Related papers: Tomographic entropy and cosmology
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
Introduced recently approach based on tomographic probability distribution of quantum states is shown to be closely related with the known notion of the quantum probability measures discussed in quantum information theory and positive…
There is a formal analogy between the evolution of the universe, when this is seen as a trajectory in the minisuperspace, and the worldline followed by a test particle in a curved spacetime. The analogy can be extended to the quantum realm,…
A review of the photon-number tomography and symplectic tomography as examples of star-product quantization is presented. The classical statistical mechanics is considered within the framework of the tomographic representation.
It is here proposed a geometric approach for the problem of describing entropy in a quantum system. We make use of an extension of tensor calculus called morphogenetic calculus. By using such formalism we express the entropy of a quantum…
The continuous quantum measurement within the probability representation of quantum mechanics is discussed. The partial classical propagator of the symplectic tomogram associated to a particular measurement outcome is introduced, for which…
The importance of the tomographic approach is that either in quantum mechanics as in classical mechanics the state of a physical system is expressed with the same family of functions, the tomograms. The extension of this procedure to…
It is often stated that quantum mechanics only makes statistical predictions and that a quantum state is described by the various probability distributions associated with it. Can we describe a quantum state completely in terms of…
A unified view on macroscopic thermodynamics and quantum transport is presented. Thermodynamic processes with an exchange of energy between two systems necessarily involve the flow of other balanceable quantities. These flows are first…
Tomograms introduced for the description of quantum states in terms of probability distributions are shown to be related to a standard star-product quantization with appropriate kernels. Examples of symplectic tomograms and spin tomograms…
Renyi entropy associated with spin tomograms of quantum states is shown to obey to new inequalities containing the dependence on quantum Fourier transform. The limiting inequality for the von Neumann entropy of spin quantum states and a new…
We investigate the question of whether the entropy and the Renyi entropies of the vacuum state reduced to a region of the space can be represented in terms of correlators in quantum field theory. In this case, the positivity relations for…
The classical thermostatics of equilibrium processes is shown to possess a quantum-mechanical dual theory with a finite-dimensional Hilbert space of quantum states. Specifically, the kernel of a certain Hamiltonian operator becomes the…
It is shown that the homogeneous and isotropic Universe is spatially flat in the limit which takes into account the moments of infinitely large orders of probabilistic distribution of a scale factor with respect to its mean value in the…
There are many theories of quantum gravity, depending on asymptotic boundary conditions, and the amount of supersymmetry. The cosmological constant is one of the fundamental parameters that characterize different theories. If it is…
The linear canonical transforms of position and momentum are used to construct the tomographic probability representation of quantum states where the fair probability distribution determines the quantum state instead of the wave function or…
Quantum cosmology in the presence of a fundamental minimal length is analyzed in the context of the flat isotropic and the Taub cosmological models. Such minimal scale comes out from a generalized uncertainty principle and the quantization…
In this talk we entertain the possibility that the synthesis of general covariance and quantum mechanics requires an extension of the basic kinematical setup of quantum mechanics. According to the holographic principle, regions of spacetime…
Polymer quantization is as a useful toy model for the mathematical aspects of loop quantum gravity and is interesting in its own right. Analyzing entropies of physically equivalent states in the standard Hilbert space and the polymer…