On a Generalization of Tellegen’s Theorem to Quantum Circuits

Tellegen’s theorem is one of the foundational topological theorems of circuit theory. In its most elementary form, it expresses an energy balance between the power supplied at the ports of the electrical circuit network and the power consumed in its internal branches. But the topological roots of Tellegen’s theorem allow it to take other forms that make it into a powerful tool for deriving several fundamental results in electrical circuit networks, linear or non-linear, reciprocal or nonreciprocal. Tellegen’s theorem admits a generalization to the field case of Maxwell’s equations that makes it useful in the analysis and modeling of microwave devices. In this paper, the field case of Shrödinger’s equation is examined, and a generalization of Tellegen’s theorem to the case of quantum wave functions is proposed. This generalization has the potential of extending the application domain of Tellegen’s theorem to the circuits used in quantum computing.