High-dimensional multi-input quantum random access codes and mutually unbiased bases

• URL: http://arxiv.org/abs/2111.08890v6
• Date: Sat, 15 Oct 2022 02:59:37 GMT
• Title: High-dimensional multi-input quantum random access codes and mutually unbiased bases
• Authors: Rui-Heng Miao, Zhao-Di Liu, Yong-Nan Sun, Chen-Xi Ning, Chuan-Feng Li and Guang-Can Guo
• Abstract summary: We present a general method to find the maximum success probability of $n(d)rightarrow1$ QRACs. Based on the analytical solution, we show the relationship between MUBs and $n(d)rightarrow1$ QRACs.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum random access codes (QRACs) provide a basic tool for demonstrating the advantages of quantum resources and protocols, which have a wide range of applications in quantum information processing tasks. However, the investigation and application of high-dimensional $(d)$ multi-input $(n)$ $n^{(d)}\rightarrow1$ QRACs are still lacking. Here, we present a general method to find the maximum success probability of $n^{(d)}\rightarrow1$ QRACs. In particular, we give the analytical solution for maximum success probability of $3^{(d)}\rightarrow1$ QRACs when measurement bases are mutually unbiased bases (MUBs). Based on the analytical solution, we show the relationship between MUBs and $n^{(d)}\rightarrow1$ QRACs. First, we provide a systematic method of searching for the operational inequivalence of MUBs (OI-MUBs) when the dimension $d$ is a prime power. Second, we theoretically prove that, surprisingly, the commonly used Galois MUBs are not the optimal measurement bases to obtain the maximum success probability of $n^{(d)}\rightarrow1$ QRACs, which indicates a breakthrough according to the traditional conjecture regarding the optimal measurement bases. Furthermore, based on high-fidelity high-dimensional quantum states of orbital angular momentum, we experimentally achieve two-input and three-input QRACs up to dimension 11. We experimentally confirm the OI-MUBs when $d=5$. Our results open alternative avenues for investigating the foundational properties of quantum mechanics and quantum network coding.

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