Quantum state identification of qutrits via a nonlinear protocol

TL;DR

This paper introduces a probabilistic nonlinear quantum protocol for qutrits that enables efficient identification of an unknown state from a finite set through iterative subset discrimination.

Contribution

It presents a novel nonlinear transformation protocol for qutrits and an algorithm that uses this to identify states from a finite set more efficiently than previous methods.

Findings

Protocol successfully distinguishes pure qutrit states.

Iterative application reduces candidate states to identify the unknown.

Uses single- and two-qutrit operations with post-selection.

Abstract

We propose a probabilistic quantum protocol to realize a nonlinear transformation of qutrit states, which by iterative applications on ensembles can be used to distinguish two types of pure states. The protocol involves single-qutrit and two-qutrit unitary operations as well as post-selection according to the results obtained in intermediate measurements. We utilize the nonlinear transformation in an algorithm to identify a quantum state provided it belongs to an arbitrary known finite set. The algorithm is based on dividing the known set of states into two appropriately designed subsets which can be distinguished by the nonlinear protocol. In most cases this is accompanied by the application of some properly defined physical (unitary) operation on the unknown state. Then, by the application of the nonlinear protocol one can decide which of the two subsets the unknown state belongs to thus reducing the number of possible candidates. By iteratively continuing this procedure until a single possible candidate remains, one can identify the unknown state.