Ptychographic reconstruction of qudits encoded in angular position and orbital angular momentum of photons

Abstract

In the context of quantum information theory, the use of certain photonic degrees of freedom allows the creation of high-dimensional quantum states, called qudits, which offer advantages over qubits in applications such as communication, cryptography, and fundamental tests of quantum mechanics. In many of these applications, it is necessary to reconstruct the quantum state to be used, since it contains all the measurable properties of a physical system. Recently, a simple method for reconstructing pure quantum states, called quantum ptychography, has been proposed. It is based on projections of the input state into various partial overlapping subspaces, each one followed by a projective measurement in the Fourier basis, which is generated by the quantum Fourier transform (QFT) of the computational basis. At the end, an iterative algorithm estimates the state from the collected data. In this work, we propose to apply this method to pure states of qudits encoded in angular position and orbital angular momentum (OAM) of single photons. For this purpose, we define these qudits based on the discretization of the spatial profile of a photon in cylindrical coordinates, through an arrangement of D angular slits, and describe their representation in the OAM basis. To apply ptychography to these qudits, we show that the intermediate projections will be implemented by simple binary spatial filters, while the measurement in the Fourier basis of the post-projection states will be performed by measuring in a basis defined by D OAM modes. Finally, we demonstrate the applicability of the ptychographic method by simulating the reconstruction of angular qudits for D = 5 and D = 12, and evaluate its experimental feasibility.