Basic Properties of Entropy in Quantum Mechanics

Ugo Farinelli, A. Gamba

W.A. van der Feltz

One of the exciting new phenomena that have risen from quantum mechanics is quantum\nentanglement. In this paper we study the basic mathematical properties of an entangled\nstate as well as its entanglement entropy. These concepts together with the formalism of\nsecond quantization will be studied with respect to finite one-dimensional transverse field\nIsing models.

Swapan Kumar Ghosh, Pratim Kumar Chattaraj

Uncertainty relations are the basic properties of quantum mechanics; in particular, we have the Heisenberg uncertainty principle1 for the product of the uncertainties in position and momentum σ σ σ σx p x p x xx x p p≥ = −( ) = −( )12 2 2 2 2, , , (22.1) 22.1 Introduction .................................................................................................. 441 22.2 Heisenberg Uncertainty Relations ................................................................442

Dėnes Petz

Norman Margolus

Maximum counts of distinct states define important physical quantities, the most famous being entropy. Here we show that energy, momentum and other basic quantities of mechanics are also maximum counts. This generalizes a property familiar in communication with classical waves: frequency-width equals maximum number of distinct values that can be sent, per unit time. Basic mechanical quantities are frequency-widths of wavefunction evolution, and similarly bound number of distinct states. Evolutions that achieve maximum distinctness are effectively discrete. These properties refine our understanding of uncertainty, measurement, classical mechanics, and relativity.