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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…
The concept of an injective affine embedding of the quantum states into a set of classical states, i.e., into the set of the probability measures on some measurable space, as well as its relation to statistically complete observables is…
We present a measure of quantum coherence by employing the concept of noncommutativity of operators in quantum mechanics. We analyse the behaviour of this noncommutative coherence and underline its similarities and differences with the…
In this paper, we investigate the connection between Classical and Quantum Mechanics by dividing Quantum Theory in two parts: - General Quantum Axiomatics (a system is described by a state in a Hilbert space, observables are self-adjoint…
Physical processes in the quantum regime possess non-classical properties of quantum mechanics. However, methods for quantitatively identifying such processes are still lacking. Accordingly, in this study, we develop a framework for…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
For a (classically) integrable quantum mechanical system with two degrees of freedom, the functional dependence $\hat{H}=H_Q(\hat{J}_1,\hat{J}_2)$ of the Hamiltonian operator on the action operators is analyzed and compared with the…
Quantum dynamics can be regarded as a generalization of classical finite-state dynamics. This is a familiar viewpoint for workers in quantum computation, which encompasses classical computation as a special case. Here this viewpoint is…
Complementarity was originally introduced as a qualitative concept for the discussion of properties of quantum mechanical objects that are classically incompatible. More recently, complementarity has become a \emph{quantitative} relation…
The control of quantum systems requires the ability to change and read-out the phase of a system. The non-commutativity of canonical conjugate operators can induce phases on quantum systems, which can be employed for implementing phase…
A general dynamical system composed by two coupled sectors is considered. The initial time configuration of one of these sectors is described by a set of classical data while the other is described by standard quantum data. These dynamical…
The ultimate goal of the classicality programme is to quantify the amount of quantumness of certain processes. Here, classicality is studied for a restricted type of process: quantum information processing (QIP). Under special conditions,…
The basic concepts of classical mechanics are given in the operator form. The dynamical equation for a hybrid system, consisting of quantum and classical subsystems, is introduced and analyzed in the case of an ideal nonselective…
Quantum entanglement describes superposition states in multi-dimensional systems, at least two partite, which cannot be factorized and are thus non-separable. Non-separable states exist also in classical theories involving vector spaces. In…
We demonstrate the surprising integrability of the classical Hamiltonian associated to a spin 1/2 system under periodic external fields. The one-qubit rotations generated by the dynamical evolution is, on the one hand, close to that of the…
A formalism is developed for describing approximate classical behaviour in finite (but possibly large) quantum systems. This is done in terms of a structure common to classical and quantum mechanics, viz. a Poisson space with a transition…
We investigate the separability of arbitrary dimensional tripartite sys- tems. By introducing a new operator related to transformations on the subsystems a necessary condition for the separability of tripartite systems is presented.
A hybrid formalism is proposed for interacting classical and quantum sytems. This formalism is mathematically consistent and reduces to standard classical and quantum mechanics in the case of no interaction. However, in the presence of…
The main goal of this paper is to give a rigorous mathematical description of systems for processing quantum information. To do it authors consider abstract state machines as models of classical computational systems. This class of machines…
We study continuous variable systems, in which quantum and classical degrees of freedom are combined and treated on the same footing. Thus all systems, including the inputs or outputs to a channel, may be quantum-classical hybrids. This…