Selective and Efficient Quantum Process Tomography in Arbitrary Finite Dimension

TL;DR

This paper introduces two new methods for quantum process tomography that are efficient and applicable to any finite-dimensional quantum system, overcoming previous limitations related to the existence of mutually unbiased bases.

Contribution

It presents two variations of quantum process tomography that work in arbitrary finite dimensions, removing the need for mutually unbiased bases only existing in prime power dimensions.

Findings

Methods are applicable to any finite dimension.

They enable selective measurement of quantum process coefficients.

The approaches are efficient and adaptable to different system sizes.

Abstract

The characterization of quantum processes is a key tool in quantum information processing tasks for several reasons: on one hand, it allows to acknowledge errors in the implementations of quantum algorithms; on the other, it allows to charcaterize unknown processes occurring in Nature. In previous works [Bendersky, Pastawski and Paz. Phys. Rev. Lett. 100, 190403 (2008) and Phys. Rev. A 80, 032116 (2009)] it was introduced a method to selectively and efficiently measure any given coefficient from the matrix description of a quantum channel. However, this method heavily relies on the construction of maximal sets of mutually unbiased bases (MUBs), which are known to exist only when the dimension of the Hilbert space is the power of a prime number. In this article, we lift the requirement on the dimension by presenting two variations of the method that work on arbitrary finite dimensions: one uses tensor products of maximally sets of MUBs, and the other uses a dimensional cutoff of a higher prime power dimension.