Almost qudits in the prepare-and-measure scenario

TL;DR

This paper explores quantum information in near-qudit systems, demonstrating how small deviations from ideal qudits impact protocols and providing methods to bound and test these near-ideal correlations.

Contribution

It introduces a framework for analyzing almost qudits, showing their significance in semi-device-independent protocols and developing a semidefinite relaxation method for bounding correlations.

Findings

Small higher-dimensional components can compromise quantum protocols.

A semidefinite relaxation method effectively bounds almost qudit correlations.

The approach improves device-independent tests of quantum dimensions.

Abstract

Quantum communication is often investigated in scenarios where only the dimension of Hilbert space is known. However, assigning a precise dimension is often an approximation of what is actually a higher-dimensional process. Here, we introduce and investigate quantum information encoded in carriers that nearly, but not entirely, correspond to standard qudits. We demonstrate the relevance of this concept for semi-device-independent quantum information by showing how small higher-dimensional components can significantly compromise the conclusions of established protocols. Then we provide a general method, based on semidefinite relaxations, for bounding the set of almost qudit correlations, and apply it to remedy the demonstrated issues. This method also offers a novel systematic approach to the well-known task of device-independent tests of classical and quantum dimensions with unentangled devices. Finally, we also consider viewing almost qubit systems as a physical resource available to the experimenter and determine the optimal quantum protocol for the well-known Random Access Code.