# Sequential discrimination of qudits by multiple observers

## TL;DR

This paper proposes a sequential state-discrimination scheme for qudits, enabling multiple observers to identify nonorthogonal quantum states with unambiguous measurements, and analyzes its robustness against eavesdropping.

## Contribution

It introduces a novel sequential discrimination protocol for qudits, extending unambiguous state discrimination to higher-dimensional systems with varying overlaps.

## Key findings

- Qudits allow more information per transmission than qubits.
- The scheme increases the likelihood of detecting eavesdroppers.
- Robustness against simple eavesdropping attacks is improved with qudits.

## Abstract

We discuss a scheme in which sequential state-discrimination measurements are performed on qudits to determine the quantum state in which they were initially prepared. The qudits belong to a set of nonorthogonal quantum states and hence cannot be distinguished with certainty. Unambiguous state discrimination allows error-free measurements at the expense of occasionally failing to give a conclusive answer about the state of the qudit. Qudits have the potential to carry more information per transmission than qubits. We considered the situation in which Alice sends one of N qudits, where the dimension of the qudits is also N. We look at two cases, one in which the states all have the same overlap and one in which the qudits are divided into two sets, with qudits in different sets having different overlaps. We also study the robustness of our scheme against a simple eavesdropping attack and found that by using qudits rather than qubits, there is a greater probability that an eavesdropper will introduce errors and be detected.