Almost qudits in the prepare-and-measure scenario

• URL: http://arxiv.org/abs/2208.07887v2
• Date: Thu, 7 Mar 2024 17:01:23 GMT
• Title: Almost qudits in the prepare-and-measure scenario
• Authors: Jef Pauwels, Stefano Pironio, Erik Woodhead and Armin Tavakoli
• Abstract summary: We introduce and investigate quantum information encoded in carriers that nearly, but not entirely, correspond to standard qudits. We show how small higher-dimensional components can significantly compromise the conclusions of established protocols. We also consider viewing almost qubit systems as a physical resource available to the experimenter.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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