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Communications in Theoretical Physics

q -Deformed Entangled States Representations and Some Applications

Ye‐Jun Xu, Jun Song, Hong‐Chun Yuan, Qiuyu Liu

Published Feb 1, 2011• 2 citations
Publisher

Abstract

The q-deformed entangled states are introduced by using deformation quantization methods and new normal ordering of the vacuum projection operator for q-deformed boson oscillator. In similar way, by virtue of the technique of integration within an ordered product (IWOP) of operators, the new completeness and orthogonality relations composed of the bra and ket, which are not mutually Hermitian conjugates are obtained. Furthermore, the property of squeezing operator represented by the q-deformed entangled states is exhibited. Lastly, the nonclassical properties of the q-deformed two-mode squeezed vacuum state are studied.

DOI
10.1088/0253-6102/55/2/08

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使 q 变形的纠缠的状态被使用为使 q 变形的波色子振荡器真空设计操作员订的变丑量子化方法和新正常介绍。以类似的方法，由在操作员的一个订的产品(IWOP ) 以内的集成的技术的优点，新完全性和 orthogonality 关系互相乳罩和 ket 创作了，它不是 Hermitian 结合被获得。而且，挤压由使 q 变形的纠缠的状态代表的操作员的性质被展出。最后，使 q 变形的二模式的挤压的真空状态的 nonclassical 性质被学习。

理论物理通讯：英文版•Jan 1, 2011•0 citations
The q-deformed entangled states are introduced by using deformation quantization methods and new normal ordering of the vacuum projection operator for q-deformed boson oscillator. In similar way, by virtue of the technique of integration within an ordered product (IWOP) of operators, the new completeness and orthogonality relations composed of the bra and ket, which are not mutually Hermitian conjugates are obtained. Furthermore, the property of squeezing operator represented by the q-deformed entangled states is exhibited. Lastly, the nonclassical properties of the q-deformed two-mode squeezed vacuum state are studied.
The q-analogues of two-mode squeezed states are introduced by virtue of deformation quantization methods and the technique of integration within an ordered product (IWOP) of operators. Some new completeness relations about these squeezed states composed of the bra and ket which are not mutually Hermitian conjugates are obtained. Furthermore, the antibunching effects of the two-mode squeezed vacuum state S'2(r) |00〉 are investigated. It is found that, in different ranges of the squeezed parameter r, both modes of the state exhibit the antibunching effects and the two modes of the state are always nonclassical correlation.
Studying bi-partite entangled state representations via the integration over ket-bra operators in Q\mathfrak{Q}Q -ordering or P\mathfrak{P}P -ordering
For two particles’ relative position and total momentum we have introduced the entangled state representation |η〉, and its conjugate state |ξ〉. In this work, for the first time, we study them via the integration over ket-bra operators in Q\mathfrak{Q}Q -ordering or P\mathfrak{P}P -ordering, where Q\mathfrak{Q}Q -ordering means all Qs are to the left of all Ps and P\mathfrak{P}P -ordering means all Ps are to the left of all Qs. In this way we newly derive P\mathfrak{P}P -ordered (or Q\mathfrak{Q}Q -ordered) expansion formulas of the two-mode squeezing operator which can show the squeezing effect on both the two-mode coordinate and momentum eigenstates. This tells that not only the integration over ket-bra operators within normally ordered, but also within P\mathfrak{P}P -ordered (or Q\mathfrak{Q}Q -ordered) are feasible and useful in developing quantum mechanical representation and transformation theory.
使 q 变形的纠缠的状态被使用为使 q 变形的波色子振荡器真空设计操作员订的变丑量子化方法和新正常介绍。以类似的方法，由在操作员的一个订的产品(IWOP ) 以内的集成的技术的优点，新完全性和 orthogonality 关系互相乳罩和 ket 创作了，它不是 Hermitian 结合被获得。而且，挤压由使 q 变形的纠缠的状态代表的操作员的性质被展出。最后，使 q 变形的二模式的挤压的真空状态的 nonclassical 性质被学习。