules per Bit

In statistical mechanics, entropy is defined as a fundamental quantity. However, its unit, J/K, involves that of temperature, which is only subsequently defined - and defined in terms of entropy. This circularity arises with the introduction of Boltzmann's constant into the very expression of entropy. The J/K carried by the constant prevents entropy from finding a unit of its own while simultaneously obfuscating its informational nature. Following the precepts of information theory, we argue that entropy is well measured in bits and coincides with information capacity at thermodynamic equilibrium. Consequently, not only is the temperature of a system in equilibrium expressed in J/bit, but it acquires a clear meaning: It is the cost in energy to increase its information capacity by 1 bit. Viewing temperature as joules per bit uncovers the strong duality exhibited by Gibbs long ago between available capacity and free energy. It also simplifies Landauer's cost and clarifies that it is a cost of displacement, not of erasure. Replacing the kelvin with the bit as an SI unit would remove Boltzmann's constant from the seven defining constants.

quant-ph↗

arXiv2023

Teleportation Revealed

Quantum teleportation is the name of a problem: how can the real-valued parameters encoding the state at Alice's location make their way to Bob's location via shared entanglement and only two bits of classical communication? Without an explanation, teleportation appears to be a conjuring trick. Investigating the phenomenon with Schrödinger states and reduced density matrices shall always leave loose ends because they are not local and complete descriptions of quantum systems. Upon demonstrating that the Heisenberg picture admits a local and complete description, Deutsch and Hayden rendered its explanatory power manifest by revealing the trick behind teleportation, namely, by providing an entirely local account. Their analysis is re-exposed and further developed.

quant-ph↗

arXiv2022

An Algorithmic Approach to Emergence

We suggest a quantitative and objective notion of emergence. Our proposal uses algorithmic information theory as a basis for an objective framework in which a bit string encodes observational data. A plurality of drops in the Kolmogorov structure function of such a string is seen as the hallmark of emergence. Our definition offers some theoretical results, in addition to extending the notions of coarse-graining and boundary conditions. Finally, we confront our proposal with applications to dynamical systems and thermodynamics.

cond-mat.stat-mech↗

arXiv2021

The ABC of Deutsch-Hayden Descriptors

It has been more than 20 years since Deutsch and Hayden proved the locality of quantum theory, using the Heisenberg picture of quantum computational networks. Of course, locality holds even in the face of entanglement and Bell's theorem. Today, most researchers in quantum foundations are still convinced not only that a local description of quantum systems has not yet been provided, but that it cannot exist. The main goal of this paper is to address this misconception by re-explaining the descriptor formalism in a hopefully accessible and self-contained way. It is a step-by-step guide to how and why descriptors work. Finally, superdense coding is revisited in the light of descriptors.

quant-ph↗

arXiv2021

The Cost of Quantum Locality

It has been more than 20 years since Deutsch and Hayden demonstrated that quantum systems can be completely described locally -- notwithstanding Bell's theorem. More recently, Raymond-Robichaud proposed two other approaches to the same conclusion. In this paper, all these means of describing quantum systems locally are proved formally equivalent. The cost of such descriptions is then quantified by the dimensionality of their underlining space. The number of degrees of freedom of a single qubit's local description is shown to grow exponentially with the total number of qubits considered as a global system. This apparently unreasonable cost to describe such a small system in a large Universe is nonetheless shown to be expected. Finally, structures that supplement the universal wave function are investigated.

quant-ph↗

arXiv2020

Relativity of Depth and Sophistication

Logical depth and sophistication are two quantitative measures of the non-trivial organization of an object. Although apparently different, these measures have been proven equivalent, when the logical depth is renormalized by the busy beaver function. In this article, the measures are relativized to auxiliary information and re-compared to one another. The ability of auxiliary information to solve the halting problem introduces a distortion between the measures. Finally, similar to algorithmic complexity, sophistication and logical depth (renormalized) each offer a relation between their expression of $(x, y)$, $(x)$ and $(y | x)$.

cs.IT↗