相关论文: Bennett and Stinespring, Together at Last

Classical block designs are important combinatorial structures with a wide range of applications in Computer Science and Statistics. Here we give a new abstract description of block designs based on the arrow category construction. We show…

The purpose of this paper is to formalize the concept that best synthesizes our intuitive understanding of quantum mechanics -- that the information carried by a system is limited -- and, from this principle, to construct the foundations of…

Bit commitment protocols whose security is based on the laws of quantum mechanics alone are generally held to be impossible. In this paper we give a strengthened and explicit proof of this result. We extend its scope to a much larger…

We continue the study of non-invertible topological dynamical systems with expanding behavior. We introduce the class of {\em finite type} systems which are characterized by the condition that, up to rescaling and uniformly bounded…

A bit-quantum map relates probabilistic information for Ising spins or classical bits to quantum spins or qubits. Quantum systems are subsystems of classical statistical systems. The Ising spins can represent macroscopic two-level…

We give a framework to produce constructible functions from natural functors between categories, without need of a morphism of moduli spaces to model the functor. We show using the Riemann-Hilbert correspondence that any natural (derived)…

We provide a universal construction of the category of finite-dimensional C*-algebras and completely positive trace-nonincreasing maps from the rig category of finite-dimensional Hilbert spaces and unitaries. This construction, which can be…

Stinespring's dilation theorem is the basic structure theorem for quantum channels: it states that any quantum channel arises from a unitary evolution on a larger system. Here we prove a continuity theorem for Stinespring's dilation: if two…

Recently, a geometric embedding of the classical space and classical phase space of an n-particle system into the space of states of the system was constructed and shown to be physically meaningful. Namely, the Newtonian dynamics of the…

We present a consistent framework of coupled classical and quantum dynamics. Our result allows us to overcome severe limitations of previous phenomenological approaches, like evolutions that do not preserve the positivity of quantum states…

We resurrect a standard construction of analytical mechanics dating from the last century. The technique allows one to pass from any dynamical system whose first order evolution equations are known, and whose bracket algebra is not…

We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…

The qualitatively new concept of dynamic complexity in quantum mechanics is based on a new paradigm appearing within a nonperturbational analysis of the Schroedinger equation for a generic Hamiltonian system. The unreduced analysis…

A universal set of gates for (classical or quantum) computation is a set of gates that can be used to approximate any other operation. It is well known that a universal set for classical computation augmented with the Hadamard gate results…

A rewriting system is a set of equations over a given set of terms called rules that characterize a system of computation and is a powerful general method for providing decision procedures of equational theories, based upon the principle of…

The classical powerset construction is a standard method converting a non-deterministic automaton into a deterministic one recognising the same language. Recently, the powerset construction has been lifted to a more general framework that…

Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching…

We present a consistent formalism to describe the dynamics of hybrid systems with mixed classical and quantum degrees of freedom. The probability function of the system, which, in general, will be a combination of the classical distribution…

Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…

We give a detailed account of the so-called "universal construction" that aims to extend invariants of closed manifolds, possibly with additional structure, to topological field theories and show that it amounts to a generalization of the…