A set theoretical approach for the partial tracing operation in quantum mechanics

Abstract

Partial trace is a very important mathematical operation in quantum mechanics. It is not only helpful in studying the subsystems of a composite quantum system but also used in computing a vast majority of quantum entanglement measures. Calculating partial trace becomes computationally very intensive with increasing number of qubits as the Hilbert space dimension increases exponentially. In this paper we discuss about our new method of partial tracing which is based on set theory and it is more efficient. The proposed method of partial tracing overcomes all the limitations of the other well known methods such as being computationally intensive and being limited to low dimensional Hilbert spaces. We give a detailed theoretical description of our method and also provide an explicit example of the computation. The merits of the new method and other key ideas are discussed.