The Simple Criteria of SLOCC Equivalence Classes

We put forward an alternative approach to the SLOCC classification of entanglement states of three-qubit and four-qubit systems. By directly solving matrix equations, we obtain the relations satisfied by the amplitudes of states. The relations are readily tested since in them only addition, subtraction and multiplication occur.Comment: The original version was submitted to PRA in Feb. 2005, the paper No. is AA10020. 14 pages for the present version. No figure

Convergent diversity-oriented side-chain macrocyclization scan for unprotected polypeptides

Here we describe a general synthetic platform for side-chain macrocyclization of an unprotected peptide library based on the S[subscript N]Ar reaction between cysteine thiolates and a new generation of highly reactive perfluoroaromatic small molecule linkers. This strategy enabled us to simultaneously “scan” two cysteine residues positioned from i, i + 1 to i, i + 14 sites in a polypeptide, producing 98 macrocyclic products from reactions of 14 peptides with 7 linkers. A complementary reverse strategy was developed; cysteine residues within the polypeptide were first modified with non-bridging perfluoroaryl moieties and then commercially available dithiol linkers were used for macrocyclization. The highly convergent, site-independent, and modular nature of these two strategies coupled with the unique chemoselectivity of a S[subscript N]Ar transformation allows for the rapid diversity-oriented synthesis of hybrid macrocyclic peptide libraries with varied chemical and structural complexities.National Institutes of Health (U.S.) (GM101762)National Institutes of Health (U.S.) (GM046059)MIT Faculty Start-up FundSontag Foundation (Distinguished Scientist Award)Deshpande Center for Technological InnovationMassachusetts Institute of Technology (Charles E. Reed Faculty Initiative Fund)Damon Runyon Cancer Research Foundatio

Angle-selective perfect absorption with two-dimensional materials

Two-dimensional (2D) materials have great potential in photonic and optoelectronic devices. However, the relatively weak light absorption in 2D materials hinders their application in practical devices. Here, we propose a general approach to achieve angle-selective perfect light absorption in 2D materials. As a demonstration of the concept, we experimentally show giant light absorption by placing large-area single-layer graphene on a structure consisting of a chalcogenide layer atop a mirror and achieving a total absorption of 77.6% in the mid-infrared wavelength range (~13 μm), where the graphene contributes a record-high 47.2% absorptivity of mid-infrared light. Construction of such an angle-selective thin optical element is important for solar and thermal energy harvesting, photo-detection and sensing applications. Our study points to a new opportunity to combine 2D materials with photonic structures to enable novel device applications