Improved Asymptotic Key Rate of the B92 Protocol

We analyze the asymptotic key rate of the single photon B92 protocol by using Renner's security analysis given in 2005. The new analysis shows that the B92 protocol can securely generate key at 6.5% depolarizing rate, while the previous analyses cannot guarantee the secure key generation at 4.2% depolarizing rate.Comment: IEEEtran.sty, 3 pages, 1 figure. Submitted to IEEE ISIT 201

Band structure and Bloch states in birefringent 1D magnetophotonic crystals: An analytical approach

An analytical formulation for the band structure and Bloch modes in elliptically birefringent magnetophotonic crystals is presented. The model incorporates both the effects of gyrotropy and linear birefringence generally present in magneto-optic thin film devices. Full analytical expressions are obtained for the dispersion relation and Bloch modes in a layered stack photonic crystal and their properties are analyzed. It is shown that other models recently discussed in the literature are contained as special limiting cases of the formulation presented herein

On algebraic endomorphisms of the Einstein gyrogroup

We describe the structure of all continuous algebraic endomorphisms of the open unit ball $\mathbf{B}$ of $\mathbb{R}^3$ equipped with the Einstein velocity addition. We show that any nonzero such transformation originates from an orthogonal linear transformation on $\mathbb{R}^3$

Experimental nonlocality-based randomness generation with non-projective measurements

We report on an optical setup generating more than one bit of randomness from one entangled bit (i.e. a maximally entangled state of two-qubits). The amount of randomness is certified through the observation of Bell non-local correlations. To attain this result we implemented a high-purity entanglement source and a non-projective three-outcome measurement. Our implementation achieves a gain of 27$\%$ of randomness as compared with the standard methods using projective measurements. Additionally we estimate the amount of randomness certified in a one-sided device independent scenario, through the observation of EPR steering. Our results prove that non-projective quantum measurements allows extending the limits for nonlocality-based certified randomness generation using current technology.Comment: 6 pages, 3 figure

Remarks on hard Lefschetz conjectures on Chow groups

We propose two conjectures of Hard Lefschetz type on Chow groups and prove them for some special cases. For abelian varieties, we shall show they are equivalent to well-known conjectures of Beauville and Murre.Comment: to appear in Sciences in China, Ser. A Mathematic

216 Jewish Hospital of St. Louis

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