We investigate monogamy relations related to the Rényi- $α$ entanglement and polygamy relations related to the Rényi- $α$ entanglement of assistance. We present new entanglement monogamy relations satisfied by the $μ$ -th power of Rényi- $α$ entanglement with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $μ\geqslant2$ , and polygamy relations satisfied by the $μ$ -th power of Rényi- $α$ entanglement of assistance with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $0\leqμ\leq1$ . These relations are shown to be tighter than the existing ones.We investigate monogamy relations related to the Rényi-$α$ entanglement and polygamy relations related to the Rényi-$α$ entanglement of assistance. We present new entanglement monogamy relations satisfied by the $μ$-th power of Rényi-$α$ entanglement with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $μ\geqslant2$, and polygamy relations satisfied by the $μ$-th power of Rényi-$α$ entanglement of assistance with $α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]$ for $0\leqμ\leq1$. These relations are shown to be tighter than the existing ones.

arXiv:1810.09131Oct 22, 20180 citations

V. Relativity Correction

Niels BohrJan 1, 19810 citations

Aspects of universally valid Heisenberg uncertainty relation

Kazuo Fujikawa, Koichiro Umetsu

A numerical illustration of a universally valid Heisenberg uncertainty relation, which was proposed recently, is presented by using the experimental data on spin-measurements by J. Erhart et al. [Nat. Phys. 8, 185 (2012)]. This uncertainty relation is closely related to a modified form of the Arthurs–Kelly uncertainty relation, which is also tested by the spin-measurements. The universally valid Heisenberg uncertainty relation always holds, but both the modified Arthurs–Kelly uncertainty relation and the Heisenberg error–disturbance relation proposed by Ozawa, which was analyzed in the original experiment, fail in the present context of spin-measurements, and the cause of their failure is identified with the assumptions of unbiased measurement and disturbance. It is also shown that all the universally valid uncertainty relations are derived from Robertson's relation and thus the essence of the uncertainty relation is exhausted by Robertson's relation, as is widely accepted.A numerical illustration of a universally valid Heisenberg uncertainty relation, which was proposed recently, is presented by using the experimental data on spin-measurements by J. Erhart et al. [Nat. Phys. 8, 185 (2012)]. This uncertainty relation is closely related to a modified form of the Arthurs–Kelly uncertainty relation, which is also tested by the spin-measurements. The universally valid Heisenberg uncertainty relation always holds, but both the modified Arthurs–Kelly uncertainty relation and the Heisenberg error–disturbance relation proposed by Ozawa, which was analyzed in the original experiment, fail in the present context of spin-measurements, and the cause of their failure is identified with the assumptions of unbiased measurement and disturbance. It is also shown that all the universally valid uncertainty relations are derived from Robertson's relation and thus the essence of the uncertainty relation is exhausted by Robertson's relation, as is widely accepted.

arXiv:1211.1828Progress of Theoretical and Experimental PhysicsJan 1, 20139 citations

Physics

Jürgen Jost

Springer eBooksJan 1, 20090 citations

Generalization of classical uncertain relation to quantum uncertain relation and it's applications to the stable properties of the world

Yong Huang

The classical statistical mean values are generally generalized to the quantum statistical mean values, the classical statistical uncertain relation is exactly generalized to quantum statistical uncertain relation, the two losed conditions in classical and quantum uncertain relations, respectively, are found, all articles and books relative to the two losed conditions need to be corrected. Finally, this paper generally expounds the relations among uncertain relation, singularity and the worlds stability, and gives the failure conditions of the quantum uncertain relation.The classical statistical mean values are generally generalized to the quantum statistical mean values, the classical statistical uncertain relation is exactly generalized to quantum statistical uncertain relation, the two losed conditions in classical and quantum uncertain relations, respectively, are found, all articles and books relative to the two losed conditions need to be corrected. Finally, this paper generally expounds the relations among uncertain relation, singularity and the worlds stability, and gives the failure conditions of the quantum uncertain relation.

Chinese journal of atomic and molecular physicsJan 1, 20020 citations

A Relativity Paradox

Arthur Stanley Eddington

NatureDec 1, 19224 citations

Tighter monogamy and polygamy relations using Rényi-

α

entropy

We investigate monogamy relations related to the Rényi-

α

entanglement and polygamy relations related to the Rényi-

α

entanglement of assistance. We present new entanglement monogamy relations satisfied by the

μ

-th power of Rényi-

α

entanglement with

α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]

for

μ\geqslant2

, and polygamy relations satisfied by the

μ

-th power of Rényi-

α

entanglement of assistance with

α\in[\sqrt{7}-1)/2,(\sqrt{13}-1)/2]

for

0\leqμ\leq1

. These relations are shown to be tighter than the existing ones.