Stationary measure for three-state quantum walk (pp0901-0912)
          Takako Endo, Takashi Komatsu, Norio Konno, Tomoyuki Terada
We focus on the three-state quantum walk(QW) in one dimension. In this paper, we give the stationary measure in general condition, originated from the eigenvalue problem. Firstly, we get the transfer matrices by our new recipe, and solve the eigenvalue problem. Then we obtain the general form of the stationary measure for concrete initial state and eigenvalue. We also show some specific examples of the stationary measure for the three-state QW. One of the interesting and crucial future problems is to make clear the whole picture of the set of stationary measures.

Security proof for quantum key recycling with noise (pp0913-0934)
          Daan Leermakers and Boris Skoric
Quantum Key Recycling aims to re-use the keys employed in quantum encryption and quantum authentication schemes. QKR protocols can achieve better round complexity than Quantum Key Distribution. We consider a QKR protocol that works with qubits, as opposed to high-dimensional qudits. A security proof was given by Fehr and Salvail~\cite{FehrSalvail2017} in the case where there is practically no noise. A high-rate scheme for the noisy case was proposed by \v{S}kori\'{c} and de Vries~\cite{SdV2017}, based on eight-state encoding. However, a  security proof was not given. In this paper we introduce a protocol modification to~\cite{SdV2017}. We provide a security proof. The modified protocol has high rate not only for 8-state encoding, but also 6-state and BB84 encoding. Our proof is based on a bound on the trace distance between the real quantum state of the system and a state in which the keys are completely secure. It turns out that the rate is higher than suggested by previous results. Asymptotically the rate equals the rate of Quantum Key Distribution with one-way postprocessing.

Teleportation improvement by noiseless linear amplification (pp0935-0951)
          Hamza Adnane and Matteo G.A. Paris
We address de-Gaussification of continuous variables Gaussian states by optimal non-deterministic noiseless linear amplifier (NLA) and analyze in details the properties of the amplified states. In particular, we investigate the entanglement content and the non-Gaussian character for the class of non-Gaussian entangled state obtained by using NL-amplification of two-mode squeezed vacua (twin-beam, TWB). We show that entanglement always increases, whereas improved EPR correlations are observed only when the input TWB has low energy. We then examine a Braunstein-Kimble-like protocol for the teleportation of coherent states, and compare the performances of TWB-based teleprotation with those obtained using NL-amplified resources. We show that teleportation fidelity and security may be improved for a large range of NLA parameters (gain and threshold).

On the quantum complexity of computing the median of continuous distributions (pp0952-0966)
          Maciej Gocwin
We study the approximation of the median of an absolutely continuous distribution with respect to the Lebesgue measure given by a probability density function $f$.  We assume that $f$ has $r$ continuous derivatives, with  derivative of order $r$ being H\"older continuous with the exponent $\rho$. We study the quantum query complexity of this problem. We show that the $\ve$-complexity up to a logarithmic factor is of order  $\ve^{-1/(r+\rho+1)}$. We also extend the results to the problem of computing the vector of quantiles of an absolutely continuous distribution.

Simpler quantum counting (pp0967-0983)
          Chu-Ryang Wie
A simpler quantum counting algorithm based on amplitude amplification is presented. This algorithm is bounded by O(sqrt(N/M)) calls to the controlled-Grover operator where M is the number of marked states and N is the total number of states in the search space.  This algorithm terminates within log(sqrt(N/M)) consecutive measurement steps when the probability p1 of measuring the state |1> is at least 0.5, and the result from the final step is used in estimating M by a classical post processing. The purpose of controlled-Grover iteration is to increase the probability p1. This algorithm requires less quantum resources in terms of the width and depth of the quantum circuit, produces a more accurate estimate of M, and runs significantly faster than the phase estimation-based quantum counting algorithm when the ratio M/N is small. We compare the two quantum counting algorithms by simulating various cases with a different M/N ratio, such as M/N > 0.125 or M/N < 0.001.