A min-entropy uncertainty relation for finite size cryptography

Apart from their foundational significance, entropic uncertainty relations play a central role in proving the security of quantum cryptographic protocols. Of particular interest are thereby relations in terms of the smooth min-entropy for BB84 and six-state encodings. Previously, strong uncertainty relations were obtained which are valid in the limit of large block lengths. Here, we prove a new uncertainty relation in terms of the smooth min-entropy that is only marginally less strong, but has the crucial property that it can be applied to rather small block lengths. This paves the way for a practical implementation of many cryptographic protocols. As part of our proof we show tight uncertainty relations for a family of Renyi entropies that may be of independent interest.Comment: 5+6 pages, 1 figure, revtex. new version changed author's name from Huei Ying Nelly Ng to Nelly Huei Ying Ng, for consistency with other publication

Information and Particle Physics

Information measures for relativistic quantum spinors are constructed to satisfy various postulated properties such as normalisation invariance and positivity. Those measures are then used to motivate generalised Lagrangians meant to probe shorter distance physics within the maximum uncertainty framework. The modified evolution equations that follow are necessarily nonlinear and simultaneously violate Lorentz invariance, supporting previous heuristic arguments linking quantum nonlinearity with Lorentz violation. The nonlinear equations also break discrete symmetries. We discuss the implications of our results for physics in the neutrino sector and cosmology

It's Hard to Learn How Gravity and Electromagnetism Couple

We construct the most general effective Lagrangian coupling gravity and electromagnetism up to mass dimension 6 by enumerating all possible non-minimal coupling terms respecting both diffeomorphism and gauge invariance. In all, there are only two unique terms after field re-definitions; one is known to arise from loop effects in QED while the other is a parity violating term which may be generated by weak interactions within the standard model of particle physics. We show that neither the cosmological propagation of light nor, contrary to earlier claims, solar system tests of General Relativity are useful probes of these terms. These non-minimal couplings of gravity and electromagnetism may remain a mystery for the foreseeable future.Comment: 9 pages. Minor corrections made. To appear in Phys. Rev.

Strategyproof Computing: Systems Infrastructures for Self-Interested Parties

The widespread deployment of high-speed internet access is ushering in a new era of distributed computing, in which parties both contribute to a global pool of shared resources and access the pooled resources to support their own computing needs. We argue that system designers must explicitly address the self-interest of individual parties if these next-generation computing systems are to flourish. We propose strategyproof computing, a vision for an open computing infrastructure in which resource allocation and negotiation schemes are incentive-compatible, and individual parties can treat other resources as their own. In this paper we outline key guiding principles for the vision of strategyproof computing, define the strategyproof computing paradigm, and lay out a systems-related research agenda.Engineering and Applied Science

Virtual Worlds: Fast and Strategyproof Auctions for Dynamic Resource Allocation

We consider the problem of designing fast and strategyproof exchanges for dynamic resource allocation problems in distributed systems. The exchange is implemented as a sequence of auctions, with dynamically arriving requests from agents matched with each auction. Each auction is associated with some consignment of the resources from a single seller. We provide a simple Virtual Worlds (VW) construction, that extends a fast and strategyproof mechanism for a single auction to apply to this sequence-of-auctions setting. Rather than match each buyer with a single auction, the VW mechanism allows buyers to be considered for multiple auctions while retaining strategyproofness.Engineering and Applied Science

The Minimal Length and Large Extra Dimensions

Planck scale physics represents a future challenge, located between particle physics and general relativity. The Planck scale marks a threshold beyond which the old description of spacetime breaks down and conceptually new phenomena must appear. Little is known about the fundamental theory valid at Planckian energies, except that it necessarily seems to imply the occurrence of a minimal length scale, providing a natural ultraviolet cutoff and a limit to the possible resolution of spacetime. Motivated by String Theory, the models of large extra dimensions lower the Planck scale to values soon accessible. These models predict a vast number of quantum gravity effects at the lowered Planck scale, among them the production of TeV-mass black holes and gravitons. Within the extra dimensional scenario, also the minimal length comes into the reach of experiment and sets a fundamental limit to short distance physics. We review the status of Planck scale physics in these effective models.Comment: 18 pages, 5 figures, brief review to appear in Mod. Phys. Let.