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

TL;DR

This paper develops a method to optimize high-dimensional quantum random access codes (QRACs), analytically solves for success probabilities with mutually unbiased bases, and experimentally demonstrates QRACs up to dimension 11, revealing new insights into quantum measurement bases.

Contribution

It introduces a general method for maximizing success probabilities of high-dimensional QRACs, analytically solves for specific cases with MUBs, and experimentally verifies QRACs up to dimension 11, challenging traditional assumptions about optimal measurement bases.

Findings

Analytical solutions for 3^{(d)}→1 QRAC success probabilities with MUBs.

Identification of operational inequivalence of MUBs in prime power dimensions.

Experimental realization of QRACs up to dimension 11 confirming theoretical predictions.

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.