An operational link between MUBs and SICs

Mutually unbiased bases and symmetric informationally complete measurements in Bell experiments

Mutually unbiased bases (MUBs) and symmetric informationally complete projectors (SICs) are crucial to many conceptual and practical aspects of quantum theory. Here, we develop their role in quantum nonlocality by: i) introducing families of Bell inequalities that are maximally violated by $d$-dimensional MUBs and SICs respectively, ii) proving device-independent certification of natural operational notions of MUBs and SICs, and iii) using MUBs and SICs to develop optimal-rate and nearly optimal-rate protocols for device independent quantum key distribution and device-independent quantum rando…

From SICs and MUBs to Eddington

This is a survey of some very old knowledge about Mutually Unbiased Bases (MUB) and Symmetric Informationally Complete POVMs (SIC). In prime dimensions the former are closely tied to an elliptic normal curve symmetric under the Heisenberg group, while the latter are believed to be orbits under the Heisenberg group in all dimensions. In dimensions 3 and 4 the SICs are understandable in terms of elliptic curves, but a general statement escapes us. The geometry of the SICs in 3 and 4 dimensions is discussed in some detail.

利用相互无偏基（MUBs）进行真正多体纠缠探测

Genuine multipartite entanglement detection with mutually unbiased bases (MUBs)

提出一种基于相互无偏基关联计算的GME探测框架，利用双可分态满足而GME态违反的界限实现充分判据，并适用于三体与四体GME认证。

高效识别互不偏正交基的不等价性 via 有限算子

Efficient Identification the Inequivalence of Mutually Unbiased Bases via Finite Operators

本文提出了一种高效方法，用于确定互不偏正交基子集的不等价性，通过减少计算复杂度和避免精度问题，实现了对高维MUBs分类的精确结果。

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

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 unbiase…

Self-testing mutually unbiased bases in the prepare-and-measure scenario

Mutually unbiased bases (MUBs) constitute the canonical example of incompatible quantum measurements. One standard application of MUBs is the task known as quantum random access code (QRAC), in which classical information is encoded in a quantum system, and later part of it is recovered by performing a quantum measurement. We analyse a specific class of QRACs, known as the $2^{d} \to 1$ QRAC, in which two classical dits are encoded in a $d$-dimensional quantum system. It is known that among rank-1 projective measurements MUBs give the best performance. We show (for every $d$) that this cannot …