Related papers: Basic Logic and Quantum Computing: Logical Judgeme…

We propose a formal framework for understanding and unifying the concept of observers across physics, computer science, philosophy, and related fields. Building on cybernetic feedback models, we introduce an operational definition of…

We develop a systematic approach to quantum probability as a theory of rational betting in quantum gambles. In these games of chance the agent is betting in advance on the outcomes of several (finitely many) incompatible measurements. One…

Logical inference leads to one of the major interpretations of probability theory called logical interpretation, in which the probability is seen as a measure of the plausibility of a logical statement under incomplete information. In this…

The question of how irreversibility can emerge as a generic phenomena when the underlying mechanical theory is reversible has been a long-standing fundamental problem for both classical and quantum mechanics. We describe a mechanism for the…

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),…

I argue that the rules of unitary quantum mechanics imply that observers who will themselves be subject to measurements in a linear combination of macroscopic states (``cat" measurements) cannot make reliable predictions on the results of…

Quantum computers are hypothetical devices, based on quantum physics, that would enable us to perform certain computations hundreds of orders of magnitude faster than digital computers. This feature is coined as "quantum supremacy" and one…

Theory of quantum measurements is often classified as decision theory. An event in decision theory corresponds to the measurement of an observable. This analogy looks clear for operationally testable simple events. However, the situation is…

This paper presents a substructural logic of sequents with very restricted exchange and weakening rules. It is sound with respect to sequences of measurements of a quantic system. A sound and complete semantics is provided. The semantic…

An intense effort is being made today to build a quantum computer. Instead of presenting what has been achieved, I invoke here analogies from the history of science in an attempt to glimpse what the future might hold. Quantum computing is…

Logical information theory is the quantitative version of the logic of partitions just as logical probability theory is the quantitative version of the dual Boolean logic of subsets. The resulting notion of information is about…

In both quantum mechanics and relativity theory, the concept of the observer plays a critical role. However, there is no consensus on the definition of observer in these theories. Following Einstein's thought experiments, one could ask:…

It has been experimentally demonstrated that quantum coherence can persist in macroscopic phenomena [J.R. Friedman et al.,Nature, 406 (2000) 43]. To face the challenge of this new fact, in this article QM in its standard form is assumed to…

Quantum theory's irreducible empirical core is a probability calculus. While it presupposes the events to which (and on the basis of which) it serves to assign probabilities, and therefore cannot account for their occurrence, it has to be…

What is the observer's role in quantum measurement? Obviously, observers prepare the apparatus, observe and interpret the measured results. Although the observer will have a certain influence on the measurement results by setting up the…

Can quantum theory be applied on all scales? While there are many arguments for the universality of quantum theory, this question remains a subject of debate. It is unknown how far the existence of macroscopic irreversibility can be derived…

By repeated trials, one can determine the fairness of a classical coin with a confidence which grows with the number of trials. A quantum coin can be in a superposition of heads and tails and its state is most generally a density matrix.…

We present a logical calculus for reasoning about information flow in quantum programs. In particular we introduce a dynamic logic that is capable of dealing with quantum measurements, unitary evolutions and entanglements in compound…

Classical logic predicts that everything (thus nothing useful at all) follows from inconsistency. A paraconsistent logic is a logic where an inconsistency does not lead to such an explosion, and since in practice consistency is difficult to…

It is shown that quantum logic is a logic in the very same way in which classical logic is a logic. Soundness and completeness of both quantum and classical logics have been proved for novel lattice models that are not orthomodular and…