Discrimination and synthesis of recursive quantum states in high-dimensional Hilbert spaces

TL;DR

This paper introduces an interferometric method for discriminating, preparing, and detecting high-dimensional quantum states, specifically photon orbital angular momentum states, enabling advanced quantum information processing and coding.

Contribution

The paper presents a novel interferometric approach for discriminating and manipulating nonorthogonal high-dimensional quantum states, including methods for switching between mutually unbiased bases.

Findings

Effective discrimination of OAM states from superpositions

Capability to prepare and detect arbitrary linear combinations of states

Simplified switching between high-dimensional mutually unbiased bases

Abstract

We propose an interferometric method for statistically discriminating between nonorthogonal states in high dimensional Hilbert spaces for use in quantum information processing. The method is illustrated for the case of photon orbital angular momentum (OAM) states. These states belong to pairs of bases that are mutually unbiased on a sequence of two-dimensional subspaces of the full Hilbert space, but the vectors within the same basis are not necessarily orthogonal to each other. Over multiple trials, this method allows distinguishing OAM eigenstates from superpositions of multiple such eigenstates. Variations of the same method are then shown to be capable of preparing and detecting arbitrary linear combinations of states in Hilbert space. One further variation allows the construction of chains of states obeying recurrence relations on the Hilbert space itself, opening a new range of possibilities for more abstract information-coding algorithms to be carried out experimentally in a simple manner. Among other applications, we show that this approach provides a simplified means of switching between pairs of high-dimensional mutually unbiased OAM bases.