Are observables necessarily Hermitian?

Abstract

Observables are believed that they must be Hermitian in quantum theory. Based on the obviously physical fact that only eigenstates of observable and its corresponding probabilities, i.e., spectrum distribution of observable are actually observed, we argue that observables need not necessarily to be Hermitian. More generally, observables should be reformulated as normal operators including Hermitian operators as a subclass. This reformulation is consistent with the quantum theory currently used and does not change any physical results. The Clauser-Horne-Shimony-Holt (CHSH) inequality is taken as an example to show that our opinion does not conflict with conventional quantum theory and gives the same physical results. Reformulation of observables as normal operators not only coincides with the physical facts but also will deepen our understanding of measurement in quantum theory.

5 pages, 1 figure

References in corpus (4)

• Making Sense of Non-Hermitian Hamiltonians
• Quantum Averages of Weak Values
• Sequential weak measurement
• Relative States and the Environment: Einselection, Envariance, Quantum Darwinism, and the Existential Interpretation

Cited by in corpus (6)

• Advances in High Dimensional Quantum Entanglement
• Non-hermitian quantum thermodynamics
• Measuring average of non-Hermitian operator with weak value in a Mach-Zehnder interferometer
• A Scheme for Performing Strong and Weak Sequential Measurements of Non-commuting Observables
• Using Weyl operators to study Mermin's inequalities in Quantum Field Theory
• Detecting strongly non-Gaussian entanglement