395 research outputs found
On routing-optimal networks for multiple unicasts
In this paper, we consider the problem of multiple unicast sessions over a directed acyclic graph. It is well known that linear network coding is insufficient for achieving the capacity region, in the general case. However, there exist networks for which routing is sufficient to achieve the whole rate region, and we refer to them as routing-optimal networks. We identify a class of routing-optimal networks, which we refer to as information-distributive networks, defined by three topological features. Due to these features, for each rate vector achieved by network coding, there is always a routing scheme such that it achieves the same rate vector, and the traffic transmitted through the network is exactly the information transmitted over the cut-sets between the sources and the sinks in the corresponding network coding scheme. We present examples of information-distributive networks, including some examples from (1) index coding and (2) from a single unicast session with hard deadline constraint. © 2014 IEEE
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
Evolution in Quantum Causal Histories
We provide a precise definition and analysis of quantum causal histories
(QCH). A QCH consists of a discrete, locally finite, causal pre-spacetime with
matrix algebras encoding the quantum structure at each event. The evolution of
quantum states and observables is described by completely positive maps between
the algebras at causally related events. We show that this local description of
evolution is sufficient and that unitary evolution can be recovered wherever it
should actually be expected. This formalism may describe a quantum cosmology
without an assumption of global hyperbolicity; it is thus more general than the
Wheeler-DeWitt approach. The structure of a QCH is also closely related to
quantum information theory and algebraic quantum field theory on a causal set.Comment: 20 pages. 8 figures. (v3: minor corrections, additional references
[2,3]) to appear in CQ
Nonperturbative dynamics for abstract (p,q) string networks
We describe abstract (p,q) string networks which are the string networks of
Sen without the information about their embedding in a background spacetime.
The non-perturbative dynamical formulation invented for spin networks, in terms
of causal evolution of dual triangulations, is applied to them. The formal
transition amplitudes are sums over discrete causal histories that evolve (p,q)
string networks. The dynamics depend on two free SL(2,Z) invariant functions
which describe the amplitudes for the local evolution moves.Comment: Latex, 12 pages, epsfig, 7 figures, minor change
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
Trapped surfaces and emergent curved space in the Bose-Hubbard model
A Bose-Hubbard model on a dynamical lattice was introduced in previous work as a spin system analogue of emergent geometry and gravity. Graphs with regions of high connectivity in the lattice were identified as candidate analogues of spacetime geometries that contain trapped surfaces. We carry out a detailed study of these systems and show explicitly that the highly connected subgraphs trap matter. We do this by solving the model in the limit of no back-reaction of the matter on the lattice, and for states with certain symmetries that are natural for our problem. We find that in this case the problem reduces to a one-dimensional Hubbard model on a lattice with variable vertex degree and multiple edges between the same two vertices. In addition, we obtain a (discrete) differential equation for the evolution of the probability density of particles which is closed in the classical regime. This is a wave equation in which the vertex degree is related to the local speed of propagation of probability. This allows an interpretation of the probability density of particles similar to that in analogue gravity systems: matter inside this analogue system sees a curved spacetime. We verify our analytic results by numerical simulations. Finally, we analyze the dependence of localization on a gradual, rather than abrupt, falloff of the vertex degree on the boundary of the highly connected region and find that matter is localized in and around that region
Quantum gravity and the standard model
We show that a class of background independent models of quantum spacetime
have local excitations that can be mapped to the first generation fermions of
the standard model of particle physics. These states propagate coherently as
they can be shown to be noiseless subsystems of the microscopic quantum
dynamics. These are identified in terms of certain patterns of braiding of
graphs, thus giving a quantum gravitational foundation for the topological
preon model proposed by one of us.
These results apply to a large class of theories in which the Hilbert space
has a basis of states given by ribbon graphs embedded in a three-dimensional
manifold up to diffeomorphisms, and the dynamics is given by local moves on the
graphs, such as arise in the representation theory of quantum groups. For such
models, matter appears to be already included in the microscopic kinematics and
dynamics.Comment: 12 pages, 21 figures, improved presentation, results unchange
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
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