Search

We consider the recent relativistic bit commitment protocol introduced by Lunghi et al. [Phys. Rev. Lett. 115, 030502 (2015)] and present a new security analysis against classical attacks. In particular, while the initial complexity of the protocol scales double exponentially with the commitment time, our analysis shows that the correct dependence is only linear. This has dramatic implications in terms of implementation: in particular, the commitment time can easily be made arbitrarily long, by only requiring both parties to communicate classically and perform efficient classical computation. [ABSTRACT FROM AUTHOR]

We demonstrate an efficient high-precision optical spectroscopy technique for single trapped ions with nonclosed transitions. In a double-shelving technique, the absorption of a single photon is first amplified to several phonons of a normal motional mode shared with a cotrapped cooling ion of a different species, before being further amplified to thousands of fluorescence photons emitted by the cooling ion using the standard electron shelving technique. We employ this extension of the photon recoil spectroscopy technique to perform the first high precision absolute frequency measurement of the 2D3/2 → 2B1/2 transition in calcium, resulting in a transition frequency of f = 346 000 234 867(96) kHz. Furthermore, we determine the isotope shift of this transition and the 2S1/2 → 2P1/2 transition for 42Ca+, 44Ca+, and 48Ca+ ions relative to 40Ca+ with an accuracy below 100 kHz. Improved field and mass shift constants of these transitions as well as changes in mean square nuclear charge radii are extracted from this high resolution data. [ABSTRACT FROM AUTHOR]

The S=1 Affleck-Kennedy-Lieb-Tasaki (AKLT) quantum spin chain was the first rigorous example of an isotropic spin system in the Haldane phase. The conjecture that the S=3/2 AKLT model on the hexagonal lattice is also in a gapped phase has remained open, despite being a fundamental problem of ongoing relevance to condensed-matter physics and quantum information theory. Here we confirm this conjecture by demonstrating the size-independent lower bound Δ>0.006 on the spectral gap of the hexagonal model with periodic boundary conditions in the thermodynamic limit. Our approach consists of two steps combining mathematical physics and high-precision computational physics. We first prove a mathematical finite-size criterion which gives an analytical, size-independent bound on the spectral gap if the gap of a particular cut-out subsystem of 36 spins exceeds a certain threshold value. Then we verify the finite-size criterion numerically by performing state-of-the-art DMRG calculations on the subsystem. [ABSTRACT FROM AUTHOR]