By constructing a new orthogonal-complete quantum mechanical entangled state representation, we show that it can provide us with a combinative view of both squeezing and quantum entanglement involved in the parametric down-conversion process. The two-mode Wigner operator in this representation is also found.
We construct a new bipartite entangled state (NBES), which describes both the squeezing and the entanglement involved in the parametric down-conversion process and can be produced using a symmetric beam splitter. Constructing asymmetric ket—bra integrations based on the NBES leads to some new squeezing operators, which clearly exhibit the relationships between squeezing and entangled state transformations. Moreover, an entangled Wigner operator with a definite physical meaning is also presented.
The coherent-intermediate-entangled state |α, x ⟩ λ,ν is proposed in the two-mode Fock Space, which exhibits both the properties of the coherent and entangled states. The |α, x ⟩ λ,ν makes up a new quantum mechanical representation, and the completeness relation of |α, x ⟩ λ,ν is proved by virtue of the technique of integral within an ordered product of operators. The corresponding squeezing operators are derived. Furthermore, Generalized P-representation is constructed in the coherent-intermediate-entangled state |α, x ⟩ λ,ν and the Schmidt decomposition of |α, x ⟩ λ,ν is investigated.
we propose the conception of entangled state representation with continuum variables. We analyze the non-factorizable properties of the state, the common eigenvector of two-particle relative position and total moment um (Fan Hongyi and J.R. Klauder, Phys. Rev. A49 (1994) 704), and recast it into the standard form as the state prepared in a parametric down conversion process which involves the entanglement of idle and signal photons. We name the set of as entangled state representation, as it is orthonormal and complete
Our primary purpose of this work is to explicitly construct the general multipartite Einstein–Podolsky–Rosen (EPR) entangled state in multi-mode Fock space for a system with different masses of particles, which makes up a new quantum mechanical representation owing to completeness relation and orthogonal property. Its entanglement can be seen more clearly by analyzing its standard Schmidt decomposition. In addition, some applications of the multipartite entanglement are proposed including deriving the generalized Wigner operator and squeezing operator.
For two unequal-mass particles, we construct the entangled state representation and then derive the corresponding squeezing operator. This squeezing operator has a natural realization in the entangled state representation, which exhibits the intrinsic relation between squeezing and quantum entanglement. This squeezing operator involves both two-mode squeezing and the direct product of two single-mode squeezings. The maximum squeezing occurs when the two particles possess equal mass. When the two particles' mass difference becomes large, the component of the two single-mode squeezings becomes dominant.