In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary c...In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary column operations on matrices over the quaternion field.展开更多
We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt d...We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.展开更多
By virtue of the entangled state representation （Hong-Yi Fan and J R Klauder 1994 Phys. Rev. A 49 704） and the two-mode squeezing operator＇s natural representation （Hong-Yi Fan and Yue Fan 1996 Phys. Rev. A 54 958...By virtue of the entangled state representation （Hong-Yi Fan and J R Klauder 1994 Phys. Rev. A 49 704） and the two-mode squeezing operator＇s natural representation （Hong-Yi Fan and Yue Fan 1996 Phys. Rev. A 54 958） we propose the squeeze-swapping mechanism which can generate quantum entanglement and new squeezed states of continuum variables.展开更多
We construct the n-particle entangled states |β>θ in n-mode Fock space, and examine their completeness relation and partly non-orthonormal property. Their Schmidt decomposition and entangled operator are manifest...We construct the n-particle entangled states |β>θ in n-mode Fock space, and examine their completeness relation and partly non-orthonormal property. Their Schmidt decomposition and entangled operator are manifestly shown. Finally, we discuss their application.展开更多
文摘In this paper we derive a practical method of solving simultaneously the problem of Schmidt decomposition of quaternion matrix and the orthonormalization of vectors in a generalized unitary space by using elementary column operations on matrices over the quaternion field.
文摘We reveal that the two-variable Hermite function hm,n, which is the generalized Bargmann representation of the two-mode Fock state, involves quantum entanglement of harmonic oscillator＇s wave functions. The Schmidt decomposition of hm,n is derived. It also turns out that hm,n can be generated by windowed Fourier transform of the single-variable Hermite functions. As an application, the wave function of the two-variable Hermite polynomial state S（γ）Hm,n （μa1^＋, μa2^＋│00〉, which is the minimum uncertainty state for sum squeezing, in （ η│representation is calculated.
基金Project supported by the Doctoral Scientific Research Startup Fund of Anhui University,China (Grant No. 33190059)the National Natural Science Foundation of China (Grant No. 10874174)the Research Fund for the Doctoral Program of Higher Education of China (New Teacher) (Grant No. 20113401120004)
文摘By virtue of the entangled state representation （Hong-Yi Fan and J R Klauder 1994 Phys. Rev. A 49 704） and the two-mode squeezing operator＇s natural representation （Hong-Yi Fan and Yue Fan 1996 Phys. Rev. A 54 958） we propose the squeeze-swapping mechanism which can generate quantum entanglement and new squeezed states of continuum variables.
文摘We construct the n-particle entangled states |β>θ in n-mode Fock space, and examine their completeness relation and partly non-orthonormal property. Their Schmidt decomposition and entangled operator are manifestly shown. Finally, we discuss their application.
