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Reasoning about Quantum Actions: A Logician’s Perspective

Sonja Smets

Springer eBooksJan 1, 20130 citations

Extending Classical Logic for Reasoning About Quantum Systems

Rohit Chadha, Paulo Mateus, Amı́lcar Sernadas +1 more

Elsevier eBooksJan 1, 200914 citations

Duality for the Logic of Quantum Actions

Jort M. Bergfeld, Kohei Kishida, Joshua Sack +1 more

Studia LogicaNov 28, 20147 citations

Reasoning about Quantum Information: An Overview of Quantum Dynamic Logic

Alexandru Baltag, Sonja Smets

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.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.

Applied SciencesApr 28, 20225 citations

Reichenbach's interpretation of quantum mechanics

Paul K. Feyerabend

In section 3 of his paper ‘Three-valued logic’, Hilary Putnam deals with Reichenbach's attempt to interpret quantum mechanics on the basis of three-valued logic, and he uses some arguments of his own in order to show that this attempt is ‘a move in the direction of simplifying the whole system of laws’ (171). I believe that the Reichenbach–Putnam procedure cannot be defended and that it leads to undesirable consequences. There are the reasons for my belief: THREE-VALUED LOGIC AND CONTACT-ACTION Putnam asserts (a) that ‘the laws of quantum mechanics … are logically incompatible with’ the principle of contact-action ‘if ordinary two-valued logic is used’; and (b) that ‘adopting a three-valued logic permits one to preserve both the laws of quantum mechanics and the principle that no causal signal travels with infinite speed’. Assuming for a moment that (a) and (b) give a correct statement of Reichenbach's position (which they do not – see section 3) and that (a) is true we can at once say that adopting the procedure suggested in (b) would violate one of the most fundamental principles of scientific methodology, namely, the principle to take refutations seriously. The statement that there is no velocity greater than the velocity of light is a well-corroborated statement of physics. If, as is asserted in (a), quantum mechanics implies the negation of that statement, we should consider it as refuted and look for a better theory. This is what has in fact happened.In section 3 of his paper ‘Three-valued logic’, Hilary Putnam deals with Reichenbach's attempt to interpret quantum mechanics on the basis of three-valued logic, and he uses some arguments of his own in order to show that this attempt is ‘a move in the direction of simplifying the whole system of laws’ (171). I believe that the Reichenbach–Putnam procedure cannot be defended and that it leads to undesirable consequences. There are the reasons for my belief: THREE-VALUED LOGIC AND CONTACT-ACTION Putnam asserts (a) that ‘the laws of quantum mechanics … are logically incompatible with’ the principle of contact-action ‘if ordinary two-valued logic is used’; and (b) that ‘adopting a three-valued logic permits one to preserve both the laws of quantum mechanics and the principle that no causal signal travels with infinite speed’. Assuming for a moment that (a) and (b) give a correct statement of Reichenbach's position (which they do not – see section 3) and that (a) is true we can at once say that adopting the procedure suggested in (b) would violate one of the most fundamental principles of scientific methodology, namely, the principle to take refutations seriously. The statement that there is no velocity greater than the velocity of light is a well-corroborated statement of physics. If, as is asserted in (a), quantum mechanics implies the negation of that statement, we should consider it as refuted and look for a better theory. This is what has in fact happened.

Cambridge University Press eBooksOct 29, 19811 citation

Reasoning About Quantum Systems

Paulo Mateus, Amı́lcar Sernadas

Lecture notes in computer scienceJan 1, 200423 citations

The logic of quantum actions: reasoning about change in quantum systems

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