Symplectic Tomography of De Broglie Wave

Hidden Correlations and Entanglement in Single-Qudit States†

“…In fact, the approach presented provides the possibility to extend all entropic and information relations known for for classical and quantum composite systems to the case of the systems without subsystems; these relations reflect the presence of correlations, either classical or quantum, of the system's degrees of freedom. The quantum correlations of the single-qudit states [46][47][48][49][50][51][52][53][54][55] can be used for quantum technologies analogously to the employment of entanglement as a quantum resource.…”

“…In this section, we describe a map of indices corresponding to the partition procedure; this map was named the map detecting hidden correlations in the system [24].…”

“…If M = 2, the general formulas (1) and (2) provide explicit expressions for y(x 1 , x 2 ), x 1 (y), and x 2 (y) presented as [24] (see also [25,26])…”

“…The map is realized using the set of "functions detecting the hidden correlations" [24]. After applying the map, the possibility arises to interpret an arbitrary probability distribution of one random variable as a joint probability distribution of M random variables.…”

Conditional Information and Hidden Correlations in Single-qudit States

“…It is worth noting that analogous functions were discussed in [33,34]. In the case where the integer N is the product of three integers N = X 1 X 2 X 3 , we introduce the functions y(x 1 , x 2 , x 3 ), x 1 (y), x 2 (y), and x 3 (y) given by the expressions [31]…”