Studying bi-partite entangled state representations via the integration over ket–bra operators in Q-ordering or P-ordering

Abstract

For two particles’ relative position and total momentum we have introduced the entangled state representation |\eta \rangle, and its conjugate state |\xi \rangle. In this work, for the first time, we study them via the integration over ket–bra operators in Q-ordering or P-ordering, where Q-ordering means all Qs are to the left of all Ps and P-ordering means all Ps are to the left of all Qs. In this way we newly derive P-ordered (or 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 Pordered (or Q-ordered) are feasible and useful in developing quantum mechanical representation and transformation theory.

Keywords

integration over ket–bra operators / Q-ordering / P-ordering / entangled state representation

References

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RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg