Quantum Mechanical Treatment of the Problem of Constraints in Nonextensive Formalism Revisited

TL;DR

This paper extends the analysis of Werner state purity in nonextensive formalism to all q values using a perturbative approach, demonstrating the necessity of both constraints for a complete solution spectrum.

Contribution

It introduces a perturbative method to solve the Werner state problem for all q values, unifying the use of ordinary and escort probabilities in nonextensive formalism.

Findings

Both constraints are necessary for full q spectrum solutions.

Negative values occur with ordinary probability outside 0<q<1.

Using both constraints ensures comprehensive nonextensive analysis.

Abstract

The purity of Werner state in nonextensive formalism associated with two different constraints has been calculated in a previous paper by G. B. Bagci et al. [G. B. Bagci et al., Int. J. Mod. Phys. 20, 2085 (2006)]. Two different results have been obtained corresponding to ordinary probability and escort probability whereas the former has been shown to result in negative values thereby leading authors to deduce the advantage of escort probabilities over ordinary probabilities. However, this results have been only for a limited interval of q values which lie between 0 and 1. In this paper, we solve the same problem for all values of nonextensive index q by using a perturbative approach and show that the simultaneous use of both types of constraint is necessary in order to obtain the solution for whole spectrum of nonextensive index. In this sense, the existence of these different constraints in nonextensive formalism must not be seen as a deficiency in the formalism but rather must be welcomed as a means of providing solution for all values of parameter q.