On the Noether charge and the gravity duals of quantum complexity

The physical relevance of the thermodynamic volumes of AdS black holes to the gravity duals of quantum complexity was recently argued by Couch et al. In this paper, by generalizing the Wald-Iyer formalism, we derive a geometric expression for the thermodynamic volume and relate its product with the thermodynamic pressure to the non-derivative part of the gravitational action evaluated on the Wheeler-DeWitt patch. We propose that this action provides an alternative gravity dual of the quantum complexity of the boundary theory. We refer this to "complexity=action 2.0" (CA-2) duality. It is significantly different from the original "complexity=action" (CA) duality as well as the "complexity=volume 2.0" (CV-2) duality proposed by Couch et al. The latter postulates that the complexity is dual to the spacetime volume of the Wheeler-DeWitt patch. To distinguish our new conjecture from the various dualities in literature, we study a number of black holes in Einstein-Maxwell-Dilation theories. We find that for all these black holes, the CA duality generally does not respect the Lloyd bound whereas the CV-2 duality always does. For the CA-2 duality, although in many cases it is consistent with the Lloyd bound, we also find a counter example for which it violates the bound as well.Comment: minor corrections, references added,29pages,7figure

Tracking Angles of Departure and Arrival in a Mobile Millimeter Wave Channel

Millimeter wave provides a very promising approach for meeting the ever-growing traffic demand in next generation wireless networks. To utilize this band, it is crucial to obtain the channel state information in order to perform beamforming and combining to compensate for severe path loss. In contrast to lower frequencies, a typical millimeter wave channel consists of a few dominant paths. Thus it is generally sufficient to estimate the path gains, angles of departure (AoDs), and angles of arrival (AoAs) of those paths. Proposed in this paper is a dual timescale model to characterize abrupt channel changes (e.g., blockage) and slow variations of AoDs and AoAs. This work focuses on tracking the slow variations and detecting abrupt changes. A Kalman filter based tracking algorithm and an abrupt change detection method are proposed. The tracking algorithm is compared with the adaptive algorithm due to Alkhateeb, Ayach, Leus and Heath (2014) in the case with single radio frequency chain. Simulation results show that to achieve the same tracking performance, the proposed algorithm requires much lower signal-to-noise-ratio (SNR) and much fewer pilots than the other algorithm. Moreover, the change detection method can always detect abrupt changes with moderate number of pilots and SNR.Comment: 6 pages, 7 figures, submitted to ICC 201