Aspects of Generic Entanglement

We study entanglement and other correlation properties of random states in high-dimensional bipartite systems. These correlations are quantified by parameters that are subject to the ``concentration of measure' phenomenon, meaning that on a large-probability set these parameters are close to their expectation. For the entropy of entanglement, this has the counterintuitive consequence that there exist large subspaces in which all pure states are close to maximally entangled. This, in turn, implies the existence of mixed states with entanglement of formation near that of a maximally entangled state, but with negligible quantum mutual information and, therefore, negligible distillable entanglement, secret key, and common randomness. It also implies a very strong locking effect for the entanglement of formation: its value can jump from maximal to near zero by tracing over a number of qubits negligible compared to the size of the total system. Furthermore, such properties are generic. Similar phenomena are observed for random multiparty states, leading us to speculate on the possibility that the theory of entanglement is much simplified when restricted to asymptotically generic states. Further consequences of our results include a complete derandomization of the protocol for universal superdense coding of quantum states.     

Invariant ideals of twisted crossed products

We will prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on -algebras. Received: 25 January 2002; in final form: 22 May 2002/Published online: 2 December 2002 This work is partially supported by Hong Kong RGC Direct Grant.     

Bipyridinophane‐containing conjugated polymers modulated with an intramolecular aromatic C?H/π interaction

Bipyridinophane–fluorene conjugated copolymers have been synthesized via Suzuki and Heck coupling reactions from 5,8‐dibromo‐2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane and suitable fluorene precursors. Poly[2,7‐(9,9‐dihexylfluorene)‐co‐alt‐5,8‐(2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane)] ( P7 ) exhibits large absorption and emission redshifts of 20 and 34 nm, respectively, with respect to its planar reference polymer Poly[2,7‐(9,9‐dihexylfluorene)‐co‐alt‐1,4‐(2,5‐dimethylbenzene)] ( P11 ), which bears the same polymer backbone as P7 . These spectral shifts originate from intramolecular aromatic C? H/π interactions, which are evidenced by ultraviolet–visible and ¹H NMR spectra as well as X‐ray single‐crystal structural analysis. However, the effect of the intramolecular aromatic C? H/π interactions on the spectral shift in poly[9,9‐dihexylfluorene‐2,7‐yleneethynylene‐co‐alt‐5,8‐(2,11‐dithia[3]paracyclo[3](4,4′)‐2,2′‐bipyridinophane)] ( P10 ) is much weaker. Most interestingly, the quenching behaviors of these two conjugated polymers are largely dependent on the polymer backbone. For example, the fluorescence of P7 is efficiently quenched by Cu²⁺, Co²⁺, Ni²⁺, Zn²⁺, Mn²⁺, and Ag⁺ ions. In contrast, only Cu²⁺, Co²⁺, and Ni²⁺ ions can partially quench the fluorescence of P10 , but much less efficiently than the fluorescence of P7 . The static Stern–Volmer quenching constants of Cu²⁺, Co²⁺, and Ni²⁺ ions toward P7 are of the order of 10⁶ M^?1, being 1300, 2500, and 37,300 times larger than those of P10 , respectively. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 4154–4164, 2006     

Elevation of the glass transition temperature in flexible‐chain semicrystalline polymers

In the idealized two‐phase model of a semicrystalline polymer, the amorphous intercrystalline layers are considered to have the same properties as the fully‐amorphous polymer. In reality, these thin intercrystalline layers can be substantially influenced by the presence of the crystals, as individual polymer molecules traverse both crystalline and amorphous phases. In polymers with rigid backbone units, such as poly(etheretherketone), PEEK, previous work has shown this coupling to be particularly severe; the glass transition temperature (T_g) can be elevated by tens of degrees celsius, with the magnitude of the elevation correlating directly with the thinness of the amorphous layer. However, this connection has not been explored for flexible‐chain polymers, such as those formed from vinyl‐type monomers. Here, we examine T_g in both isotactic polystyrene (iPS) and syndiotactic polystyrene (sPS), crystallized under conditions that produce a range of amorphous layer thicknesses. T_g is indeed shown to be elevated relative to fully‐amorphous iPS and sPS, by an amount that correlates with the thinness of the amorphous layer; the magnitude of the effect is severalfold less than that in PEEK, consistent with the minimum lengths of polymer chain required to make a fold in the different cases. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1198–1204, 2007     

Effects of the H-bond donor structure on the properties of supramolecular side chain liquid crystalline polymers based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane)s and stilbazoles

Supramolecular side chain liquid crystalline polymers (SCLCPs) based on poly(3-carboxypropylmethylsiloxane-co-dimethylsiloxane) (PSIX, X=100, 76, 60, 41 or 23, denoting the mole percentage of 3-carboxypropylmethylsiloxane unit in the polymer) and stilbazole derivatives have been obtained through intermolecular hydrogen bonding (H-bonding) interactions between the carboxylic acid and the pyridyl moieties. The formation of H-bonding and self-assembly results in the formation of new mesogenic units, in which H-bonds function as molecular connectors. FTIR shows the existence of H-bonding in the complexes. The polymeric complexes behave as single component liquid crystalline polymers and exhibit stable and enantiotropic mesophases. The liquid crystalline properties of the supramolecular SCLCPs were studied using differential scanning calorimetry, polarizing optical microscopy and X-ray diffraction, and were found to exhibit smectic A phases with focal-conic textures. The thermal stability of the SCLCP increases on increasing the carboxylic acid content in the polysiloxane and the concentration of the stilbazole derivative in the complex. However, the thermal stability decreases on increasing the chain length of the stilbazole derivative. The crystal phase was not formed even on cooling to the glass transition temperature of the polymeric complex.     

Fluorescence detection and quantitation of recombinant proteins containing oligohistidine tag sequences directly in sodium dodecyl sulfate-polyacrylamide gels

Two fluorophore-nitrilotriacetic acid conjugates, Pro-Q Sapphire 365 and Pro-Q Sapphire 488 oligohistidine gel stains, have been developed for the fluorescence detection of fusion proteins containing oligohistidine tags directly in sodium dodecyl sulfate polyacrylamide gels, without the requirement for electroblotting, reporter enzymes or secondary detection reagents. Pro-Q Sapphire 365 oligohistidine gel stain exhibits bright-blue fluorescence (emission maximum = 450 nm) when illuminated with UV-A or UV-B light from a standard ultraviolet transilluminator. Pro-Q Sapphire 488 oligohistidine gel stain exhibits bright-green fluorescence (emission maximum = 515 nm) when illuminated with visible light from a laser-based gel scanner equipped with a 470 nm second-harmonic generation (SHG) or 488 nm argon-ion laser source. Typically, 25-65 ng of oligohistidine-tagged fusion protein in whole cell lysates is detectable using either stain. After documenting the fluorescence signal from the Pro-Q Sapphire dyes, gels may be post-stained with the red-fluorescent SYPRO Ruby protein gel stain in order to reveal the total protein pattern.     

Half-sandwich titanium(IV) complexes with Kläui's tripod ligand

Treatment of [Ti(O-i-Pr)(2)Cl(2)] with NaL(OEt) (L(OEt)(-) = [CpCo[P(O)(OEt)(2)](3)](-), Cp = eta(5)-C(5)H(5)) afforded [L(OEt)Ti(O-i-Pr)(2)Cl] that reacted with HCl in ether to give [L(OEt)TiCl(3)] (1). The average Ti-O and Ti-Cl distances in 1 are 1.975 and 2.293 A, respectively. Reaction of titanyl sulfate with NaL(OEt) in water followed by addition of HBF(4) afforded [L(OEt)TiF(3)] (2), the Ti-O and Ti-F distances of which are 2.020(2) and 1.792(2) A, respectively. The Zr(IV) analogue [L(OEt)ZrF(3)] (3) was prepared similarly from zirconyl nitrate, NaL(Oet), and HBF(4) in water. The Zr-O and average Zr-F distances in 3 are 2.139(2) and 1.938(2) A, respectively. Treatment of 1 with tetrachlorocatechol (H(2)Cl(4)cat) afforded [L(OEt)Ti(Cl(4)cat)Cl] (4). The average Ti-O(P), Ti-O(C), and Ti-Cl distances in 4 are 1.972, 1.926, and 2.334 A, respectively. Hydrolysis of 4 in the presence of Et(3)N yielded the mu-oxo dimer [(L(OEt))(2)Ti(2)(Cl(4)cat)(2)(mu-O)] (5). The average Ti-O(P), Ti-O(C), and Ti-O(Ti) distances in 5 are 2.027, 1.926, and 1.7977(9) A. Treatment of 1 with 1,1'-binaphthol (BINOLH(2)) in the presence of Et(3)N afforded [(L(OEt))(2)Ti(2)(mu-O)(2)(mu-BINOL)] x 2BINOLH(2) (6.2BINOLH(2)). Complex 1 is capable of catalyzing ring opening of epoxides with Me(3)SiN(3) under solvent-free conditions presumably via a Ti-azide intermediate.     

An evaluation of exogenous application of protoporphyrin IX and its dimethyl ester as a photodynamic diagnostic agent in poorly differentiated human nasopharyngeal carcinoma

5-Aminolevulinic acid and its esterified analogues have been under much investigation to enhance the endogenous production of protoporphyrin IX (PpIX) in tumor cells. However, in this work, we studied the in vitro and in vivo efficacy of exogenously administered PpIX and its esterified analogue, PpIX dimethyl ester (PME), in poorly differentiated human nasopharyngeal carcinoma (NPC/CNE-2) as a photodynamic diagnostic (PDD) agent. NPC/CNE-2 at its earliest time, 1 h after incubation with PME in in vitro studies, has exhibited 64% (P <0.01) higher tumor to normal cell (T/N) fluorescence ratio than with PpIX. In an in vivo mouse xenograft model, comparable photosensitizer concentration in tumor after intravenous administration was observed at 1-3 h time points, but at 9 h, PME had 31% (P=0.05) greater concentration in tumor compared with PpIX. In addition, by constituting PME and PpIX in different topical gel composites, of which, PME gel composition of 8:2 Plasdone and Gantrez resulted in the highest T/N ratio at 6 h after application (34%; P <0.05) in comparison with other gel composites. Evaluation of PME and PpIX constituted in the delivery vehicles investigated showed comparable selectivity for tumor at 1-3 h, thus neither photosensitizer is more efficient than the other for PDD at the early time points; however, beyond 6 h, PME had higher selectivity for tumor compared with PpIX. Thus, further investigation is warranted to improve the drug delivery vehicle for greater tumor selectivity at a shorter incubation time.