The concept of quantum coherence, including various ways to quantify the degree of coherence with respect to the prescribed basis, is currently the subject of active research. The complementarity of quantum coherence in different bases was studied by deriving upper bounds on the sum of the corresponding measures. To obtain a two-sided estimate, lower bounds on the coherence quantifiers are also of interest. Such bounds are naturally referred to as uncertainty relations for quantum coherence. We obtain new uncertainty relations for coherence quantifiers averaged with respect to a set of mutually unbiased bases (MUBs). To quantify the degree of coherence, the relative entropy of coherence and the geometric coherence are used. Further, we also derive novel state-independent uncertainty relations for a set of MUBs in terms of the min-entropy.
We investigate the $l_{1}$ norm of coherence of quantum states in mutually unbiased bases. We find that the sum of squared $l_{1}$ norm of coherence of the mixed state single qubit is less than two. We derive the $l_{1}$ norm of coherence of three classes of $X$ states in nontrivial mutually unbiased bases for $4$-dimensional Hilbert space is equal. We proposed "autotensor of mutually unbiased basis(AMUB)" by the tensor of mutually unbiased bases, and depict the level surface of constant the sum of the $l_{1}$ norm of coherence of Bell-diagonal states in AMUB. We find the $l_{1}$ norm of coher…
Semi-quantum key distribution is traditionally based on two-level quantum systems. In this paper, an unconditional security of a semi quantum key distribution protocol based on higher-dimensional systems using various mutually unbiased bases is presented. We first consider the three dimensional case using three and four mutually unbiased bases and derive a lower bound for the key rate as a function of the quantum channel's noise. We then generalize the result to a semi-quantum key distribution protocol that employs different number of mutually unbiased bases for four-dimensional states. It is …
The thesis is mainly about the construction and implementation of cyclic mutually unbiased bases, dealing with different entanglement structures by discussing the related group structures. A recursive construction for Fermat number dimensions is given and related to Wiedemann's conjecture for systems with more than 2048 qubits. The second part of the thesis analyses a quantum public-key encryption scheme.
We develop a new technique to construct mutually unbiased tripartite absolutely maximally entangled bases. We first explore the tripartite absolutely maximally entangled bases and mutually unbiased bases in $\mathbb{C}^{d} \otimes \mathbb{C}^{d} \otimes \mathbb{C}^{d}$ based on mutually orthogonal Latin squares. Then we generalize the approach to the case of $\mathbb{C}^{d_{1}} \otimes \mathbb{C}^{d_{2}} \otimes \mathbb{C}^{d_{1}d_{2}}$ by mutually weak orthogonal Latin squares. The concise direct constructions of mutually unbiased tripartite absolutely maximally entangled bases are remarkably…
We study entanglement witness and present a construction of entanglement witnesses in terms of the mutually unbiased measurements (MUMs). These witnesses include the entanglement witnesses constructed from mutually unbiased bases (MUBs) as a special case. Comparing with the dimension dependence of MUBs, the witnesses can be always constructed from a complete set of $d+1$ MUMs for any dimension $d$. We show that our witness can detect entanglement better than previous separability criterion given also by MUMs. And the approach can be experimentally implemented.
Mutually Unbiased Coarse-Grained Measurements of Two or More Phase-Space Variables
相空间算符本征态的相互无偏性，如位置和动量，或它们的标准粗粒化版本，只存在于无限压缩的极限情况下。在[Phys. Rev. Lett. 120，040403（2018）]表明，对于这两个算子的周期性粗粒化，可以恢复相互无偏性。在这里，我们调查的相互无偏的粗粒度测量两个以上的相空间变量。我们发现，相互无偏性可以恢复之间的任何两个非平行的相空间运营商的周期性粗粒化。我们说明了这些结果，通过光学实验，使用分数傅里叶变换来制备和测量相互无偏的相空间变量。两个和三个相互无偏测量之间的差异进行了讨论。我们的结果有助于弥合连续和离散量子力学之间的差距，并可能是有用的量子信息协议。
Akin to the idea of complete sets of Mutually Unbiased Bases for prime dimensional Hilbert spaces, $\mathcal{H}_d$, we study its analogue for a $d$ dimensional subspace of $M (d,\mathbb{C})$, i.e. Mutually Unbiased Unitary Bases (MUUBs) comprising of unitary operators. We note an obvious isomorphism between the vector spaces and beyond that, we define a relevant monoid structure for $\mathcal{H}_d$ isomorphic to one for the subspace of $M (d,\mathbb{C})$. This provides us not only with the maximal number of such MUUBs, but also a recipe for its construction.
