A tight analysis of Kierstead-Trotter algorithm for online unit interval coloring

Kierstead and Trotter (Congressus Numerantium 33, 1981) proved that their algorithm is an optimal online algorithm for the online interval coloring problem. In this paper, for online unit interval coloring, we show that the number of colors used by the Kierstead-Trotter algorithm is at most $3 \omega(G) - 3$, where $\omega(G)$ is the size of the maximum clique in a given graph $G$, and it is the best possible.Comment: 4 page

Circular solution of two unequal mass particles in post-Minkowski approximation

A Fokker action for post-Minkowski approximation with the first post-Newtonian correction is introduced in our previous paper, and a solution for the helically symmetric circular orbit is obtained. We present supplemental results for the circular solution of two unequal mass point-particles. Circular solutions for selected mass ratios are found numerically, and analytic formulas in the extreme mass ratio limit are derived. The leading terms of the analytic formulas agree with the first post-Newtonian formulas in this limit.Comment: 4 pages, 4 figures, 4/27/0

Optimal entanglement manipulation via coherent-state transmission

We derive an optimal bound for arbitrary entanglement manipulation based on the transmission of a pulse in coherent states over a lossy channel followed by local operations and unlimited classical communication (LOCC). This stands on a theorem to reduce LOCC via a local unital qubit channel to local filtering. We also present an optimal protocol based on beam splitters and a quantum nondemolition (QND) measurement on photons. Even if we replace the QND measurement with photon detectors, the protocol outperforms known entanglement generation schemes.Comment: 5 pages, 1 figur

N-Body Nuclear Forces at Short Distances in Holographic QCD

We provide a calculation of N-body (N>2) nucleon interactions at short distances in holographic QCD. In the Sakai-Sugimoto model of large N_c massless QCD, N baryons are described by N Yang-Mills instantons in 5 spacetime dimensions. We compute a classical short distance interaction hamiltonian for N 'tHooft instantons. This corresponds to N baryons sharing identical classical spins and isospins. We find that genuine N-body nuclear forces turn out to vanish for N>2, at the leading order. This suggests that classical N-body forces are always suppressed compared with 2-body forces.Comment: 4 page

Package of facts and theorems for efficiently generating entanglement criteria for many qubits

We present a package of mathematical theorems, which allow to construct multipartite entanglement criteria. Importantly, establishing bounds for certain classes of entanglement does not take an optimization over continuous sets of states. These bonds are found from the properties of commutativity graphs of operators used in the criterion. We present two examples of criteria constructed according to our method. One of them detects genuine 5-qubit entanglement without ever referring to correlations between all five qubits.Comment: 5 pages, 4 figure

Kochen-Specker theorem as a precondition for secure quantum key distribution

We show that (1) the violation of the Ekert 91 inequality is a sufficient condition for certification of the Kochen-Specker (KS) theorem, and (2) the violation of the Bennett-Brassard-Mermin 92 (BBM) inequality is, also, a sufficient condition for certification of the KS theorem. Therefore the success in each QKD protocol reveals the nonclassical feature of quantum theory, in the sense that the KS realism is violated. Further, it turned out that the Ekert inequality and the BBM inequality are depictured by distillable entanglement witness inequalities. Here, we connect the success in these two key distribution processes into the no-hidden-variables theorem and into witness on distillable entanglement. We also discuss the explicit difference between the KS realism and Bell's local realism in the Hilbert space formalism of quantum theory.Comment: 4 pages, To appear in Phys. Rev.