Related papers: Bridging Classical and Quantum Worlds: Maps, State…
We give a review of concepts related to connection of classical and quantum theories, from the phase space perspective. Quantum theory is described by non-commutative operators of coordinates and momenta, results in values having a certain…
In our daily life experiences we face localized objects which are "here or there" not "here and there". The state of a cat could be "dead and alive" at the same time from a quantum mechanical point of view, which is not in agreement with…
We present general mappings between classical spin systems and quantum physics. More precisely, we show how to express partition functions and correlation functions of arbitrary classical spin models as inner products between 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…
Quantum correlations can be naturally formulated in a classical statistical system of infinitely many degrees of freedom. This realizes the underlying non-commutative structure in a classical statistical setting. We argue that the quantum…
A direct classical analog of quantum decoherence is introduced. Similarities and differences between decoherence dynamics examined quantum mechanically and classically are exposed via a second-order perturbative treatment and via a strong…
The transition from quantum to classical statistics is studied in light of Huggett's finding that the empirical data do not support the usual claim that the distinction between classical and quantum objects consists in the capacity of…
A consistent description of interactions between classical and quantum systems is relevant to quantum measurement theory, and to calculations in quantum chemistry and quantum gravity. A solution is offered here to this longstanding problem,…
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 pursue the view that quantum theory may be an emergent structure related to large space-time scales. In particular, we consider classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a…
In this paper, we explore two different ways of implementing quantum effects in a classical structure. The first one is through an external field. The other one is modifying the classical conservation laws. In both cases, the consequences…
The quantization of particle trajectories gives rise to remarkable features such as the coherent superposition of quantum channels and the quantum switch, which offer significant advantages in the communication of both classical and quantum…
We study a quantum version of the sequential game illustrating problems connected with making rational decisions. We compare the results that the two models (quantum and classical) yield. In the quantum model intransitivity gains importance…
In this paper, we analyze classical and quantum physical systems from an optimal control perspective. Specifically, we explore whether their associated dynamics can correspond to an open or closed-loop feedback evolution of a control…
A quantum algorithm succeeds not because the superposition principle allows 'the computation of all values of a function at once' via 'quantum parallelism,' but rather because the structure of a quantum state space allows new sorts of…
The Hilbert space formalism of quantum theory manifests a map between bipartite states and time evolutions, known as Jamiolkowski isomorphism. We extend this map in a physical setting to prove the equality of spatial correlations in…
Identifying the real and imaginary parts of wave functions with coordinates and momenta, quantum evolution may be mapped onto a classical Hamiltonian system. In addition to the symplectic form, quantum mechanics also has a positive-definite…
Von Neumann's statistical theory of quantum measurement interprets the instantaneous quantum state and derives instantaneous classical variables. In realty, quantum states and classical variables coexist and can influence each other in a…
Effective classicality of a property of a quantum system can be defined using redundancy of its record in the environment. This allows quantum physics to approximate the situation encountered in the classical world: The information about a…
We investigate the correlations of initially separable probability distributions in a globally pure bipartite system with two degrees of freedom for classical and quantum systems. A classical version of the quantum linear mutual information…