The purpose of this note is to establish a general representation of Hankel matrices of Bell numbers and the convoluted Bell numbers. As a special case, the results of Aigner are extended.
In this paper, one introduces the polynomials R<sub>n</sub>(x) and numbers R<sub>n</sub> and derives some interesting identities related to the numbers and polynomials: R<sub>n</sub>...In this paper, one introduces the polynomials R<sub>n</sub>(x) and numbers R<sub>n</sub> and derives some interesting identities related to the numbers and polynomials: R<sub>n</sub> and R<sub>n</sub>(x). We also give relation between the Stirling numbers, the Bell numbers, the R<sub>n</sub> and R<sub>n</sub>(x).展开更多
We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser Home inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotatio...We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser Home inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotational asymmetry of the quantum state, the ratio of Os to ls varies with the measurement bases. The experimental partners can then use their measurement outcomes to generate the biased random bit string. The bias of their bit string can be adjusted by altering their choices of measurement bases. When this protocol is implemented in a device-independent way, we show that the bias of the bit string can still be ensured under the collective attack.展开更多
文摘The purpose of this note is to establish a general representation of Hankel matrices of Bell numbers and the convoluted Bell numbers. As a special case, the results of Aigner are extended.
文摘In this paper, one introduces the polynomials R<sub>n</sub>(x) and numbers R<sub>n</sub> and derives some interesting identities related to the numbers and polynomials: R<sub>n</sub> and R<sub>n</sub>(x). We also give relation between the Stirling numbers, the Bell numbers, the R<sub>n</sub> and R<sub>n</sub>(x).
基金Supported by the National Natural Science Foundation of China under Grant Nos 61378011,U1204616 and 11447143the Program for Science and Technology Innovation Talents in Universities of Henan Province under Grant No 2012HASTIT028the Program for Science and Technology Innovation Research Team in University of Henan Province under Grant No 13IRTSTHN020
文摘We propose a biased random number generation protocol whose randomness is based on the violation of the Clauser Home inequality. Non-maximally entangled state is used to maximize the Bell violation. Due to the rotational asymmetry of the quantum state, the ratio of Os to ls varies with the measurement bases. The experimental partners can then use their measurement outcomes to generate the biased random bit string. The bias of their bit string can be adjusted by altering their choices of measurement bases. When this protocol is implemented in a device-independent way, we show that the bias of the bit string can still be ensured under the collective attack.
