27,493 research outputs found
Quantum Causal Graph Dynamics
Consider a graph having quantum systems lying at each node. Suppose that the
whole thing evolves in discrete time steps, according to a global, unitary
causal operator. By causal we mean that information can only propagate at a
bounded speed, with respect to the distance given by the graph. Suppose,
moreover, that the graph itself is subject to the evolution, and may be driven
to be in a quantum superposition of graphs---in accordance to the superposition
principle. We show that these unitary causal operators must decompose as a
finite-depth circuit of local unitary gates. This unifies a result on Quantum
Cellular Automata with another on Reversible Causal Graph Dynamics. Along the
way we formalize a notion of causality which is valid in the context of quantum
superpositions of time-varying graphs, and has a number of good properties.
Keywords: Quantum Lattice Gas Automata, Block-representation,
Curtis-Hedlund-Lyndon, No-signalling, Localizability, Quantum Gravity, Quantum
Graphity, Causal Dynamical Triangulations, Spin Networks, Dynamical networks,
Graph Rewriting.Comment: 8 pages, 1 figur
Quantum Causal Networks
Intervention theories of causality define a relationship as causal if
appropriately specified interventions to manipulate a putative cause tend to
produce changes in the putative effect. Interventionist causal theories are
commonly formalized by using directed graphs to represent causal relationships,
local probability models to quantify the relationship between cause and effect,
and a special kind of conditioning operator to represent the effects of
interventions. Such a formal model represents a family of joint probability
distributions, one for each allowable intervention policy. This paper
interprets the von Neumann formalization of quantum theory as an
interventionist theory of causality, describes its relationship to
interventionist theories popular in the artificial intelligence literature, and
presents a new family of graphical models that extends causal Bayesian networks
to quantum systems.Comment: 10 page
Quantum causal histories in the light of quantum information
We use techniques of quantum information theory to analyze the quantum causal
histories approach to quantum gravity. We show that while it is consistent to
introduce closed timelike curves (CTCs), they cannot generically carry
independent degrees of freedom. Moreover, if the effective dynamics of the
chronology-respecting part of the system is linear, it should be completely
decoupled from the CTCs. In the absence of a CTC not all causal structures
admit the introduction of quantum mechanics. It is possible for those and only
for those causal structures that can be represented as quantum computational
networks. The dynamics of the subsystems should not be unitary or even
completely positive. However, we show that other commonly maid assumptions
ensure the complete positivity of the reduced dynamics.Comment: 9 pages, 8 eps figure
Event-based simulation of single-photon beam splitters and Mach-Zehnder interferometers
We demonstrate that networks of locally connected processing units with a
primitive learning capability exhibit behavior that is usually only attributed
to quantum systems. We describe networks that simulate single-photon
beam-splitter and Mach-Zehnder interferometer experiments on a causal,
event-by-event basis and demonstrate that the simulation results are in
excellent agreement with quantum theory.Comment: EuroPhys. Lett. (in press); http://www.compphys.net/dl
Causality in Spin Foam Models
We compute Teitelboim's causal propagator in the context of canonical loop
quantum gravity. For the Lorentzian signature, we find that the resultant power
series can be expressed as a sum over branched, colored two-surfaces with an
intrinsic causal structure. This leads us to define a general structure which
we call a ``causal spin foam''. We also demonstrate that the causal evolution
models for spin networks fall in the general class of causal spin foams.Comment: 19 pages, LaTeX2e, many eps figure
New method to simulate quantum interference using deterministic processes and application to event-based simulation of quantum computation
We demonstrate that networks of locally connected processing units with a
primitive learning capability exhibit behavior that is usually only attributed
to quantum systems. We describe networks that simulate single-photon
beam-splitter and Mach-Zehnder interferometer experiments on a causal,
event-by-event basis and demonstrate that the simulation results are in
excellent agreement with quantum theory. We also show that this approach can be
generalized to simulate universal quantum computers.Comment: J. Phys. Soc. Jpn. (in press) http://www.compphys.net/dl
Causal evolution of spin networks
A new approach to quantum gravity is described which joins the loop
representation formulation of the canonical theory to the causal set
formulation of the path integral. The theory assigns quantum amplitudes to
special classes of causal sets, which consist of spin networks representing
quantum states of the gravitational field joined together by labeled null
edges. The theory exists in 3+1, 2+1 and 1+1 dimensional versions, and may also
be interepreted as a theory of labeled timelike surfaces. The dynamics is
specified by a choice of functions of the labelings of d+1 dimensional
simplices,which represent elementary future light cones of events in these
discrete spacetimes. The quantum dynamics thus respects the discrete causal
structure of the causal sets. In the 1+1 dimensional case the theory is closely
related to directed percolation models. In this case, at least, the theory may
have critical behavior associated with percolation, leading to the existence of
a classical limit.Comment: latex, 32 pages, 17 figure
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