Three-dimensional entanglement of orbital angular momentum states of an atomic qutrit and a single photon qutrit has been observed. Their full state was reconstructed using quantum state tomography. The fidelity to the maximally entangled state of Schmidt rank 3 exceeds the threshold 2/3. This result confirms that the density matrix cannot be decomposed into an ensemble of pure states of Schmid...

Inverse formulas for the tensor product are used to develop an algorithm to compute Schmidt decompositions of Finite Schmidt Rank (FSR) bounded operators on the tensor product of separable Hilbert spaces. The algorithm is then applied to solve inverse problems related to the tensor product of bounded operators. In particular, we show how properties of a FSR bounded operator are reflected by the...

Photon pair states and multiple-photon squeezed states have many applications in quantum information science. In this paper, Green functions are derived for spontaneous four-wave mixing in the low- and high-gain regimes. Nondegenerate four-wave mixing in a strongly-birefringent medium generates signal and idler photons that are associated with only one pair of temporal (Schmidt) modes, for a wi...

X. Sun, Dr. C. Yan, Dr. Y. Chen, W. Si, J. Deng, Prof. O. G. Schmidt Institute for Integrative Nanosciences IFW Dresden, Helmholtzstrasse 20 Dresden , 01069 , Germany E-mail: [email protected] X. Sun, W. Si, J. Deng, Prof. O. G. Schmidt Material Systems for Nanoelectronics Chemnitz University of Technology Reichenhainer Strasse 70 , Chemnitz , 09107 , Germany S. Oswald Institute for Complex ...

If X,Y are normed spaces, let B(X,Y ) be the set of all bounded linear maps X → Y . If T : X → Y is a linear map, I take it as known that T is bounded if and only if it is continuous if and only if E ⊆ X being bounded implies that T (E) ⊆ Y is bounded. I also take it as known that B(X,Y ) is a normed space with the operator norm, that if Y is a Banach space then B(X,Y ) is a Banach space, that ...

Ruth Curtain Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands. E-mail:[email protected], Kalle Mikkola Helsinki University of Technology, Institute of Mathematics, Box 1100, 02015 HUT, Finland. E-mail:[email protected], Amol Sasane Department of Mathematics, London School of Economics, Houghton Street, London WC2A 2AE, United Kingdom....

For any integer r > 2, define a sequence of numbers {c (r) k }k=0,1,..., independent of the parameter n, by n

The intramolecular Schmidt reaction of ketones and tethered azides is an efficient method for the generation of amides and lactams. This reaction is catalyzed by Lewis acids, which tightly bind the strongly basic amide product and result in product inhibition. We report herein conditions to achieve a catalytic Schmidt reaction using substoichiometric amounts of the heat-stable Lewis acid Sc(OTf...

One method to account for parameters errors in the Kalman filter is to ‘consider’ their effect in the so-called Schmidt-Kalman filter. This paper addresses issues that arise when implementing a consider Kalman filter as a real-time, recursive algorithm. A favorite implementation of the Kalman filter as an onboard navigation subsystem is the UDU formulation. A new way to implement a UDU Schmidt-...

A series of domino reactions in which the intramolecular Schmidt reaction is combined with either a Sakurai reaction, an aldol reaction, or both is reported. The Sakurai reaction of an allylsilane with an azido-containing enone under Lewis acidic conditions followed by protonation of the resulting titanium enolate species allowed for a subsequent intramolecular Schmidt reaction. Alternatively, ...