Almost qudits in the prepare-and-measure scenario
Jef Pauwels, Stefano Pironio, Erik Woodhead, Armin Tavakoli

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…
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Taxonomy
TopicsQuantum Information and Cryptography · Quantum Computing Algorithms and Architecture · Quantum and electron transport phenomena
