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

Productivity and farm size in Australian agriculture: reinvestigating the returns to scale

Higher productivity among large farms is often assumed to be a result of increasing returns to scale. However, using farm-level data for the Australian broadacre industry, it was found that constant or mildly decreasing returns to scale is more typical. On examining the monotonic change in marginal input returns as farm operating size increases, it was found that large farms achieve higher productivity through changes in production technology rather than through changes in scale. The results highlight the disparity between ‘returns to scale’ and ‘returns to size’ in Australian agriculture. They also suggest that improving productivity in smaller farms would depend more on their ability to access advanced technologies than their ability to simply expand. The implications for ongoing structural adjustment in Australian agriculture are discussed.returns to scale, returns to size, production function, technology progress, structural adjustment, Australian agriculture, Agricultural and Food Policy,

Weak Decays of Doubly Heavy Baryons: the 1/2→1/21/2\to 1/2 case

Very recently, the LHCb collaboration has observed in the final state $\Lambda_c^+ K^-\pi^+\pi^+$ a resonant structure that is identified as the doubly-charmed baryon $\Xi_{cc}^{++}$. Inspired by this observation, we investigate the weak decays of doubly heavy baryons $\Xi_{cc}^{++}$, $\Xi_{cc}^{+}$, $\Omega_{cc}^{+}$, $\Xi_{bc}^{(\prime)+}$, $\Xi_{bc}^{(\prime)0}$, $\Omega_{bc}^{(\prime)0}$, $\Xi_{bb}^{0}$, $\Xi_{bb}^{-}$ and $\Omega_{bb}^{-}$ and focus on the decays into spin $1/2$ baryons in this paper. At the quark level these decay processes are induced by the $c\to d/s$ or $b\to u/c$ transitions, and the two spectator quarks can be viewed as a scalar or axial vector diquark. We first derive the hadronic form factors for these transitions in the light-front approach and then apply them to predict the partial widths for the semi-leptonic and non-leptonic decays of doubly heavy baryons. We find that a number of decay channels are sizable and can be examined in future measurements at experimental facilities like LHC, Belle II and CEPC.Comment: 40 pages, 4 figures, to appear in EPJ

Efficient two-step entanglement concentration for arbitrary W states

We present two two-step practical entanglement concentration protocols (ECPs) for concentrating an arbitrary three-particle less-entangled W state into a maximally entangled W state assisted with single photons. The first protocol uses the linear optics and the second protocol adopts the cross-Kerr nonlinearity to perform the protocol. In the first protocol, based on the post-selection principle, three parties say Alice, Bob and Charlie in different distant locations can obtain the maximally entangled W state from the arbitrary less-entangled W state with a certain success probability. In the second protocol, it dose not require the parties to posses the sophisticated single-photon detectors and the concentrated photon pair can be retained after performing this protocol successfully. Moreover, the second protocol can be repeated to get a higher success probability. Both protocols may be useful in practical quantum information applications.Comment: 10 pages, 4 figure