At high school as well as undergraduate level, Quantum Mechanics (QM) is usually introduced through an overview of the main experiments and theoretical attempts which took place at the beginning of 20-th century. Even if retracing the historical path which led to the introduction of the new conceptual and mathematical framework has undoubted advantages, there are also significant drawbacks, mainly in contexts, such as a high school, where students' lack of advanced mathematical tools puts severe constraints to the understanding of quantum concepts.

Indeed QM implies major changes in understanding the physical reality. Introducing issues such as probability, uncertainty and entanglement, is a highly non trivial task. Students have to face with a matter, which is in conflict with the usual classical view of the physical world. Furthermore, the introduction of wave functions and Schroedinger equation implies the solution of second order ordinary differential equations, which are usually beyond high school students' knowledge in calculus.

All these considerations led us to think that a better strategy could be to introduce, from the very beginning, a simple 2х2 matrix formulation of QM, where quantum states are identified with 2-vectors belonging to a finite vector space and observables are 2х2 matrices. In this way students have the possibility to become familiar with the unique conceptual issues of QM, such as superposition principle, non locality and entanglement without an advanced mathematical background. That allows them to have also a glimpse to topics such as qubits and quantum computers.

The inspiring source of our proposal is the 1925 seminal paper by Heisenberg (Z. Phys. 33 (1925) 879), which provides a simple calculational method to deal with quantum mechanical states and observables, based on the identification of the physical quantities of interest with transition frequencies and amplitudes. Indeed such frequencies and amplitudes form matrices.