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SCIENCE CHINA Information Sciences, Volume 60, Issue 12: 122501(2017) https://doi.org/10.1007/s11432-016-0569-2

Quantum correlations generation and distribution in a universal covariant quantum cloning circuit

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  • ReceivedAug 23, 2016
  • AcceptedOct 30, 2016
  • PublishedApr 1, 2017

Abstract

We discussed the distribution and generation of quantum correlations in a universal covariant quantum cloning circuit. Specifically, we first considered the distribution of quantum correlation, i.e., quantum discord, among the four qubits of the circuit. Then, we analyzed the generation of genuine 3- or 4-qubit entanglement in the cloning process. It is found that the circuit generates genuine 4-qubit GHZ (Greenberger-Horne-Zeilinger)-type state while only W-type 3-qubit state could be generated. These results illustrate the special quantum correlation manipulation capabilities of the cloning circuit.


Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant No. U1204114).


References

[1] Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature, 1982, 299: 802-803 CrossRef ADS Google Scholar

[2] Scarani V, Iblisdir S, Gisin N. Quantum cloning. Rev Mod Phys, 2005, 77: 1225-1256 CrossRef ADS Google Scholar

[3] Fan H, Wang Y N, Jing L. Quantum cloning machines and the applications. Phys Rep, 2014, 544: 241-322 CrossRef ADS arXiv Google Scholar

[4] Horodecki R, Horodecki P, Horodecki M. Quantum entanglement. Rev Mod Phys, 2009, 81: 865-942 CrossRef ADS Google Scholar

[5] Bu?ek V, Hillery M, Ziman M. Programmable Quantum Processors. Quantum Inf Process, 2006, 5: 313-420 CrossRef Google Scholar

[6] Li J, Chen X, Sun X. Quantum network coding for multi-unicast problem based on 2D and 3D cluster states. Sci China Inf Sci, 2016, 59: 042301 CrossRef Google Scholar

[7] Zhang Z, Li J X, Liu L. Distributed state estimation and data fusion in wireless sensor networks using multi-level quantized innovation. Sci China Inf Sci, 2016, 59: 022316. Google Scholar

[8] Wang F, Luo M, Li H. Improved quantum ripple-carry addition circuit. Sci China Inf Sci, 2016, 59: 042406 CrossRef Google Scholar

[9] Bu?ek V, Hillery M. Quantum copying: Beyond the no-cloning theorem. Phys Rev A, 1996, 54: 1844-1852 CrossRef ADS Google Scholar

[10] Bu?ek V, Braunstein S L, Hillery M. Quantum copying: A network. Phys Rev A, 1997, 56: 3446-3452 CrossRef ADS Google Scholar

[11] Szabó L, Koniorczyk M, Adam P. Optimal universal asymmetric covariant quantum cloning circuits for qubit entanglement manipulation. Phys Rev A, 2010, 81: 032323 CrossRef ADS arXiv Google Scholar

[12] Wootters W K. Entanglement of Formation of an Arbitrary State of Two Qubits. Phys Rev Lett, 1998, 80: 2245-2248 CrossRef ADS Google Scholar

[13] Ollivier H, Zurek W H. Quantum discord: a measure of the quantumness of correlations. Phys Rev Lett, 2002, 88: 017901. Google Scholar

[14] Knill E, Laflamme R. Power of One Bit of Quantum Information. Phys Rev Lett, 1998, 81: 5672-5675 CrossRef ADS Google Scholar

[15] Datta A, Shaji A, Caves C M. Quantum Discord and the Power of One Qubit. Phys Rev Lett, 2008, 100: 050502 CrossRef PubMed ADS arXiv Google Scholar

[16] Coffman V, Kundu J, Wootters W K. Distributed entanglement. Phys Rev A, 2000, 61: 052306 CrossRef ADS Google Scholar

[17] Verstraete F, Dehaene J, De Moor B. Four qubits can be entangled in nine different ways. Phys Rev A, 2002, 65: 052112 CrossRef ADS Google Scholar

[18] Osterloh A, Siewert J. Constructing N -qubit entanglement monotones from antilinear operators. Phys Rev A, 2005, 72: 012337 CrossRef ADS Google Scholar

[19] Ren X J, Jiang W, Zhou X. Permutation-invariant monotones for multipartite entanglement characterization. Phys Rev A, 2008, 78: 012343 CrossRef ADS arXiv Google Scholar

[20] Ren X J, Fan H. Quantum circuits for asymmetric $1\rightarrow~n$ quantum cloning. Quantum Inf Comput, 2015, 15: 914--922. Google Scholar

[21] Ali M, Rau A R P, Alber G. Quantum discord for two-qubit X states. Phys Rev A, 2010, 81: 042105 CrossRef ADS arXiv Google Scholar

[22] Chen Q, Zhang C, Yu S. Quantum discord of two-qubit X states. Phys Rev A, 2011, 84: 042313 CrossRef ADS arXiv Google Scholar

[23] Ou Y C, Fan H. Bounds on negativity of superpositions. Phys Rev A, 2007, 76: 022320 CrossRef ADS arXiv Google Scholar

[24] Yu C, Yi X X, Song H. Concurrence of superpositions. Phys Rev A, 2007, 75: 022332 CrossRef ADS Google Scholar

[25] Song W, Liu N L, Chen Z B. Bounds on the multipartite entanglement of superpositions. Phys Rev A, 2007, 76: 054303 CrossRef ADS arXiv Google Scholar

[26] Parashar P, Rana S. Entanglement and discord of the superposition of Greenberger-Horne-Zeilinger states. Phys Rev A, 2011, 83: 032301 CrossRef ADS Google Scholar

  • Figure 1

    (Color online) Quantum discords between the following pairs of qubits at the output of the cloning circuits: 1-2, 3-4, 1-3, 2-4. (a) The upper figure corresponds to $D_{3\rightarrow~4}$ and the lower one to $D_{1\rightarrow~2}$; (b) the upper one corresponds to $D_{2\rightarrow~4}$ and the lower one to $D_{1\rightarrow~3}$.

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