6,021 research outputs found
Consistency of a system of equations: What does that mean?
The concept of (structural) consistency also called structural solvability is an important basic tool for analyzing the structure of systems of equations. Our aim is to provide a sound and practically relevant meaning to this concept. The implications of consistency are expressed in terms of explicit density and stability results. We also illustrate, by typical examples, the limitations of the concept
Continuous-variable entanglement of two bright coherent states that never interacted
We study continuous-variable entanglement of bright quantum states in a pair
of evanescently coupled nonlinear waveguides operating in the
regime of degenerate down-conversion. We consider the case where only the
energy of the nonlinearly generated fields is exchanged between the waveguides
while the pump fields stay independently guided in each original waveguide. We
show that this device, when operated in the depletion regime, entangles the two
non-interacting bright pump modes due to a nonlinear cascade effect. It is also
shown that two-colour quadripartite entanglement can be produced when certain
system parameters are appropriately set. This device works in the
traveling-wave configuration, such that the generated quantum light shows a
broad spectrum. The proposed device can be easily realized with current
technology and therefore stands as a good candidate for a source of bipartite
or multipartite entangled states for the emerging field of optical
continuous-variable quantum information processing.Comment: 10 pages, 12 figure
The Canada Day Theorem
The Canada Day Theorem is an identity involving sums of minors
of an arbitrary symmetric matrix. It was discovered as a
by-product of the work on so-called peakon solutions of an integrable nonlinear
partial differential equation proposed by V. Novikov. Here we present another
proof of this theorem, which explains the underlying mechanism in terms of the
orbits of a certain abelian group action on the set of all -edge matchings
of the complete bipartite graph .Comment: 16 pages. pdfLaTeX + AMS packages + TikZ. Fixed a hyperlink problem
and a few typo
Zero supermode-based multipartite entanglement in nonlinear waveguides arrays
We show that arrays of nonlinear waveguides in the second
harmonic generation regime are a promising source of continuous-variable
entanglement. We indeed demonstrate analytically that optical arrays with odd
number of waveguides injected with the zero-eigenvalue fundamental supermode
entangle this fundamental supermode with a collective harmonic field. Moreover
the fundamental individual modes are multipartite entangled and their
entanglement grows with propagation length. The device is scalable, robust to
losses, does not rely on specific values of nonlinearity and coupling and is
easily realized with current technology. It thus stands as an unprecedented
candidate for generation of multipartite continuous-variable entanglement for
optical quantum information processing.Comment: Main text: 7 pages, 6 figures. Supplemental material: 5 pages, 2
figure. v2 closer to published versio
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