相关论文: Deduction, Ordering, and Operations in Quantum Log…

We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in…

In categorical quantum mechanics, classical structures characterize the classical interfaces of quantum resources on one hand, while on the other hand giving rise to some quantum phenomena. In the standard Hilbert space model of quantum…

Quantum computations operate in the quantum world. For their results to be useful in any way, there is an intrinsic necessity of cooperation and communication controlled by the classical world. As a consequence, full formal descriptions of…

The idea that symmetries simplify or reduce the complexity of a system has been remarkably fruitful in physics, and especially in quantum mechanics. On a mathematical level, symmetry groups single out a certain structure in the Hilbert…

We investigate modifications of quantum mechanics (QM) that replace the unitary group in a finite dimensional Hilbert space with a finite group and determine the minimal sequence of subgroups necessary to approximate QM arbitrarily closely…

The classical Hilbert space formulation of the axioms of Quantum Mechanics appears to leave open the question whether the Hermitian operators which are associated with the observables of a finite non-relativistic quantum system are uniquely…

We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…

Quantum information science provides powerful technologies beyond the scope of classical physics. In practice, accurate control of quantum operations is a challenging task with current quantum devices. The implementation of high fidelity…

Quantum mechanics is widely regarded as a complete theory, yet we argue it is a tractable projection of a deeper, computationally-inaccessible classical variational structure. By analyzing the coupled partial differential equations of the…

By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…

Quantum computers have the potential to explore the vast Hilbert space of entangled states that play an important role in the behavior of strongly interacting matter. This opportunity motivates reconsidering the Hamiltonian formulation of…

Classical physics and quantum physics suggest two meta-physical types of reality: the classical notion of a objectively definite reality with properties "all the way down," and the quantum notion of an objectively indefinite type of…

In this work we build a quantum logic that allows us to refer to physical magnitudes pertaining to different contexts from a fixed one without the contradictions with quantum mechanics expressed in no-go theorems. This logic arises from…

Quantum algorithms are a very promising field. However, creating and manipulating these kind of algorithms is a very complex task, specially for software engineers used to work at higher abstraction levels. The work presented here is part…

We present, in a pedagogical style, many instances of reduction procedures appearing in a variety of physical situations, both classical and quantum. We concentrate on the essential aspects of any reduction procedure, both in the algebraic…

We show that the category OS of operator spaces, with complete contractions as morphisms, is locally countably presentable and a model of Intuitionistic Linear Logic in the sense of Lafont. We then describe a model of Classical Linear…

This thesis is a study of quantum error-correction codes from an algebraic perspective. We concern ourselves not only with quantum codes but also protocols to perform logical quantum computation using such codes. We derive new methods of…

Classical electrodynamics is reformulated in terms of wave functions in the classical phase space of electrodynamics, following the Koopman-von Neumann-Sudarshan prescription for classical mechanics on Hilbert spaces {\em sans} the…

The main contribution of the present paper is the introduction of a simple yet expressive hybrid-dynamic logic for describing quantum programs. This version of quantum logic can express quantum measurements and unitary evolutions of states…

Representations of quantum computations are almost always based on a tensor product $\otimes$-structure. This coincides with what we are able to execute in our experiments, as well as what we observe in Nature, but it makes certain familiar…