Dense coding or super-dense coding in the case of high-dimension quantum states between two parties and multi-parties has been studied in this paper. We construct explicitly the measurement basis and the forms of the single-body unitary operations corresponding to the basis chosen, and the rules for selecting the one-body unitary operations in a multi-party case. Quantum dense-coding or super-dense coding[1] is one of the important branches of quantum information theory. It has been widely studied both in theory and in experiment [1,2]. The basic idea of quantum dense coding is that quantum mechanics allows one to encode information in the quantum states that is more dense than classical coding. Bell-basis statesare used in dense coding. Bell basis states are in the Hilbert space of 2 particles, each with 2-dimension, and they are the maximally entangled states. Supposed Alice and Bob share the maximally entangled state |Ψ + . Bob then operates locally on the particle he shares with Alice one of the four unitary transformations I, σ x , iσ y , σ z , and this will transform |Ψ + into |Ψ + , |φ + , |φ − and |Ψ − respectively. Bob sends his particle back to Alice. Because the four manipulations result in four orthogonal Bell states, four distinguishable messages, i.e., 2 bits of information then can be obtained by Alice via collective-measurement on the two particles. The scheme has been experimentally demonstrated by Mattle et. al. [3]. With the realization of preparing high-dimension quantum state [4], it is of practical importance to study the highdimensional aspects of various topics in quantum information. For example, multi-particle high-dimensional quantum teleportation has been constructed recently [5]. Teleportation and quantum dense coding are closely related. In this paper, we presents a quantum dense coding scheme between multi-parties in an arbitrary high dimensional Hilbert space. As two-party dense coding is of primary importance, we first present the two-party dense coding scheme in arbitrary high dimension. Then we present the general scheme for dense coding between multi-parties using high dimensional state.To present our scheme clearer. Let's first begin with dense coding between two parties in 3-dimension. The general Bell-basis of the Hilbert space of two particles with 3-dimension are [5,6]:where n, m, j =0, 1, 2. Explicitly,|Ψ 10 = (|00 + e 2πi/3 |11 + e 4πi/3 |22 )/ √ 3, |Ψ 20 = (|00 + e 4πi/3 |11 + e 2πi/3 |22 )/ √ 3,|Ψ 11 = (|01 + e 2πi/3 |12 + e 4πi/3 |20 )/ √ 3, |Ψ 21 = (|01 + e 4πi/3 |12 + e 2πi/3 |20 )/ √ 3,|Ψ 12 = (|02 + e 2πi/3 |10 + e 4πi/3 |21 )/ √ 3, |Ψ 22 = (|02 + e 4πi/3 |10 + e 2πi/3 |21 )/ √ 3.
Because of China's rapid economic development, its freight transportation system has grown to become one of China's high‐pollution‐emission sectors. However, there are few studies that pay close attention to measuring and improving the environmental performance of China's freight transportation system, especially in regard to seaports. In this paper, data envelopment analysis (DEA) is applied to measure the environmental performance of freight transportation seaports. In addition, we also provide benchmarking information to point the way to improving environmental performance effectively. Our proposed DEA model is based on the closest targets, which satisfies the strong monotonicity and can yield the most relevant solution for the inefficient seaports. An empirical study of 21 of China's primary freight transportation seaports shows that most of them have relatively good environmental performance. Among the five coastal port groups, the Bohai‐rim port group had the best environmental performance, whereas the Pearl River port group had the worst. Our data show significant differences between the best and worst performances, indicating that more measures should be taken to balance and coordinate the development between the five coastal port groups.
Isolated single-walled carbon nanotubes ͑SWNTs͒, SWNT bundles, and ropes ͑or strands͒ show a structural self-similar characteristic. By calculating the Hausdorff dimension, it was found that their self-similar organization leads to surface fractality and the value of the surface dimension (D s ) depends on self-similar patterns. Experimentally, D s obtained by nitrogen adsorption measurements at 77.3 K and by the small-angle x-ray scattering technique in our study proved our calculation that the surface dimension of SWNTs is nonintegral, 2ϽD s Ͻ3, which indicates that the surface of SWNTs is fractal. According to our calculation and analysis, the fractality is determined by the self-similar arrangement of SWNTs, but the value of D s is also influenced by the effect of finite length and irregular aggregation of real SWNT samples.
With the development of urbanization and the expansion of floating populations, rental housing has become an increasingly common living choice for many people, and housing rental prices have attracted great attention from individuals, enterprises and the government. The housing rental prices are principally estimated based on structural, locational and neighborhood variables, among which the relationships are complicated and can hardly be captured entirely by simple one-dimensional models; in addition, the influence of the geographic objects on the price may vary with the increase in their quantities. However, existing pricing models usually take those structural, locational and neighborhood variables as one-dimensional inputs into neural networks, and often neglect the aggregated effects of geographical objects, which may lead to fluctuating rental price estimations. Therefore, this paper proposes a rental housing price model based on the convolutional neural network (CNN) and the synthetic spatial density of points of interest (POIs). The CNN can efficiently extract the complex characteristics among the relevant variables of housing, and the two-dimensional locational and neighborhood variables, based on the synthetic spatial density, effectively reflect the aggregated effects of the urban facilities on rental housing prices, thereby improving the accuracy of the model. Taking Wuhan, China, as the study area, the proposed method achieves satisfactory and accurate rental price estimations (coefficient of determination (R2) = 0.9097, root mean square error (RMSE) = 3.5126) in comparison with other commonly used pricing models.
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