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Deterministic remote preparation of an arbitrary qubit state using a partially entangled state and finite classical communication

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Abstract

We propose a deterministic remote state preparation (RSP) scheme for preparing an arbitrary (including pure and mixed) qubit, where a partially entangled state and finite classical communication are used. To our knowledge, our scheme is the first RSP scheme that fits into this category. One other RSP scheme proposed by Berry shares close features, but can only be used to prepare an arbitrary pure qubit. Even so, our scheme saves classical communication by approximate 1 bit per prepared qubit under equal conditions. When using a maximally entangled state, the classical communication for our scheme is 2 bits, which agrees with Lo’s conjecture on the resource cost. Furthermore Alice can switch between our RSP scheme and a standard teleportation scheme without letting Bob know, which makes the quantum channel multipurpose.

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Acknowledgments

We thank Cheng Guan Koay and Lin Chen for valuable discussion. We also gratefully acknowledge the support by NNSF of China, Grant No. 11375150.

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Authors and Affiliations

  1. Zhejiang Institute of Modern Physics, Zhejiang University, Hangzhou, 310027, China

    Congyi Hua & Yi-Xin Chen

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  1. Congyi Hua
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Correspondence to Yi-Xin Chen.

Appendix: Uniform distribution of antipodally symmetric points on the unit sphere

Appendix: Uniform distribution of antipodally symmetric points on the unit sphere

On a sphere, point sets with antipodal symmetry have special importance in both scientific and engineering fields, many works has been published for generating such sets. The methods for generating a 2K-element set with antipodal symmetry usually contain a minimization procedure of electrostatic potential energy. For the number of elements within a few hundreds, the point sets are tabulated online [30]. However, for the number of points in these point sets beyond a few hundreds, the optimization procedure will become unwieldy. To solve this problem, we can use instead some constructive methods to generate nearly uniform point sets with antipodal symmetry, which give very close results especially when K is large. In this work for generating antipodally symmetric point sets with \(K\ge 256\) , we use a simple deterministic points construction scheme proposed by Koay [31]. For the unit sphere, the spherical coordinates \(\left( 1,\theta _i,\phi _{i,j}\right) \) of the points on the upper hemisphere are given by:

$$\begin{aligned} \theta _i&=\left( i-\frac{1}{2}\right) \frac{\pi }{[N]},&i&=1,2,\ldots ,[N],\\ \phi _{i,j}&=\left( j-\frac{1}{2}\right) \frac{2\pi }{K_i},&j&=1,2,\ldots ,K_i. \end{aligned}$$

where N is the solution to \(N=\frac{K}{2}\sin {\frac{\pi }{4N}}\), \([\cdot ]\) is the function which gives the integer closest to the input, and

$$\begin{aligned} K_i= {\left\{ \begin{array}{ll} \left[ \frac{2 \pi \sin \theta _i}{\pi \csc {\frac{\pi }{4[N]}}}K\right] , &{}i=1,2,\ldots ,[N]-1,\\ K-\sum \nolimits _{i=1}^{[N]-1}K_i, &{}i=[N]. \end{array}\right. } \end{aligned}$$

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Hua, C., Chen, YX. Deterministic remote preparation of an arbitrary qubit state using a partially entangled state and finite classical communication. Quantum Inf Process 15, 4773–4783 (2016). https://doi.org/10.1007/s11128-016-1423-8

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