Quantum causal histories

Quantum causal histories are defined to be causal sets with Hilbert spaces attached to each event and local unitary evolution operators. The reflexivity, antisymmetry, and transitivity properties of a causal set are preserved in the quantum history as conditions on the evolution operators. A quantum causal history in which transitivity holds can be treated as ``directed'' topological quantum field theory. Two examples of such histories are described.Comment: 16 pages, epsfig latex. Some clarifications, minor corrections and references added. Version to appear in Classical and Quantum Gravit

Conserved Quantities in Background Independent Theories

We discuss the difficulties that background independent theories based on quantum geometry encounter in deriving general relativity as the low energy limit. We follow a geometrogenesis scenario of a phase transition from a pre-geometric theory to a geometric phase which suggests that a first step towards the low energy limit is searching for the effective collective excitations that will characterize it. Using the correspondence between the pre-geometric background independent theory and a quantum information processor, we are able to use the method of noiseless subsystems to extract such coherent collective excitations. We illustrate this in the case of locally evolving graphs.Comment: 11 pages, 3 figure

Factorization and Entanglement in Quantum Systems

We discuss the question of entanglement versus separability of pure quantum states in direct product Hilbert spaces and the relevance of this issue to physics. Different types of separability may be possible, depending on the particular factorization or split of the Hilbert space. A given orthonormal basis set for a Hilbert space is defined to be of type (p,q) if p elements of the basis are entangled and q are separable, relative to a given bi-partite factorization of that space. We conjecture that not all basis types exist for a given Hilbert space.Comment: 11 page

Network coding meets multimedia: a review

While every network node only relays messages in a traditional communication system, the recent network coding (NC) paradigm proposes to implement simple in-network processing with packet combinations in the nodes. NC extends the concept of "encoding" a message beyond source coding (for compression) and channel coding (for protection against errors and losses). It has been shown to increase network throughput compared to traditional networks implementation, to reduce delay and to provide robustness to transmission errors and network dynamics. These features are so appealing for multimedia applications that they have spurred a large research effort towards the development of multimedia-specific NC techniques. This paper reviews the recent work in NC for multimedia applications and focuses on the techniques that fill the gap between NC theory and practical applications. It outlines the benefits of NC and presents the open challenges in this area. The paper initially focuses on multimedia-specific aspects of network coding, in particular delay, in-network error control, and mediaspecific error control. These aspects permit to handle varying network conditions as well as client heterogeneity, which are critical to the design and deployment of multimedia systems. After introducing these general concepts, the paper reviews in detail two applications that lend themselves naturally to NC via the cooperation and broadcast models, namely peer-to-peer multimedia streaming and wireless networkin

A discrete, unitary, causal theory of quantum gravity

A discrete model of Lorentzian quantum gravity is proposed. The theory is completely background free, containing no reference to absolute space, time, or simultaneity. The states at one slice of time are networks in which each vertex is labelled with two arrows, which point along an adjacent edge, or to the vertex itself. The dynamics is specified by a set of unitary replacement rules, which causally propagate the local degrees of freedom. The inner product between any two states is given by a sum over histories. Assuming it converges (or can be Abel resummed), this inner product is proven to be hermitian and fully gauge-degenerate under spacetime diffeomorphisms. At least for states with a finite past, the inner product is also positive. This allows a Hilbert space of physical states to be constructed.Comment: 38 pages, 9 figures, v3 added to exposition and references, v4 expanded prospects sectio

The linearization of the Kodama state

We study the question of whether the linearization of the Kodama state around classical deSitter spacetime is normalizable in the inner product of the theory of linearized gravitons on deSitter spacetime. We find the answer is no in the Lorentzian theory. However, in the Euclidean theory the corresponding linearized Kodama state is delta-functional normalizable. We discuss whether this result invalidates the conjecture that the full Kodama state is a good physical state for quantum gravity with positive cosmological constant.Comment: 14 pages, statement on the corresponding Yang-Mills case correcte

Quantum Histories and Quantum Gravity

This paper reviews the histories approach to quantum mechanics. This discussion is then applied to theories of quantum gravity. It is argued that some of the quantum histories must approximate (in a suitable sense) to classical histories, if the correct classical regime is to be recovered. This observation has significance for the formulation of new theories (such as quantum gravity theories) as it puts a constraint on the kinematics, if the quantum/classical correspondence principle is to be preserved. Consequences for quantum gravity, particularly for Lorentz symmetry and the idea of "emergent geometry", are discussed.Comment: 35 pages (29 pages main body), two figure

Causal Set Dynamics: A Toy Model

We construct a quantum measure on the power set of non-cyclic oriented graphs of N points, drawing inspiration from 1-dimensional directed percolation. Quantum interference patterns lead to properties which do not appear to have any analogue in classical percolation. Most notably, instead of the single phase transition of classical percolation, the quantum model displays two distinct crossover points. Between these two points, spacetime questions such as "does the network percolate" have no definite or probabilistic answer.Comment: 28 pages incl. 5 figure

Loss Tomography in General Topologies with Network Coding

Network tomography infers internal network characteristics by sending and collecting probe packets from the network edge. Traditional tomographic techniques for general topologies typically use a mesh of multicast trees and/or unicast paths to cover the entire graph, which is suboptimal from the point of view of bandwidth efficiency and estimation accuracy. In this paper, we investigate an active probing method for link loss inference in a general topology, where multiple sources and receivers are used and intermediate nodes are equipped with network coding, in addition to unicast and multicast, capabilities. With our approach, each link is traversed by exactly one packet, which is in general a linear combination of the original probes. The receivers infer the loss rate on all links by observing not only the number but also the contents of the received probes. In this paper: (i) we propose an orientation algorithm that creates an acyclic graph with the maximum number of identifiable edges (ii) we define probe combining coding schemes and discuss some of their properties and (iii) we present simulation results over realistic topologies using Belief-Propagation (BP) algorithms

Action functionals of single scalar fields and arbitrary--weight gravitational constraints that generate a genuine Lie algebra

We discuss the issue initiated by Kucha\v{r} {\it et al}, of replacing the usual Hamiltonian constraint by alternative combinations of the gravitational constraints (scalar densities of arbitrary weight), whose Poisson brackets strongly vanish and cast the standard constraint-system for vacuum gravity into a form that generates a true Lie algebra. It is shown that any such combination---that satisfies certain reality conditions---may be derived from an action principle involving a single scalar field and a single Lagrange multiplier with a non--derivative coupling to gravity.Comment: 26 pages, plain TE