Related papers: No-Cloning In Categorical Quantum Mechanics
We present a categorical construction for modelling causal structures within a general class of process theories that include the theory of classical probabilistic processes as well as quantum theory. Unlike prior constructions within…
This is the first paper in a series where we generalize the Categorical Quantum Mechanics program (due to Abramsky, Coecke, et al) to braided systems. In our view a uniform description of quantum information for braided systems has not yet…
We consider classical and quantum algorithms which have a duality property: roughly, either the algorithm provides some nontrivial improvement over random or there exist many solutions which are significantly worse than random. This enables…
We argue with claims of the paper [Agostini F., Caprara S. and Ciccotti G., Europhys. Lett. EPL, 78 (2007) Art. 30001, 6] that the quantum-classic bracket introduced in [arXiv:quant-ph/0506122] produces "artificial coupling" and has…
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 develop further the theory of monoidal bicategories by introducing and studying bicategorical counterparts of the notions of a linear exponential comonad, as considered in the study of linear logic, and of a codereliction transformation,…
Intuitionistic logic, in which the double negation law not-not-P = P fails, is dominant in categorical logic, notably in topos theory. This paper follows a different direction in which double negation does hold. The algebraic notions of…
Bohm Mechanics and Nelson Stochastic Mechanics are confronted with Quantum Mechanics in presence of non-interacting subsystems. In both cases, it is shown that correlations at different times of compatible position observables on stationary…
Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. Quantum mechanical systems can produce probability distributions that exhibit quantum correlations…
This article develops a practical technique for studying representations of $\Bbbk$-linear categories arising in the categorification of quantum groups. We work in terms of locally unital algebras which are $\mathbb{Z}$-graded with graded…
The apparent difficulty in recovering classical nonlinear dynamics and chaos from standard quantum mechanics has been the subject of a great deal of interest over the last twenty years. For open quantum systems - those coupled to a…
This paper presents two unconventional links between quantum and classical physics. The first link appears in the study of quantum cryptography. In the presence of a spy, the quantum correlations shared by Alice and Bob are imperfect. One…
This note is concerned with a formal analysis of the problem of non-monotonic reasoning in intelligent systems, especially when the uncertainty is taken into account in a quantitative way. A firm connection between logic and probability is…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
We introduce a quantum analogue of classical first-order logic (FO) and develop a theory of quantum first-order logic as a basis of the productive discussions on the power of logical expressiveness toward quantum computing. The purpose of…
We provide an algebraic formulation of C.Rovelli's relational quantum theory that is based on suitable notions of "non-commutative" higher operator categories, originally developed in the study of categorical non-commutative geometry. As a…
Here we provide the contributions' abstracts published in a volume we edited as a special issue in International Journal of Modern Physics B. The volume deals with the recent progress in quantifying quantum correlations beyond the generic…
We argue that it is the assumption of counterfactual definiteness and not locality or realism that results in Bell inequality violations. Furthermore, this assumption of counterfactual definiteness is not supported in classical mechanics.…
Nonlocality is a property of paramount importance both conceptually and computationally exhibited by quantum systems, which has no classical counterpart. Conceptually, it is important because it implies that the evolving system has…
This paper extends the tools of C*-algebraic strict quantization toward analyzing the classical limits of unbounded quantities in quantum theories. We introduce the approach first in the simple case of finite systems. Then we apply this…