Multi-Qubit Systems: Highly Entangled States and Entanglement Distribution

A comparison is made of various searching procedures, based upon different entanglement measures or entanglement indicators, for highly entangled multi-qubits states. In particular, our present results are compared with those recently reported by Brown et al. [J. Phys. A: Math. Gen. 38 (2005) 1119]. The statistical distribution of entanglement values for the aforementioned multi-qubit systems is also explored.Comment: 24 pages, 3 figure

Observation of Bs0→J/ψf0(980)B_s^0\to J/\psi f_0(980) and Evidence for Bs0→J/ψf0(1370)B_s^0\to J/\psi f_0(1370)

We report the first observation of $B_s^0\to J/\psi f_0(980)$ and first evidence for $B_s^0\to J/\psi f_0(1370)$, which are CP eigenstate decay modes. These results are obtained from $121.4\;\mathrm{fb}^{-1}$ of data collected at the $\Upsilon(5S)$ resonance with the Belle detector at the KEKB $e^+e^-$ collider. We measure the branching fractions $\mathcal{B}(B_s^0\to J/\psi f_0(980);f_0(980)\to\pi^+\pi^-)=(1.16^{+0.31}_{-0.19}(\mathrm{stat.})^{+0.15}_{-0.17}(\mathrm{syst.})^{+0.26}_{-0.18}(N_{B_s^{(*)}\bar B_s^{(*)}})) \times 10^{-4}$ with a significance of $8.4\sigma$, and $\mathcal{B}(B_s^0\to J/\psi f_0(1370);f_0(1370)\to\pi^+\pi^-)=(0.34^{+0.11}_{-0.14}(\mathrm{stat.})^{+0.03}_{-0.02}(\mathrm{syst.})^{+0.08}_{-0.05}(N_{B_s^{(*)}\bar B_s^{(*)}})) \times 10^{-4}$ with a significance of $4.2\sigma$. The last error listed is due to uncertainty in the number of produced $B_s^{(*)}\bar B_s^{(*)}$ pairs.Comment: 5 pages, 2 figures, 2 tables, published in PR

Measurements of Branching Fractions and Time-dependent CP Violating Asymmetries in B0→D(∗)±D∓B^{0} \to D^{(*)\pm}D^{\mp} Decays

We report measurements of branching fractions and time-dependent CP asymmetries in $B^{0} \to D^{+}D^{-}$ and $B^{0} \to D^{*\pm}D^{\mp}$ decays using a data sample that contains $(772 \pm 11)\times 10^6 B\bar{B}$ pairs collected at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+ e^-$ collider. We determine the branching fractions to be $\mathcal{B}(B^{0} \to D^{+}D^{-})=(2.12 \pm 0.16 \pm 0.18)\times 10^{-4}$ and $\mathcal{B}(B^{0} \to D^{*\pm}D^{\mp}=(6.14 \pm 0.29 \pm 0.50)\times 10^{-4}$. We measure CP asymmetry parameters $\mathcal{S}_{D^{+}D^{-}} = -1.06_{-0.14}^{+0.21} \pm 0.08$ and $\mathcal{C}_{D^{+}D^{-}} = -0.43 \pm 0.16 \pm 0.05$ in $B^{0} \to D^{+}D^{-}$ and $\mathcal{A}_{D^{*}D} = +0.06 \pm 0.05 \pm 0.02$, $\mathcal{S}_{D^{*}D} = -0.78 \pm 0.15 \pm 0.05$, $\mathcal{C}_{D^{*}D} = -0.01 \pm 0.11 \pm 0.04$, $\Delta\mathcal{S}_{D^{*}D} = -0.13 \pm 0.15 \pm 0.04$ and $\Delta\mathcal{C}_{D^{*}D} = +0.12 \pm 0.11 \pm 0.03$ in $B^{0} \to D^{*\pm}D^{\mp}$, where the first uncertainty is statistical and the second is systematic. We exclude the conservation of CP symmetry in both decays at equal to or greater than $4\sigma$ significance.Comment: 7 pages, 2 figure

Evidence for the Suppressed Decay B- -> DK-, D -> K+pi-

The suppressed decay chain B- -> DK-, D -> K+pi-, where D indicates a anti-D0 or D0 state, provides important information on the CP-violating angle phi_3. We measure the ratio R_{DK} of the decay rates to the favored mode B- -> DK-, D -> K-pi+ to be R_{DK} = [1.63^{+0.44}_{-0.41}(stat)^{+0.07}_{-0.13}(syst)] x 10^{-2}, which indicates the first evidence of the signal with a significance of 4.1sigma. We also measure the asymmetry A_{DK} between the charge-conjugate decays to be A_{DK} = -0.39^{+0.26}_{-0.28}(stat)^{+0.04}_{-0.03}(syst). The results are based on the full 772 x 10^6 B anti-B pair data sample collected at the Upsilon(4S) resonance with the Belle detector.Comment: 6 pages, 2 figures, 2 tables, accepted by Physical Review Letter

Measurement of CP violating asymmetries in B^0 -> K^+K^- K^0_S decays with a time-dependent Dalitz approach

We report a measurement of $CP$ violating asymmetries in $B^0(\overline{B}^0) \to K^+ K^- K^0_S$ decays with a time-dependent Dalitz approach. This analysis is based on a data sample of $657\times 10^6$ $B\overline{B}$ pairs accumulated at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. As the result of an unbinned maximum likelihood fit to the selected candidates, the mixing-induced and direct $CP$ violation parameters, $\phi^{\rm eff}_1$ and ${\cal A}_{CP}$ are obtained for $B^0 \to \phi(1020) K^0_S$, $B^0 \to f_0(980) K^0_S$ and other $B^0 \to K^+ K^- K^0_S$ decays. We find four solutions that describe the data. There are \{eqnarray*} \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (32.2 \pm 9.0 \pm 2.6 \pm 1.4)^{\circ}; \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (26.2 \pm 8.8 \pm 2.7 \pm 1.2)^{\circ};\\ \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (27.3 \pm 8.6 \pm 2.8 \pm 1.3)^{\circ}\; {\rm and}\\ \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (24.3 \pm 8.0 \pm 2.9 \pm 5.2)^{\circ}.{eqnarray*}\ The values for the $CP$ violating phase in $B^0\to \phi(1020) K^0_S$ are similar but other properties of the Dalitz plot are quite different for the four solutions. These four solutions have consistent $\phi^{\rm eff}_1$ values for all three $B$ meson decay channels and none of them deviates significantly from the values measured in $B \to (c\bar{c}) K^0$ decays with the currently available statistics. In addition, we find no significant direct $CP$ violation.Comment: submitted to PR

Measurement of CP violating asymmetries in B^0 -> K^+K^- K^0_S decays with a time-dependent Dalitz approach

We report a measurement of $CP$ violating asymmetries in $B^0(\overline{B}^0) \to K^+ K^- K^0_S$ decays with a time-dependent Dalitz approach. This analysis is based on a data sample of $657\times 10^6$ $B\overline{B}$ pairs accumulated at the $\Upsilon(4S)$ resonance with the Belle detector at the KEKB asymmetric-energy $e^+e^-$ collider. As the result of an unbinned maximum likelihood fit to the selected candidates, the mixing-induced and direct $CP$ violation parameters, $\phi^{\rm eff}_1$ and ${\cal A}_{CP}$ are obtained for $B^0 \to \phi(1020) K^0_S$, $B^0 \to f_0(980) K^0_S$ and other $B^0 \to K^+ K^- K^0_S$ decays. We find four solutions that describe the data. There are \{eqnarray*} \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (32.2 \pm 9.0 \pm 2.6 \pm 1.4)^{\circ}; \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (26.2 \pm 8.8 \pm 2.7 \pm 1.2)^{\circ};\\ \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (27.3 \pm 8.6 \pm 2.8 \pm 1.3)^{\circ}\; {\rm and}\\ \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (24.3 \pm 8.0 \pm 2.9 \pm 5.2)^{\circ}.{eqnarray*}\ The values for the $CP$ violating phase in $B^0\to \phi(1020) K^0_S$ are similar but other properties of the Dalitz plot are quite different for the four solutions. These four solutions have consistent $\phi^{\rm eff}_1$ values for all three $B$ meson decay channels and none of them deviates significantly from the values measured in $B \to (c\bar{c}) K^0$ decays with the currently available statistics. In addition, we find no significant direct $CP$ violation.Comment: submitted to PR

First observation of CP violation and improved measurement of the branching fraction and polarization of B0 -> D*+ D*- decays

We report the measurement of the branching fraction, the polarization, and the parameters of the time-dependent CP violation in B0 -> D*+ D*- decays using a data sample of 772 million BB pairs, collected at the Y(4S) resonance with the Belle detector at the KEKB asymmetric-energy e+e- collider. We obtain a branching fraction of B = (7.82 +- 0.38 +- 0.63) x10^{-4}, a CP-odd fraction of R_\perp = 0.138 +- 0.024 +- 0.006 and, additionally, a fraction of the longitudinal component in the transversity base of R_0 = 0.624 +- 0.029 +- 0.011. The measured values of the parameters of the CP violation are S_{D*+ D*-} = -0.79 +- 0.13 +- 0.03 and A_{D*+ D*-} = 0.15 +- 0.08 +- 0.04