1,507 research outputs found
Local symmetry properties of pure 3-qubit states
Entanglement types of pure states of 3 qubits are classified by means of
their stabilisers in the group of local unitary operations. It is shown that
the stabiliser is generically discrete, and that a larger stabiliser indicates
a stationary value for some local invariant. We describe all the exceptional
states with enlarged stabilisers.Comment: 32 pages, 5 encapsulated PostScript files for 3 figures. Published
version, with minor correction
Revenue Management of Reusable Resources with Advanced Reservations
Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/137568/1/poms12672_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/137568/2/poms12672.pd
General flux to a trap in one and three dimensions
The problem of the flux to a spherical trap in one and three dimensions, for
diffusing particles undergoing discrete-time jumps with a given radial
probability distribution, is solved in general, verifying the Smoluchowski-like
solution in which the effective trap radius is reduced by an amount
proportional to the jump length. This reduction in the effective trap radius
corresponds to the Milne extrapolation length.Comment: Accepted for publication, in pres
Drawing Graphs within Restricted Area
We study the problem of selecting a maximum-weight subgraph of a given graph
such that the subgraph can be drawn within a prescribed drawing area subject to
given non-uniform vertex sizes. We develop and analyze heuristics both for the
general (undirected) case and for the use case of (directed) calculation graphs
which are used to analyze the typical mistakes that high school students make
when transforming mathematical expressions in the process of calculating, for
example, sums of fractions
A bipartite class of entanglement monotones for N-qubit pure states
We construct a class of algebraic invariants for N-qubit pure states based on
bipartite decompositions of the system.
We show that they are entanglement monotones, and that they differ from the
well know linear entropies of the sub-systems. They therefore capture new
information on the non-local properties of multipartite systems.Comment: 6 page
Parallel transport in an entangled ring
This paper defines a notion of parallel transport in a lattice of quantum
particles, such that the transformation associated with each link of the
lattice is determined by the quantum state of the two particles joined by that
link. We focus particularly on a one-dimensional lattice--a ring--of entangled
rebits, which are binary quantum objects confined to a real state space. We
consider states of the ring that maximize the correlation between nearest
neighbors, and show that some correlation must be sacrificed in order to have
non-trivial parallel transport around the ring. An analogy is made with lattice
gauge theory, in which non-trivial parallel transport around closed loops is
associated with a reduction in the probability of the field configuration. We
discuss the possibility of extending our result to qubits and to higher
dimensional lattices.Comment: 31 pages, no figures; v2 includes a new example of a qubit rin
On Existence and Properties of Approximate Pure Nash Equilibria in Bandwidth Allocation Games
In \emph{bandwidth allocation games} (BAGs), the strategy of a player
consists of various demands on different resources. The player's utility is at
most the sum of these demands, provided they are fully satisfied. Every
resource has a limited capacity and if it is exceeded by the total demand, it
has to be split between the players. Since these games generally do not have
pure Nash equilibria, we consider approximate pure Nash equilibria, in which no
player can improve her utility by more than some fixed factor through
unilateral strategy changes. There is a threshold (where
is a parameter that limits the demand of each player on a specific
resource) such that -approximate pure Nash equilibria always exist for
, but not for . We give both
upper and lower bounds on this threshold and show that the
corresponding decision problem is -hard. We also show that the
-approximate price of anarchy for BAGs is . For a restricted
version of the game, where demands of players only differ slightly from each
other (e.g. symmetric games), we show that approximate Nash equilibria can be
reached (and thus also be computed) in polynomial time using the best-response
dynamic. Finally, we show that a broader class of utility-maximization games
(which includes BAGs) converges quickly towards states whose social welfare is
close to the optimum
A dynamic management framework for socio-ecological system stewardship: A case study for the United States Bureau of Ocean Energy Management
An effective and efficient stewardship of natural resources requires consistency across all decision-informing approaches and components involved, i.e., managerial, governmental, political, and legal. To achieve this consistency, these elements must be aligned under an overarching management goal that is consistent with current and well-accepted knowledge. In this article, we investigate the adoption by the US Bureau of Ocean Energy Management of an environmental resilience-centered system that manages for resilience of marine ecological resources and its associated social elements. Although the framework is generally tailored for this Bureau, it could also be adapted to other federal or non-federal organizations. This paper presents a dynamic framework that regards change as an inherent element of the socio-ecological system in which management structures, e.g., federal agencies, are embedded. The overall functioning of the management framework being considered seeks to mimic and anticipate environmental change in line with well-accepted elements of resilience-thinking. We also investigate the goal of using management for resilience as a platform to enhance socio-ecological sustainability by setting specific performance metrics embedded in pre-defined and desired social and/or ecological scenarios. Dynamic management frameworks that couple social and ecological systems as described in this paper can facilitate the efficient and effective utilization of resources, reduce uncertainty for decision and policy makers, and lead to more defensible decisions on resources
Quantum Sign Permutation Polytopes
Convex polytopes are convex hulls of point sets in the -dimensional space
\E^n that generalize 2-dimensional convex polygons and 3-dimensional convex
polyhedra. We concentrate on the class of -dimensional polytopes in \E^n
called sign permutation polytopes. We characterize sign permutation polytopes
before relating their construction to constructions over the space of quantum
density matrices. Finally, we consider the problem of state identification and
show how sign permutation polytopes may be useful in addressing issues of
robustness
Quantum cobwebs: Universal entangling of quantum states
Entangling an unknown qubit with one type of reference state is generally
impossible. However, entangling an unknown qubit with two types of reference
states is possible. To achieve this, we introduce a new class of states called
zero sum amplitude (ZSA) multipartite, pure entangled states for qubits and
study their salient features. Using shared-ZSA state, local operation and
classical communication we give a protocol for creating multipartite entangled
states of an unknown quantum state with two types of reference states at remote
places. This provides a way of encoding an unknown pure qubit state into a
multiqubit entangled state. We quantify the amount of classical and quantum
resources required to create universal entangled states. This is possibly a
strongest form of quantum bit hiding with multiparties.Comment: Invited talk in II Winter Institute on FQTQO: Quantum Information
Processing, held at S. N. Bose Center for Basic Science, Kolkata, during Jan
2-11, 2002. (To appear in Pramana-J. of Physics, 2002.
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