Related papers: Density conditions for quantum propositions
We explore a simple approach to quantum logic based on hybrid and dynamic modal logic, where the set of states is given by some Hilbert space. In this setting, a notion of quantum clause is proposed in a similar way the notion of Horn…
Quantum theory can be derived from purely informational principles. Five elementary axioms-causality, perfect distinguishability, ideal compression, local distinguishability, and pure conditioning-define a broad class of theories of…
We elaborate the idea of quantum computation through measuring the correlation of a gapped ground state, while the bulk Hamiltonian is utilized to stabilize the resource. A simple computational primitive, by pulling out a single spin…
We derive Born's rule and the density-operator formalism for quantum systems with Hilbert spaces of dimension two or larger. Our extension of Gleason's theorem only relies upon the consistent assignment of probabilities to the outcomes of…
The aim of this note is to recast somewhat informal axiom system of quantum mechanics used by physicists (Dirac calculus) in the language of Continuous Logic. We note an analogy between Tarski's notion of cylindric algebras, as a tool of…
Principle of ``Superrelativity'' has been proposed in order to avoid the contradiction between principle of relativity and foundations of quantum theory. Solutions of a newly derived non-linear Klein-Gordon equation presumably may be…
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations…
We develop and defend the thesis that the Hilbert space formalism of quantum mechanics is a new theory of probability. The theory, like its classical counterpart, consists of an algebra of events, and the probability measures defined on it.…
In quantum mechanics, the selfadjoint Hilbert space operators play a triple role as observables, generators of the dynamical groups and statistical operators defining the mixed states. One might expect that this is typical of Hilbert space…
We show that Hilbert schemes for quantum planes are projective.
Our main theorem is in the generality of the axioms of Hilbert space, and the theory of unbounded operators. Consider two Hilbert spaces such that their intersection contains a fixed vector space D. It is of interest to make a precise…
Quantum decision theory is introduced here, and new basis for this theory is proposed. It is first based upon the author's general arguments for the Hilbert space formalism in quantum theory, next on arguments for the Born rule, that is,…
An orthodox formulation of quantum mechanics relies on a set of postulates in Hilbert space supplemented with rules to connect it with classical mechanics such as quantisation techniques, correspondence principle, etc. Here we deduce a…
A quantum system can be entirely described by the K\"ahler structure of the projective space P(H) associated to the Hilbert space H of possible states; this is the so-called geometrical formulation of quantum mechanics. In this paper, we…
We introduce quantum monadic and quantum cylindric algebras. These are adaptations to the quantum setting of the monadic algebras of Halmos, and cylindric algebras of Henkin, Monk and Tarski, that are used in algebraic treatments of…
Classical planning asks for a sequence of operators reaching a given goal. While the most common case is to compute a plan, many scenarios require more than that. However, quantitative reasoning on the plan space remains mostly unexplored.…
Continuous first-order logic is used to apply model-theoretic analysis to analytic structures (e.g. Hilbert spaces, Banach spaces, probability spaces, etc.). Classical computable model theory is used to examine the algorithmic structure of…
The geometric formulation of quantum mechanics is a very interesting field of research which has many applications in the emerging field of quantum computation and quantum information, such as schemes for optimal quantum computers. In this…
The primary resource for quantum computation is Hilbert-space dimension. Whereas Hilbert space itself is an abstract construction, the number of dimensions available to a system is a physical quantity that requires physical resources.…
For the classical mind, quantum mechanics is boggling enough; nevertheless more bizarre behavior could be imagined, thereby concentrating on propositional structures (empirical logics) that transcend the quantum domain. One can also…