A Gramian approach to entanglement in bipartite finite dimensional systems: the case of pure states (pp1081-1108)
          Roman Gielerak,and Marek Sawerwain
It has been observed that the reduced density matrices of bipartite qudit pure states possess a Gram matrix structure. This observation has opened a possibility of analysing the entanglement in such systems from the purely geometrical point of view. In particular, a new quantitative measure of an entanglement of the geometrical nature, has been proposed. Using the invented Gram matrix approach, a version of a non-linear purification of mixed states describing the system analysed has been presented.

Faster amplitude estimation (pp1109-1123)
          Kouhei Nakaji
In this paper, we introduce an efficient algorithm for the quantum amplitude estimation task which is tailored for near-term quantum computers. The quantum amplitude estimation is an important problem which has various applications in fields such as quantum chemistry, machine learning, and finance. Because the well-known algorithm for the quantum amplitude estimation using the phase estimation does not work in near-term quantum computers, alternative approaches have been proposed in recent literature. Some of them provide a proof of the upper bound which almost achieves the Heisenberg scaling. However, the constant factor is large and thus the bound is loose. Our contribution in this paper is to provide the algorithm such that the upper bound of query complexity almost achieves the Heisenberg scaling and the constant factor is small.

Coherent preorder of quantum states (pp1124-1137)
          Zhaofang Bai and Shuanping Du
As an important quantum resource, quantum coherence play key role in quantum information processing. It is often concerned with  manipulation of families of quantum states rather than individual states in isolation. Given two pairs of coherent states $(\rho_1,\rho_2)$ and $(\sigma_1,\sigma_2)$, we are aimed to study how can we determine if there exists a strictly incoherent operation $\Phi$ such that $\Phi(\rho_i) =\sigma_i,i = 1,2$. This is also a classic question in quantum hypothesis testing. In this note, structural characterization of coherent preorder under strongly incoherent operations is provided. Basing on the characterization, we propose an approach to realize coherence distillation  from rank-two mixed coherent states to $q$-level maximally coherent states.  In addition, one scheme of coherence manipulation between rank-two mixed states is also presented.

Analysis of lackadaisical quantum walks (pp1138-1153)
          Peter Hoyer and Zhan Yu
The lackadaisical quantum walk is a quantum analogue of the lazy random walk obtained by adding a self-loop to each vertex in the graph.  We analytically   prove that lackadaisical quantum walks can find a unique marked vertex on any regular locally arc-transitive graph with constant success probability   quadratically faster than the hitting time. This result proves several speculations and numerical findings in previous work, including the conjectures that the lackadaisical quantum walk finds a unique marked vertex with constant success probability on the torus, cycle, Johnson graphs, and other classes of vertex-transitive graphs.  Our proof establishes and uses a relationship between lackadaisical quantum walks and quantum interpolated walks for any regular locally arc-transitive graph.

Generating W states with braiding operators (pp1154-1162)
          Pramod Padmanabhan, Fumihiko Sugino, and Diego Trancanelli
Braiding operators can be used to create entangled states out of product states, thus establishing a correspondence between topological and quantum entanglement. This is well-known for maximally entangled Bell and GHZ states and their equivalent states under Stochastic Local Operations and Classical Communication, but so far a similar result for W states was missing. Here we use generators of extraspecial 2-groups to obtain the W state in a four-qubit space and partition algebras to generate the W state in a three-qubit space. We also present a unitary generalized Yang-Baxter operator that embeds the W$_n$ state in a $(2n-1)$-qubit space.