# Implementation of generalized measurements on a qudit via quantum walks

## TL;DR

This paper presents a straightforward method to implement any generalized quantum measurement on a qudit using a one-dimensional quantum walk, significantly simplifying the process of realizing complex measurements.

## Contribution

It introduces a universal recipe for implementing generalized measurements on qudits via quantum walks, reducing complexity and resource requirements.

## Key findings

- Any discrete quantum measurement can be realized with twice the number of steps as measurement outcomes.
- Provides a unified approach for symmetric informationally complete measurements in dimension 3.
- Simplifies the implementation of complex quantum measurements.

## Abstract

Quantum measurements play a fundamental role in quantum mechanics and quantum information processing, but it is not easy to implement generalized measurements, the most powerful measurements allowed by quantum mechanics. Here we propose a simple recipe for implementing generalized measurements on a qudit via quantum walks. With this recipe, any discrete quantum measurement can be implemented via a one-dimensional discrete quantum walk; the number of steps is only two times the number of measurement outcomes. As an illustration, we present a unified solution for implementing arbitrary symmetric informationally complete measurements in dimension 3.