相关论文: A logical description for perfect measurements

In arXiv: math.LO/0011208 we proposed the {\sl intuitionistic or disjunctive representation of quantum logic}, i.e., a representation of the property lattice of physical systems as a complete Heyting algebra of logical propositions on these…

Many fundamental and key objects in quantum mechanics are linear mappings between particular affine/linear spaces. This structure includes basic quantum elements such as states, measurements, channels, instruments, non-signalling channels…

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…

The paper reviews and discusses four ideas scattered in previous papers of the author. First, objective properties of quantum systems are not associated with observables but are defined by preparations. Second, measurable results of…

Quotients and comprehension are fundamental mathematical constructions that can be described via adjunctions in categorical logic. This paper reveals that quotients and comprehension are related to measurement, not only in quantum logic,…

This article describes recent work on the topic of specifying properties of transition systems. By giving a suitably abstract description of transition systems as coalgebras, it is possible to derive logics for capturing properties of these…

The term quantum logic has different connotations for different people, having been considered as everything from a metaphysical attack on classical reasoning to an exercise in abstract algebra. Our aim here is to give a uniform…

We present a description of the measurement process based on the parametric representation with environmental coherent states. This representation is specifically tailored for studying quantum systems whose environment needs being…

We have recently introduced a realistic, covariant, interpretation for the reduction process in relativistic quantum mechanics. The basic problem for a covariant description is the dependence of the states on the frame within which collapse…

The notion of perfect correlations between arbitrary observables, or more generally arbitrary POVMs, is introduced in the standard formulation of quantum mechanics, and characterized by several well-established statistical conditions. The…

In Quantum Physics, a measurement is represented by a projection on some closed subspace of a Hilbert space. We study algebras of operators that abstract from the algebra of projections on closed subspaces of a Hilbert space. The properties…

Operating quantum sensors and quantum computers would make data in the form of quantum states available for purely quantum processing, opening new avenues for studying physical processes and certifying quantum technologies. In this…

We establish a connection between measurement-based quantum computation and the field of mathematical logic. We show that the computational power of an important class of quantum states called graph states, representing resources for…

This paper surveys some recent developments towards a dynamic quantum logic and outlines its explicite construction -- some analogies and contrasts with other logics of dynamics are indicated. Abstract: The development of ``(static)…

We consider symmetry as a foundational concept in quantum mechanics and rewrite quantum mechanics and measurement axioms in this description. We argue that issues related to measurements and physical reality of states can be better…

We introduce a quantitative relational Hoare logic for quantum programs. Assertions of the logic range over a new infinitary extension of positive semidefinite operators. We prove that our logic is sound, and complete for bounded…

We suggest solving the measurement problem by postulating the existence of a special future final boundary condition for the universe. Although this is an extension of the way boundary conditions are usually chosen (in terrestrial…

The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…

Recently, it has been suggested that operational properties connected to quantum computation can be alternative indicators of quantum phase transitions. In this work we systematically study these operational properties in 1D systems that…

Quantum theory brings into question the compatibility of the twin desiderata of exact knowability of the present state of the physical world and perfect predictability of its future states. Bohr's coordination-causality complementarity…