Conditions for Nondistortion Interrogation of Quantum System

Under some physical considerations, we present a universal formulation to study the possibility of localizing a quantum object in a given region without disturbing its unknown internal state. When the interaction between the object and probe wave function takes place only once, we prove the necessary and sufficient condition that the object's presence can be detected in an initial state preserving way. Meanwhile, a conditioned optimal interrogation probability is obtained.Comment: 5 pages, Revtex, 1 figures, Presentation improved, corollary 1 added. To appear in Europhysics Letter

Quantum insulating states of F=2 cold atoms in optical lattices

In this Letter we study various spin correlated insulating states of F=2 cold atoms in optical lattices. We find that the effective spin exchange interaction due to virtual hopping contains an {\em octopole} coupling between two neighboring lattice sites. Depending on scattering lengths and numbers of particles per site the ground states are either rotationally invariant dimer or trimer Mott insulators or insulating states with various spin orders. Three spin ordered insulating phases are ferromagnetic, cyclic and nematic Mott insulators. We estimate the phase boundaries for states with different numbers of atoms per lattice site.Comment: 4 pages, 1 figure include

Central limit theorem for signal-to-interference ratio of reduced rank linear receiver

Let $\mathbf{s}_k=\frac{1}{\sqrt{N}}(v_{1k},...,v_{Nk})^T,$ with $\{v_{ik},i,k=1,...\}$ independent and identically distributed complex random variables. Write $\mathbf{S}_k=(\mathbf{s}_1,...,\mathbf {s}_{k-1},\mathbf{s}_{k+1},... ,\mathbf{s}_K),$ $\mathbf{P}_k=\operatorname {diag}(p_1,...,p_{k-1},p_{k+1},...,p_K)$, $\mathbf{R}_k=(\mathbf{S}_k\mathbf{P}_k\mathbf{S}_k^*+\sigma ^2\mathbf{I})$ and $\mathbf{A}_{km}=[\mathbf{s}_k,\mathbf{R}_k\mathbf{s}_k,... ,\mathbf{R}_k^{m-1}\mathbf{s}_k]$. Define $\beta_{km}=p_k\mathbf{s}_k^*\mathbf{A}_{km}(\mathbf {A}_{km}^*\times\ mathbf{R}_k\mathbf{A}_{km})^{-1}\mathbf{A}_{km}^*\mathbf{s}_k$, referred to as the signal-to-interference ratio (SIR) of user$k$under the multistage Wiener (MSW) receiver in a wireless communication system. It is proved that the output SIR under the MSW and the mutual information statistic under the matched filter (MF) are both asymptotic Gaussian when$N/K\to c>0$. Moreover, we provide a central limit theorem for linear spectral statistics of eigenvalues and eigenvectors of sample covariance matrices, which is a supplement of Theorem 2 in Bai, Miao and Pan [Ann. Probab. 35 (2007) 1532--1572]. And we also improve Theorem 1.1 in Bai and Silverstein [Ann. Probab. 32 (2004) 553--605].Comment: Published in at http://dx.doi.org/10.1214/07-AAP477 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org