The Quantum Statistical Density Matrix.

C. Di Castro, Roberto Raimondi

Alexander Shalyt-Margolin

This work presents a comparison of Quantum and Statistical Mechanics at Planck scale. The statistical mechanics deformation is constructed by analogy to the earlier quantum mechanical results. As previously, the primary object is a density matrix, but now the statistical one. The obtained deformed object is referred to as a statistical density pro-matrix. This object is explicitly described, and it is demonstrated that there is a complete analogy in the construction and properties of quantum mechanics and statistical density matrices at Plank scale (i.e. density pro-matrices). It is shown that an ordinary statistical density matrix occurs in the low-temperature limit at temperatures much lower than the Plank's. The associated deformation of a canonical Gibbs distribution is given explicitly.

Giacomo Mauro D’Ariano, Chiara Macchiavello, Nicoletta Sterpi

We study both systematic and statistical errors in radiation density matrix measurements. First we estimate the minimum number of scanning phases needed to reduce systematic errors to below a fixed threshold. Then, we calculate the statistical errors, intrinsic in the procedure that gives the density matrix. We present a detailed study of such errors versus the detectors' quantum efficiency and the matrix indices in the number representation, for different radiation states. For unit quantum efficiency, and for both coherent and squeezed states, the statistical errors of the diagonal matrix elements saturate for large n. In contrast, off-diagonal errors increase with the distance from the diagonal. For non-unit quantum efficiency the statistical errors along the diagonal do not saturate and increase dramatically versus both and the matrix indices.

Selenu Simone

In this article, a statistical approach to the calculus of quantum Selenu’s phase on a measured data set of expectation values of quantum operators is reported, to calculate the density matrix of a quantum system. A new mathematical model, based on the calculus of groupal derivatives [1] of expectation values shows density matrix to be the integrated correlation Wigner density function of quantum states.

Apoorva Patel