Multi-Step Multi-Input One-Way Quantum Information by Ryuji Ukai

By Ryuji Ukai

In this thesis, the writer develops for the 1st time an implementation method for arbitrary Gaussian operations utilizing temporal-mode cluster states. the writer additionally provides 3 experiments regarding continuous-variable one-way quantum computations, the place their non-classical nature is proven through gazing entanglement on the outputs. The experimental simple constitution of one-way quantum computation over two-mode enter kingdom is verified via the controlled-Z gate and the optimal nonlocal gate experiments. in addition, the writer proves that the operation should be managed through the gain-tunable entangling gate experiment.

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The mean value is constantly zero, while the fluctuations do not depend on time. 1 Definition We define a squeezing operator: ˆ ) = e 2 (aˆ 2 −aˆ †2 ) , r ∈ R, S(r r Fig. 39) p x 22 2 Quantum Optics E O t Fig. 4 Representation in time where r is called a squeezing parameter. 40) where |0 is the vacuum state. 44) and thus 2 xˆ = 2 e−2r , 2 pˆ = 2 e2r , xˆ sd = 2 e−r , pˆ sd = 2 er . 45) Note that the variance of xˆ is not equal to that of pˆ for r = 0. However, they satisfy xˆ sd pˆ sd = 2 . 46) Therefore, the squeezed vacuum state is also a minimum uncertainty state.

IEEE Press, Los Alamitos, CA (1994) 5. : Polynomial-time algorithms for prime factorization and discrete logorithms on a quantum computer. SIAM J. Computing 26, 1484 (1997) 6. : Quantum mechanics helps in searching for a needle in a Haystack. Phys. Rev. Lett. 79, 325 (1997) 7. S. J. , and L. H. Kauffman, Quantum Hidden Subgroup Problems: A Mathematical Perspective, e-print arXiv:0201095 [quant-ph] 8. J. : A Continuous Variable Shor Algorithm, e-print arXiv:0210141 [quant-ph] References 13 9. : Experimental tests of realistic local theories via Bell’s theorem.

1 Definition The vacuum state is a coherent state with α = 0. 1. Fig. 2 Several Quantum States xˆ = pˆ = 0, 21 xˆ 2 = pˆ 2 = 2 , xˆ sd = pˆ sd = 2 . 37) These equations show that the mean values of xˆ and pˆ are equal to zero. The vacuum state is a minimum uncertainty state with finite fluctuations derived from the uncertainty principle. 3 Representation in Phase Space Phase space representation of the vacuum state is shown in Fig. 3. 38) for the vacuum state, we get the graph of the electric field in the time domain (Fig.

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