相关论文: Bennett and Stinespring, Together at Last

Our earlier twisted-face-pairing construction showed how to modify an arbitrary orientation-reversing face-pairing on a faceted 3-ball in a mechanical way so that the quotient is automatically a closed, orientable 3-manifold. The…

This is a review paper concerned with the global consistency of the quantum dynamics of non-commutative systems. Our point of departure is the theory of constrained systems, since it provides a unified description of the classical and…

Equational reasoning about circuits is central in quantum software for validation, optimisation, and verification. For qubits, the CNOT-dihedral fragment supports efficient rewriting via phase polynomials and layered normal forms, yielding…

Our aim is to introduce a category-theoretic framework sufficiently general to describe a wide variety of open kinematic systems in classical mechanics while uniquely characterizing systems with specified simplest components. The framework…

In the study of open quantum systems modeled by a unitary evolution of a bipartite Hilbert space, we address the question of which parts of the environment can be said to have a "classical action" on the system, in the sense of acting as a…

Reversibility is a key issue in the interface between computation and physics, and of growing importance as miniaturization progresses towards its physical limits. Most foundational work on reversible computing to date has focussed on…

We take a unifying and new approach toward polynomial and trigonometric approximation in an arbitrary number of variables, resulting in a precise and general ready-to-use tool that anyone can easily apply in new situations of interest. The…

Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…

We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of…

We discuss classical and quantum computations in terms of corresponding Hamiltonian dynamics. This allows us to introduce quantum computations which involve parallel processing of both: the data and programme instructions. Using mixed…

Using a representation of multichannel quantum defect theory in terms of a quantum Poincar\'e map for bound Rydberg molecules, we apply Jung's scattering map to derive a generalized quantum map, that includes the continuum. We show, that…

Some mathematical theories in physics justify their explanatory superiority over earlier formalisms by the clarity of their postulates. In particular, axiomatic reconstructions drive home the importance of the composition rule and the…

We describe a scheme for constructing quantum mechanics in which a quantum system is considered as a collection of open classical subsystems. This allows using the formal classical logic and classical probability theory in quantum…

Let $\mathcal{S}$ be a small category, and suppose that we are given a full subcategory $\mathcal{U}$ such that every object of $\mathcal{S}$ can be embedded into some object of $\mathcal{U}$ in the same way as every quasi-projective…

Many deep, mysterious connections have been observed between collections of mutually unbiased bases (MUBs) and combinatorial designs called $k$-nets (and in particular, between complete collections of MUBs and finite affine - or…

We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…

This essay aims to propose construction theory, a new domain of theoretical research on machine construction, and use it to shed light on a fundamental relationship between living and computational systems. Specifically, we argue that…

Quantum computing offers advantages over classical computation, yet the precise features that set the two apart remain unclear. In the standard quantum circuit model, adding a 1-qubit basis-changing gate -- commonly chosen to be the…

Understanding the large-scale physics is crucial for the spin foam approach to quantum gravity. We tackle this challenge from a statistical physics perspective using simplified, yet feature-rich models. In particular, this allows us to…

Newtonian and Schrodinger dynamics can be formulated in a physically meaningful way within the same Hilbert space framework. This fact was recently used to discover an unexpected relation between classical and quantum motions that goes…