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A Generalized Hadamard-Fresnel Complementary Transformation Derived by Virtue of New Coherent-Entangled State

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Abstract

The new coherent-entangled state |z,x;θ〉 is proposed in the two-mode Fock space, which exhibits both the properties of coherent and entangled states. The completeness relation of |z,x;θ〉 is proved by virtue of the technique of integral within an ordered product of operators. A generalized Hadamard-Fresnel complementary transformation derived by virtue of the coherent-entangled state |z,x;θ〉, which is unitary. The new unitary operator plays the role of both Hadamard transformation for \((\hat{a}_{1}\sin\theta -\hat{a}_{2}\cos\theta)\) and Fresnel transformation for \((\hat{a}_{1}\cos\theta +\hat{a}_{2}\sin\theta)\), respectively.

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Authors and Affiliations

  1. Department of Physics, Heze University, Shandong, 274015, China

    Xing-Lei Xu, Shi-Min Xu & Hong-Qi Li

  2. Key Laboratory of Quantum Communication and Calculation, Heze University, Shandong, 274015, China

    Xing-Lei Xu, Shi-Min Xu & Hong-Qi Li

  3. Department of Physics, Liaocheng University, Shandong, 252059, China

    Ji-Suo Wang

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  1. Xing-Lei Xu
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  2. Shi-Min Xu
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  3. Hong-Qi Li
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  4. Ji-Suo Wang
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Correspondence to Xing-Lei Xu.

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Xu, XL., Xu, SM., Li, HQ. et al. A Generalized Hadamard-Fresnel Complementary Transformation Derived by Virtue of New Coherent-Entangled State. Int J Theor Phys 50, 385–394 (2011). https://doi.org/10.1007/s10773-010-0540-x

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  • DOI: https://doi.org/10.1007/s10773-010-0540-x

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