Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [Phys. Rev. Lett. 105(2010) 190502] as the quantifier. F...Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [Phys. Rev. Lett. 105(2010) 190502] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed.展开更多
As a typical immiscible binary system, copper (Cu) and lithium (Li) show no alloying and chemical intermixing under normal circumstances. Here we show that, when decreasing Cu nanoparticle sizes into ultrasmall range,...As a typical immiscible binary system, copper (Cu) and lithium (Li) show no alloying and chemical intermixing under normal circumstances. Here we show that, when decreasing Cu nanoparticle sizes into ultrasmall range, the nanoscale size effect can play a subtle yet critical role in mediating the chemical activity of Cu and therefore its miscibility with Li, such that the electrochemical alloying and solidstate amorphization will occur in such an immiscible system. This unusual observation was accomplished by performing in-situ studies of the electrochemical lithiation processes of individual CuO nanowires inside a transmission electron microscopy (TEM). Upon lithiation, CuO nanowires are first electrochemically reduced to form discrete ultrasmall Cu nanocrystals that, unexpectedly, can in turn undergo further electrochemical lithiation to form amorphous Cu Lixnanoalloys. Real-time TEM imaging unveils that there is a critical grain size (ca. 6 nm), below which the nanocrystalline Cu particles can be continuously lithiated and amorphized. The possibility that the observed solid-state amorphization of Cu-Li might be induced by electron beam irradiation effect can be explicitly ruled out; on the contrary, it was found that electron beam irradiation will lead to the dealloying of as-formed amorphous Cu Lixnanoalloys.展开更多
The quantum discord was introduced by Ollivier,Zurek,Henderson,and Vedral as an indicator of the degree of quantumness of mixed states.In this paper,we provide a decomposition condition for quantum discord.Moreover,we...The quantum discord was introduced by Ollivier,Zurek,Henderson,and Vedral as an indicator of the degree of quantumness of mixed states.In this paper,we provide a decomposition condition for quantum discord.Moreover,we show that under the condition,the quantum correlations between the quantum systems can be captured completely by the entanglement measure.Finally,we present examples of our conclusions.展开更多
基金Supported by the National Natural Science Foundation of China(NNSFC)under Grant Nos.11375011 and 11372122the Natural Science Foundation of Anhui Province under Grant No.1408085MA12the 211 Project of Anhui University
文摘Quantum correlations in a family of states comprising any mixture of a pair of arbitrary bi-qubit product pure states are studied by employing geometric discord [Phys. Rev. Lett. 105(2010) 190502] as the quantifier. First, the inherent symmetry in the family of states about local unitary transformations is revealed. Then, the analytic expression of geometric discords in the states is worked out. Some concrete discussions and analyses on the captured geometric discords are made so that their distinct features are exposed. It is found that, the more averagely the two bi-qubit product states are mixed, the bigger geometric discord the mixed state owns. Moreover, the monotonic relationships of geometric discord with different parameters are revealed.
基金supported by the National Natural Science Foundation of China (11474337, 51472267, 21773303, and 51421002)the Program by Chinese Academy of Sciences (ZDYZ2015-1 and XDB07030100)Austrian-Chinese Cooperative R&D Projects, FFG and Chinese Academy of Sciences (112111KYSB20150002)
文摘As a typical immiscible binary system, copper (Cu) and lithium (Li) show no alloying and chemical intermixing under normal circumstances. Here we show that, when decreasing Cu nanoparticle sizes into ultrasmall range, the nanoscale size effect can play a subtle yet critical role in mediating the chemical activity of Cu and therefore its miscibility with Li, such that the electrochemical alloying and solidstate amorphization will occur in such an immiscible system. This unusual observation was accomplished by performing in-situ studies of the electrochemical lithiation processes of individual CuO nanowires inside a transmission electron microscopy (TEM). Upon lithiation, CuO nanowires are first electrochemically reduced to form discrete ultrasmall Cu nanocrystals that, unexpectedly, can in turn undergo further electrochemical lithiation to form amorphous Cu Lixnanoalloys. Real-time TEM imaging unveils that there is a critical grain size (ca. 6 nm), below which the nanocrystalline Cu particles can be continuously lithiated and amorphized. The possibility that the observed solid-state amorphization of Cu-Li might be induced by electron beam irradiation effect can be explicitly ruled out; on the contrary, it was found that electron beam irradiation will lead to the dealloying of as-formed amorphous Cu Lixnanoalloys.
基金Supported by Research Fund,Kumoh National Institute of Technology
文摘The quantum discord was introduced by Ollivier,Zurek,Henderson,and Vedral as an indicator of the degree of quantumness of mixed states.In this paper,we provide a decomposition condition for quantum discord.Moreover,we show that under the condition,the quantum correlations between the quantum systems can be captured completely by the entanglement measure.Finally,we present examples of our conclusions.
