Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs

We present two realistic entanglement concentration protocols (ECPs) for pure partially entangled photons. A partially entangled photon pair can be concentrated to a maximally entangled pair with only an ancillary single photon in a certain probability, while the conventional ones require two copies of partially entangled pairs at least. Our first protocol is implemented with linear optics and the second one is implemented with cross-Kerr nonlinearities. Compared with other ECPs, they do not need to know the accurate coefficients of the initial state. With linear optics, it is feasible with current experiment. With cross-Kerr nonlinearities, it does not require the sophisticated single-photon detectors and can be repeated to get a higher success probability. Moreover, the second protocol can get the higher entanglement transformation efficiency and it maybe the most economical one by far. Meanwhile, both of protocols are more suitable for multi-photon system concentration, because they need less operations and classical communications. All these advantages make two protocols be useful in current long-distance quantum communications

bsuˉdˉbs\bar u\bar d : A Promising Detectable Tetraquark

We propose to investigate a particle with four different flavors, $bs\bar u\bar d$, which is a promising detectable tetraquark state. Its $BK$ threshold, 5773 MeV, is 270 MeV higher than the $B_s\pi$ threshold of $bd\bar u\bar s$ and $bu\bar d\bar s$, leading to a large mass region to be stable. If the lowest-lying \bsud state exists below threshold, it can be definitely observed via the weak decay mode $J/\Psi K^-K^-\pi^+$, with the expectation of hundreds of events in the current LHCb data sample but rejecting backgrounds due to its long lifetime. This can be a benchmark of the existence of $X(5568)$ which is a partner of $bs\bar u\bar d$ under the flavor $SU(3)$ symmetry. If no signal is observed in this mode, it constrain the mass of the ground tetraquark state to be larger than the threshold. In the case above threshold, it can be detected via the strong decay mode $\overline B^0K^-$. The $cs\bar u\bar d$ state has similar features.Comment: 5 pages, 2 figures and 2 table