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arXiv · 2208.07887

Almost qudits in the prepare-and-measure scenario

Jef Pauwels·Stefano Pironio·Erik Woodhead·Armin Tavakoli
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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.

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Jef Pauwels, Stefano Pironio, Erik Woodhead, Armin Tavakoli. 2022-08-16. Almost qudits in the prepare-and-measure scenario. https://doi.org/10.1103/physrevlett.129.250504

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