759 research outputs found
Quantum teleportation in the commuting operator framework
We introduce a notion of teleportation scheme between subalgebras of
semi-finite von Neumann algebras in the commuting operator model of locality.
Using techniques from subfactor theory, we present unbiased teleportation
schemes for relative commutants of a large class of finite-index
inclusions of tracial von Neumann algebras, where the unbiased
condition means that no information about the teleported observables are
contained in the classical communication sent between the parties. For a large
class of subalgebras of matrix algebras , including those
relevant to hybrid classical/quantum codes, we show that any tight
teleportation scheme for necessarily arises from an orthonormal unitary
Pimsner-Popa basis of over , generalising work of Werner.
Combining our techniques with those of Brannan-Ganesan-Harris, we compute
quantum chromatic numbers for a variety of quantum graphs arising from
finite-dimensional inclusions .Comment: 33 page
PageRank Optimization by Edge Selection
The importance of a node in a directed graph can be measured by its PageRank.
The PageRank of a node is used in a number of application contexts - including
ranking websites - and can be interpreted as the average portion of time spent
at the node by an infinite random walk. We consider the problem of maximizing
the PageRank of a node by selecting some of the edges from a set of edges that
are under our control. By applying results from Markov decision theory, we show
that an optimal solution to this problem can be found in polynomial time. Our
core solution results in a linear programming formulation, but we also provide
an alternative greedy algorithm, a variant of policy iteration, which runs in
polynomial time, as well. Finally, we show that, under the slight modification
for which we are given mutually exclusive pairs of edges, the problem of
PageRank optimization becomes NP-hard.Comment: 30 pages, 3 figure
A fault-tolerant continuous-variable measurement-based quantum computation architecture
Continuous variable measurement-based quantum computation on cluster states
has in recent years shown great potential for scalable, universal, and
fault-tolerant quantum computation when combined with the
Gottesman-Kitaev-Preskill (GKP) code and quantum error correction. However, no
complete fault-tolerant architecture exists that includes everything from
cluster state generation with finite squeezing to gate implementations with
realistic noise and error correction. In this work, we propose a simple
architecture for the preparation of a cluster state in three dimensions in
which gates by gate teleportation can be efficiently implemented. To
accommodate scalability, we propose architectures that allow for both spatial
and temporal multiplexing, with the temporal encoded version requiring as
little as two squeezed light sources. Due to its three-dimensional structure,
the architecture supports topological qubit error correction, while GKP error
correction is efficiently realized within the architecture by teleportation. To
validate fault-tolerance, the architecture is simulated using surface-GKP
codes, including noise from GKP-states as well as gate noise caused by finite
squeezing in the cluster state. We find a fault-tolerant squeezing threshold of
13.2 dB with room for further improvement
Twisted Photons: New Quantum Perspectives in High Dimensions
Quantum information science and quantum information technology have seen a
virtual explosion world-wide. It is all based on the observation that
fundamental quantum phenomena on the individual particle or system-level lead
to completely novel ways of encoding, processing and transmitting information.
Quantum mechanics, a child of the first third of the 20th century, has found
numerous realizations and technical applications, much more than was thought at
the beginning. Decades later, it became possible to do experiments with
individual quantum particles and quantum systems. This was due to technological
progress, and for light in particular, the development of the laser. Hitherto,
nearly all experiments and also nearly all realizations in the fields have been
performed with qubits, which are two-level quantum systems. We suggest that
this limitation is again mainly a technological one, because it is very
difficult to create, manipulate and measure more complex quantum systems. Here,
we provide a specific overview of some recent developments with
higher-dimensional quantum systems. We mainly focus on Orbital Angular Momentum
(OAM) states of photons and possible applications in quantum information
protocols. Such states form discrete higher-dimensional quantum systems, also
called qudits. Specifically, we will first address the question what kind of
new fundamental properties exist and the quantum information applications which
are opened up by such novel systems. Then we give an overview of recent
developments in the field by discussing several notable experiments over the
past 2-3 years. Finally, we conclude with several important open questions
which will be interesting for investigations in the future.Comment: 15 pages, 7 figure
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