Operational Quantum Physics

J. Brooke

Badriyah Badriyah, Bambang Supriadi, Chilwatun Nasiroh +1 more

Classical physics began to be superseded by quantum physics because it could not explain microscopic phenomena. Quantum physics employs mathematical approaches such as wave mechanics and matrix mechanics, one of which is the eigenvalue problem involving matrix operators. There are many types of matrix operators; however, not all are suitable for measuring physical quantities in quantum physics. Operators in quantum physics must be Hermitian to ensure that their eigenvalues are real. Eigenvalue problems for matrix operators can be solved either analytically or numerically. Therefore, the objective of this research is to analyze symmetric and antisymmetric matrix operators in the measurement of physical quantities through eigenvalue problems. The research method utilized is a theoretical computational approach. The results demonstrate that symmetric matrix operators are Hermitian and yield real eigenvalues. In contrast, antisymmetric matrix operators are non Hermitian, yielding imaginary or complex eigenvalues. The results of solving eigen problems using Python obtained relative errors between 0 and orders., while the absolute error remained below 10%, thus confirming the validity of the results. Based on the findings, symmetric matrix operators satisfy the requirements for use in physical problems through eigenvalue analysis. The eigenvalues of antisymmetric matrices cannot represent the measurement of physical quantities directly and serve only as rotation operators. However, antisymmetric matrices can be utilized in quantum physics for physical measurements if they are transformed into Hermitian matrices. Furthermore, solving eigenvalue problems with Python is effective due to its high accuracy and small error margins.

Z. Ficek

This chapter considers the idea of representing physical as well as nonphysical quantities by operators and collect together some frequently used operator techniques. It postulates that any quantity in quantum physics is specified by a linear operator. In a manipulation with operators, it is very important to maintain the order of the operators because operator algebra is not in general commutative for multiplication. An important concept in quantum physics is a commutator. The chapter focuses on to define a special class of operators called Hermitian operators. They are distinguished by the relationship of  and † The Hermitian operators are of great importance in quantum physics, as they represent physical (measurable) quantities. The chapter defines a very important property of wave functions: orthogonality. This property, for example, allows to identify whether the given wave functions belong to the same operator or not. The orthogonality condition of two functions is analogous to the orthogonality condition of two vectors.

Paul Busch, Marian Grabowski, PEKKA J. LAHTI

Heinrich Saller

Masashi Ban

A partially reversible operation is introduced in quantum measurement processes and the information-theoretical property is investigated. The dual map of a partially reversible operation becomes reversible with respect to the intrinsic observable of a physical system. It is shown that the amount of information about the intrinsic observable of the physical system, obtained in a quantum measurement process described by a partially reversible operation, is equal to the decrease of the entropy of the measured physical system.