Galois unitaries, mutually unbiased bases, and mub-balanced states (pp1261-1294)
          D. Marcus Appleby, Ingermar Bengtsson, and Hoan Bui Dang
A Galois unitary is a generalization of the notion of anti-unitary operators. They act only on those vectors in Hilbert space whose entries belong to some chosen number field. For Mutually Unbiased Bases the relevant number field is a cyclotomic field. By including Galois unitaries we are able to remove a mismatch between the finite projective group acting on the bases on the one hand, and the set of those permutations of the bases that can be implemented as transformations in Hilbert space on the other hand. In particular we show that there exist transformations that cycle through all the bases in all dimensions $d = p^n$ where
$p$ is an odd prime and the exponent $n$ is odd. (For even primes unitary MUB-cyclers exist.) These transformations have eigenvectors, which are MUB-balanced states (i.e.\ rotationally symmetric states in the original terminology of Wootters and Sussman) if and only if $d = 3$ modulo 4. We conjecture that this construction yields all such states in odd prime power dimension.

A qutrit Quantum Key Distribution protocol using Bell inequalities with larger violation capabilities (pp1295-1306)
          Zoe Amblard and Francois Arnault
The Ekert quantum key distribution protocol~\cite{Ekert1991} uses pairs of entangled qubits and performs checks based on a Bell inequality to detect eavesdropping. The 3DEB protocol~\cite{3DEB} uses instead pairs of entangled qutrits to achieve better noise resistance than the Ekert protocol. It performs checks based on a Bell inequality for qutrits named CHSH-3 and found in~\cite{CHSH3,ViolCHSH3GHZ}. In this paper, we present a new protocol, which also uses pairs of entangled qutrits, but gaining advantage of a Bell inequality which achieves better noise resistance than the one used in 3DEB. The latter inequality is called here hCHSH-3 and was discovered in~\cite{Arnault2012}. For each party, the hCHSH-3 inequality involves four observables already used in CHSH-3 but also two products of observables which do not commute. We explain how the parties can measure the observables corresponding to these products and thus are able to check the violation of hCHSH-3. In the presence of noise, this violation guarantees the security against a local Trojan horse attack. We also designed a version of our protocol which is secure against individual attacks.

Coherence measures and optimal conversion for coherent states (pp1307-1316)
          Shuanping Du, Zhaofang Bai, and Xiaofei Qi
We discuss a general strategy to construct coherence measures. One can build an important class of coherence measures which cover the relative entropy measure for pure states, the $l_1$-norm measure for pure states and the $\alpha$-entropy measure. The optimal conversion of coherent states under incoherent operations is presented which sheds some light on the coherence of a single copy of a pure state.

Unbounded entanglement in nonlocal games (pp1317-1332)
          Laura Mančinska and Thomas Vidick
Quantum entanglement is known to provide a strong advantage in many two-party distributed tasks. We investigate the question of how much entanglement is needed to reach optimal performance. For the first time we show that there exists a purely classical scenario for which no finite amount of entanglement suffices. To this end we introduce a simple two-party nonlocal game $H$, inspired by Lucien Hardy's paradox. In our game each player has only two possible questions and can provide bit strings of any finite length as answer. We exhibit a sequence of strategies which use entangled states in increasing dimension $d$ and succeed with probability $1-O(d^{-c})$ for some $c\geq 0.13$. On the other hand, we show that any strategy using an entangled state of local dimension $d$ has success probability at most $1-\Omega(d^{-2})$. In addition, we show that any strategy restricted to producing answers in a set of cardinality at most $d$ has success probability at most $1-\Omega(d^{-2})$. Finally, we generalize our construction to derive similar results starting from any game $G$ with two questions per player and finite answers sets in which quantum strategies have an advantage.

Monotonicity of quantum relative entropy and recoverability (pp1333-1354)
          Mario Berta, Marius Lemm, and Mark M. Wilde
The relative entropy is a principal measure of distinguishability in quantum information theory, with its most important property being that it is non-increasing with respect to noisy quantum operations. Here, we establish a remainder term for this inequality that quantifies how well one can recover from a loss of information by employing a rotated Petz recovery map. The main approach for proving this refinement is to combine the methods of [Fawzi and Renner, 2014] %arXiv:1410.0664] with the notion of a relative typical subspace from [Bjelakovic and Siegmund-Schultze, 2003]. %arXiv:quant-ph/0307170]. Our paper constitutes partial progress towards a remainder term which features just the Petz recovery map (not a rotated Petz map), a conjecture which would have many consequences in quantum information theory. A well known result states that the monotonicity of relative entropy with respect to quantum operations is equivalent to each of the following inequalities: strong subadditivity of entropy, concavity of conditional entropy, joint convexity of relative entropy, and monotonicity of relative entropy with respect to partial trace. We show that this equivalence holds true for refinements of all these inequalities in terms of the Petz recovery map. So either all of these refinements are true or all are false.

Maximally coherent states (pp1355-1364)
          Zhaofang Bai and Shuanping Du
The relative entropy measure quantifying coherence, a key property of quantum system, is proposed recently. In this note, we firstly investigate structural characterization of maximally coherent states with respect to the relative entropy measure. (denoted by $\mathcal C_{RE}$.  It is shown that mixed maximally coherent states do not exist and every pure maximally coherent state has the form $U|\psi\rangle\langle \psi|U^\dag$, $|\psi\rangle=\frac{1}{\sqrt{d}}\sum_{k=1}^{d}|k\rangle,$ $U$ is diagonal unitary. Based on the characterization of pure maximally coherent states, for a bipartite maximally coherent state with $d_A=d_B$, we obtain that the super-additivity equality of relative entropy measure holds if and only if the state is a product state of its reduced states. From the viewpoint of resource in quantum information, we find there exists a maximally coherent state with maximal entanglement. Originated from the behaviour of quantum correlation under the influence of quantum operations, we further classify the incoherent operations which send maximally coherent states to themselves.

Correcting for potential barriers in quantum walk search (pp1365-1372)
          Andris Ambainis, Thomas G. Wong
A randomly walking quantum particle searches in Grover's $\Theta(\sqrt{N})$ iterations for a marked vertex on the complete graph of $N$ vertices by repeatedly querying an oracle that flips the amplitude at the marked vertex, scattering by a ``coin'' flip, and hopping. Physically, however, potential energy barriers can hinder the hop and cause the search to fail, even when the amplitude of not hopping decreases with $N$. We correct for these errors by interpreting the quantum walk search as an amplitude amplification algorithm and modifying the phases applied by the coin flip and oracle such that the amplification recovers the $\Theta(\sqrt{N})$ runtime.

Limit theorems of a two-phase quantum walk with one defect (pp1373-1396)
          Shimpei Endo, Takako Endo, Norio Konno, Masato Takei, and Etsuo Segawa
We treat a position dependent quantum walk (QW) on the line which we assign two different time-evolution operators to positive and negative parts respectively. We call the model ``the two-phase QW" here, which has been expected to be a mathematical model of the topological insulator. We obtain the stationary and time-averaged limit measures related to localization for the two-phase QW with one defect. This is the first result on localization for the two-phase QW.  The analytical methods are mainly based on the splitted generating function of the solution for the eigenvalue problem, and the generating function of the weight of the passages of the model.  In this paper, we call the methods ``the splitted generating function method'' and ``the generating function method'', respectively. The explicit expression of the stationary measure is asymmetric for the origin, and depends on the initial state and the choice of the parameters of the model. On the other hand, the time-averaged limit measure has a starting point symmetry and localization effect heavily depends on the initial state and the parameters of the model. Regardless of the strong effect of the initial state and the parameters, the time-averaged limit measure also suggests that localization can be always observed for our two-phase QW. Furthermore, our results imply that there is an interesting relation between the stationary and time-averaged limit measures when the parameters of the model have specific periodicities, which suggests that there is a possibility that we can analyze localization of the two-phase QW with one defect from the stationary measure.

Teleportation of a controlled-NOT gate for photon and electron-spin qubits assisted by the nitrogen-vacancy center (pp1397-1419)
          Ming-Xing Luo and Hui-Ran Li
 

Quantum Merlin-Arthur with Clifford Arthur (pp1420-1430)
          Tomoyuki Morimae, Masahito Hayashi, Harumichi Nishimura, and Keisuke Fujii