An example of non-attainability of expected quantum information

Introduction Braunstein and Caves [1] have clarified the relation between classical expected information i(`), in the sense of Fisher, and the analogous concept of expected quantum information I(`), by showing that I(`) is an upper bound of i(`; M) with respect to all (dominated) generalized measurements M of the state ae = ae(`) where ` is an unknown parameter and i(`; M) is the Fisher expected information for ` in the distribution of the outcome of the measurement of M . They indicate moreover that a measurement exists achieving the bound. In the present paper we show by an example, for an elementary spin- 1 2 situation, that in general there does not exist

QCD Sum Rules for the production of the X(3872) as a mixed molecule-charmonium state in B meson decay

We use QCD sum rules to calculate the branching ratio for the production of the meson X(3872) in the decay $B\to X(3872)K$, assumed to be a mixture between charmonium and exotic molecular $[c\bar{q}][q\bar{c}]$ states with $J^{PC}=1^{++}$. We find that in a small range for the values of the mixing angle, $5^\circ\leq\theta\leq13^\circ$, we get the branching ratio ${\mathcal{B}}(B\to XK)=(1.00\pm0.68)\times10^{-5}$, which is in agreement with the experimental upper limit. This result is compatible with the analysis of the mass and decay width of the mode $J/\psi(n\pi)$ and the radiative decay mode $J/\psi\gamma$ performed in the same approach.Comment: 6 pages, 3 figures; revised versions to appear on Phys. Lett.

A Comparative Study of Pentaquark Interpolating Currents

In a diquark-diquark-antiquark picture of pentaquarks, we use two interpolating currents to calculate the mass of the recently measured $\Xi^{--}$ state in the framework of QCD sum rules. We show that, even though yielding similar values for $m_{\Xi^{--}}$ (and close to the experimental value), these currents differ from each other in what concerns the strength of the pole, convergence of the OPE and sensitivity to the continuum threshold parameter.Comment: 19 pages, 8 figures, replaced version accepted for publication in Phys. Lett.

Diquark-Antidiquark with open charm in QCD sum rules

Using the QCD sum rule approach we investigate the possible four-quark structure of the recently observed charmed scalar mesons $D_0^{0}(2308)$ (BELLE) and $D_0^{0,+}(2405)$ (FOCUS) and also of the very narrow $D_{sJ}^{+}(2317)$, firstly observed by BABAR. We use diquak-antidiquark currents and work to the order of $m_s$ in full QCD, without relying on $1/m_c$ expansion. Our results indicate that a four-quark structure is acceptable for the resonances observed by BELLE and BABAR: $D_0^{0}(2308)$ and $D_{sJ}^{+}(2317)$ respectively, but not for the resonances observed by FOCUS: $D_0^{0,+}(2405)$.Comment: 6 pages, 5 eps figures; Contribution to the 'Workshop on Light-Cone QCD and Nonperturbative Hadron Physics 2005 (LC2005)', Cairns-Australi

The J/ψDDJ/\psi D D Vertex in QCD Sum Rules

The $J/\psi D D$ form factor is evaluated in a QCD sum rule calculation for both $D$ and $J/\psi$ off-shell mesons. We study the double Borel sum rule for the three point function of two pseudoscalar and one vector meson current. We find that the momentum dependence of the form factors is different if the $D$ or the $J/\psi$ meson is off-shell, but they lead to the same coupling constant in the $J/\psi D D$ vertex.Comment: 11 pages, Latex, 4 eps figure

Are Θ+\Theta^+ and the Roper resonance diquark-diquark-antiquark states?

We consider a $[ud]^2\bar{s}$ current in the QCD sum rule framework to study the mass of the recently observed pentaquark state $\Theta^+(1540)$, obtaining good agreement with the experimental value. We also study the mass of the pentaquark $[ud]^2\bar{d}$. Our results are compatible with the interpretation of the $[ud]^2\bar{d}$ state as being the Roper resonance N(1440), as suggested by Jaffe and Wilczek.Comment: 9 pages RevTex4 and 3 eps figures. Revised version accepted for publication in Phys. Lett.

A model for string-breaking in QCD

We present a model for string breaking based on the existence of chromoelectric flux tubes. We predict the form of the long-range potential, and obtain an estimate of the string breaking length. A prediction is also obtained for the behaviour with temperature of the string breaking length near the deconfinement phase transition. We plan to use this model as a guide for a program of study of string breaking on the lattice.Comment: 7 pages, minor improvements of the text and of the reference lis

Optimal estimation of qubit states with continuous time measurements

We propose an adaptive, two steps strategy, for the estimation of mixed qubit states. We show that the strategy is optimal in a local minimax sense for the trace norm distance as well as other locally quadratic figures of merit. Local minimax optimality means that given $n$ identical qubits, there exists no estimator which can perform better than the proposed estimator on a neighborhood of size $n^{-1/2}$ of an arbitrary state. In particular, it is asymptotically Bayesian optimal for a large class of prior distributions. We present a physical implementation of the optimal estimation strategy based on continuous time measurements in a field that couples with the qubits. The crucial ingredient of the result is the concept of local asymptotic normality (or LAN) for qubits. This means that, for large $n$, the statistical model described by $n$ identically prepared qubits is locally equivalent to a model with only a classical Gaussian distribution and a Gaussian state of a quantum harmonic oscillator. The term `local' refers to a shrinking neighborhood around a fixed state $\rho_{0}$. An essential result is that the neighborhood radius can be chosen arbitrarily close to $n^{-1/4}$. This allows us to use a two steps procedure by which we first localize the state within a smaller neighborhood of radius $n^{-1/2+\epsilon}$, and then use LAN to perform optimal estimation.Comment: 32 pages, 3 figures, to appear in Commun. Math. Phy

On the complexity of strongly connected components in directed hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which do not reach any components but themselves). "Almost linear" here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor alpha(n), where alpha is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all SCCs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the SCCs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure