We give a logical analysis of quantum measurements as forms of information update. We enumerate some of the “lessons ” that Logic can learn from Quantum Mechanics: (1) the importance of logical dynamics; (2) the fact that quantum physics does not require any modification of the classical laws of “static ” propositional logic, but only a non-classical dynamics of information flow; (3) the fact that all information-gathering actions have ontic side-effects; (4) the fact that this ontic impact might in its turn affect the flow of information, leading to non-classical epistemic effects and to states of “objectively imperfect information”. 1
We give a logical analysis of quantum measurements as forms of information update. We enumerate some of the “lessons ” that Logic can learn from Quantum Mechanics: (1) the importance of logical dynamics; (2) the fact that quantum physics does not require any modification of the classical laws of “static ” propositional logic, but only a non-classical dynamics of information flow; (3) the fact that all information-gathering actions have ontic side-effects; (4) the fact that this ontic impact might in its turn affect the flow of information, leading to non-classical epistemic effects and to states of “objectively imperfect information”. 1
We address the old question whether a logical understanding of Quantum Mechanics requires abandoning some of the principles of classical logic. Against Putnam and others (Among whom we may count or not E. W. Beth, depending on how we interpret some of his statements), our answer is a clear “no”. Philosophically, our argument is based on combining a formal semantic approach, in the spirit of E. W. Beth’s proposal of applying Tarski’s semantical methods to the analysis of physical theories, with an empirical–experimental approach to Logic, as advocated by both Beth and Putnam, but understood by us in the view of the operational- realistic tradition of Jauch and Piron, i.e. as an investigation of “the logic of yes–no experiments” (or “questions”). Technically, we use the recently-developed setting of Quantum Dynamic Logic (Baltag and Smets 2005, 2008) to make explicit the operational meaning of quantum-mechanical concepts in our formal semantics. Based on our recent results (Baltag and Smets 2005), we show that the correct interpretation of quantum-logical connectives is dynamical, rather than purely propositional. We conclude that there is no contradiction between classical logic and (our dynamic reinterpretation of) quantum logic. Moreover, we argue that the Dynamic-Logical perspective leads to a better and deeper understanding of the “non-classicality” of quantum behavior than any perspective based on static Propositional Logic.
This paper provides an overview of quantum dynamic logics, showing how they have been designed and illustrating how these logics can be applied to verify the correctness of quantum protocols. Similar to the advantages of using dynamic logics to reason about the flow of classical information, the quantum analogues of these logics are tailored to the task of reasoning about the flow of quantum information. We present our logical systems in a modular way, starting with the qualitative logic of quantum measurements and unitary evolutions in single quantum systems, which can already express non-classical effects, e.g., the state-changing interference induced by quantum tests, their non-commutativity, etc. We then move on to logics for compound quantum systems that can capture the non-local features of quantum information: separability, entanglement, correlated measurements, Bell states, etc. We then briefly summarize the logic of quantum probabilities and sketch some applications to quantum protocols.
Current research in Logic is no longer confined to the traditional study of logical consequence or valid inference. As can be witnessed by the range of topics covered in this special issue, the subject matter of logic encompasses several kinds of informational processes ranging from proofs and inferences to dialogues, observations, measurements, communication and computation. What interests us here is its application to quantum physics: how does logic handle informational processes such as observations and measurements of quantum systems? What are the basic logical principles fit to handle and reason about quantum physical processes? These are the central questions in this paper. It is my aim to provide the reader with some food for thought and to give some pointers to the literature that provide an easy access to this field of research. In the next section I give a brief historical sketch of the origin of the quantum logic project. Next I will explain the theory of orthomodular lat-tices in section 2. Section 3 covers the syntax and semantics of traditional
Information is treated by classical physics, relativity theory, and quantum mechanics as an epistemic variable, with no significance in their mathematical models. All currently accepted conceptions of information and entropy are subjective, observer-related. We have proposed (Ospino 2026) considering information as an ontic category with energy equivalence and energetic meaningfulness, and making it part of the complete balance of physical evolution. The history of science is the history of useful but incomplete models derived under the reliance of approximations and simplifications. Every such model was contemporarily considered complete until the contrary fact was demonstrated. Unitarity and determinism are generally regarded as a complete understanding of physical evolution. The empirical success and practical usefulness of such assumptions is undeniable, as every model before was also for a certain time, until it was not. Motivated by the information-energy equivalence (Landauer, Vopson), and by the possibility of resolving some open questions not explainable under the current understanding, we introduced ontic information into consideration, and we are presenting here some derived conclusions for further analysis and discussion. We emphasize that the epistemic nature of information and entropy as per Shannon and von Neumann (and related approaches) needs to be consequently updated with the ontic understanding, or else the analysis will be flawed when using epistemic approaches. Also, since unitarity is the concept in question here, we rely on acceptance, for the purpose of the discussion, that unitarity could be incomplete.
Abstract Quantum theory has an epistemic horizon, i.e. exact values cannot be assigned simultaneously to incompatible physical quantities. As shown by Spekkens’ toy theory, positing an epistemic horizon akin to Heisenberg’s uncertainty principle in a classical mechanical setting also leads to a plethora of quantum phenomena. We introduce a deterministic theory—nomic toy theory—in which information gathering agents are explicitly modelled as physical systems. Our main result shows the presence of an epistemic horizon for such agents. They can only simultaneously learn the values of observables whose Poisson bracket vanishes. Therefore, nomic toy theory has incompatible measurements and the complete state of a physical system cannot be known. The best description of a system by an agent is via an epistemic state of Spekkens’ toy theory. Our result reconciles us to measurement uncertainty as an aspect of the inseparability of subjects and objects. Significantly, the claims follow even though nomic toy theory is essentially classical. This work invites further investigations of epistemic horizons, such as the one of (full) quantum theory.
There is no such thing as “The Quantum Logical Interpretation of Quantum Mechanics”. Rather, there is a cluster of interpretations, all of which can be described as “quantum logical”. Here I provide a general framework for discussing interpretations of this kind, and then locate various suggestions within it. The presentation owes much to van Fraassen (see, in particular, van Fraassen 1974 ); his “modal interpretation” is one of those I discuss, along with those of Jauch, Putnam and Kochen. I begin by rehearsing some orthodox quantum theory. Within quantum mechanics we deal with a set 0 of measurable quantities, orobservables(position, momentum, components of spin and so on). Experiment can determine the value of an observable for a given system: the values so determined will be real numbers. A maximal amount of information about what the result would be for a given system, whatever experiment we chose to perform on it, is available once we know thestateof the system.