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A de Finetti representation for finite symmetric quantum states

Consider a symmetric quantum state on an n-fold product space, that is, the state is invariant under permutations of the n subsystems. We show that, conditioned on the outcomes of an informationally complete measurement applied to a number of subsystems, the state in the remaining subsystems is close to having product form. This immediately generalizes the so-called de Finetti representation to the case of finite symmetric quantum states.Comment: 22 pages, LaTe

Strengths and Weaknesses of Quantum Computing

Recently a great deal of attention has focused on quantum computation following a sequence of results suggesting that quantum computers are more powerful than classical probabilistic computers. Following Shor's result that factoring and the extraction of discrete logarithms are both solvable in quantum polynomial time, it is natural to ask whether all of NP can be efficiently solved in quantum polynomial time. In this paper, we address this question by proving that relative to an oracle chosen uniformly at random, with probability 1, the class NP cannot be solved on a quantum Turing machine in time $o(2^{n/2})$. We also show that relative to a permutation oracle chosen uniformly at random, with probability 1, the class $NP \cap coNP$ cannot be solved on a quantum Turing machine in time $o(2^{n/3})$. The former bound is tight since recent work of Grover shows how to accept the class NP relative to any oracle on a quantum computer in time $O(2^{n/2})$.Comment: 18 pages, latex, no figures, to appear in SIAM Journal on Computing (special issue on quantum computing

The trouble with ODE : polymerization during nanocrystal synthesis

1-Octadecene is a widely used solvent for high temperature nanocrystal synthesis (120-320 degrees C). Here, we show that 1-octadecene spontaneously polymerizes under these conditions, and the resulting poly(1-octadecene) has a comparable solubility and size to nanocrystals stabilized by hydrophobic ligands. Typical purification procedures (precipitation/redispersion cycles or size exclusion chromatography) fail to separate the poly(1-octadecene) impurity from the nanocrystal product. To avoid formation of poly(1-octadecene), we replace 1-octadecene with saturated, aliphatic solvents. Alternatively, the nanocrystals' native ligands are exchanged for polar ligands, leading to significant solubility differences between nanocrystals and poly(1-octadecene), therefore allowing isolation of pure nanocrystals, free from polymer impurities. These results will help design superior syntheses and improve nanocrystal purity, an important factor in many applications

Quantification of Continuous Variable Entanglement with only Two Types of Simple Measurements

Here we propose an experimental set-up in which it is possible to measure the entanglement of a two-mode Gaussian state, be it pure or mixed, using only simple linear optical devices. After a proper unitary manipulation of the two-mode Gaussian state only number and purity measurements of just one of the modes suffice to give us a complete and exact knowledge of the state's entanglement.Comment: v1: 4 pages, 1 figure, RevTex4; v2: Title and abstract changed, new discussion paragraph added; v3: published versio

Roll diffusion bonding of titanium alloy panels

Roll diffusion bonding technique is used for fabricating T-stiffened panel assemblies from titanium alloy. The single unit fabrication exhibits excellent strength characteristics under tensile and compressive loads. This program is applied to structures in which weight/strength ratio and integral construction are important considerations

Bounds on New Physics from the New Data on Parity Violation in Atomic Cesium

We assume the latest experimental determination of the weak charge of atomic cesium and analyze its implications for possible new physics. We notice that the data would imply positive upper and lower bounds on the new physics contribution to the weak charge, $\delta_NQ_W$. The required new physics should be of a type not severely constrained by the high energy precision data. A simplest possibility would be new neutral vector bosons almost un-mixed to the $Z$ and with sizeable couplings to fermions. The lower positive bound would however forbid zero or negative $\delta_NQ_W$ and exclude not only the standard model but also models with sequential $Z^\prime$, in particular simple-minded towers of $Z$-like excitations from extra-dimensions. The bound would also imply an upper limit on the $Z^\prime$ mass within the models allowed. Conclusions are also derived for models of four-fermion contact interactions.Comment: 11 pages, Latex, 1 PS figure, final version for Physics Letter