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.
This is a preview of subscription content, access via your institution.
References
- 1
Wootters W K, Zurek W H. A single quantum cannot be cloned. Nature (London), 1982, 299: 802–803
- 2
Scarani V, Iblisdir S, Gisin N, et al. Quantum cloning. Rev Mod Phys, 2005, 77: 1225–1256
- 3
Fan H, Wang Y N, Jing L, et al. Quantum cloning machines and the applications. Phys Rep, 2014, 544: 241–322
- 4
Horodecki R, Horodecki P, Horodecki M, et al. Quantum entanglement. Rev Mod Phys, 2009, 81: 865–942
- 5
Bužek V, Hillery M, Ziman M, et al. Programmable quantum processors. Quantum Inf Process, 2006, 5: 313–420
- 6
Li J, Chen X B, Sun X M, et al. Quantum network coding for multi-unicast problem based on 2D and 3D cluster states. Sci China Inf Sci, 2016, 59: 042301
- 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
- 8
Wang F, Luo M X, Li H R, et al. Improved quantum ripple-carry addition circuit. Sci China Inf Sci, 2016, 59: 042406
- 9
Bužek V, Hillery M. Quantum copying: beyond the no-cloning theorem. Phys Rev A, 1996, 54: 1844–1852
- 10
Bužek V, Braunstein S L, Hillery M, et al. Quantum copying: a network. Phys Rev A, 1997, 56: 3446–3452
- 11
Szabó L, Koniorczyk M, Adam P, et al. Optimal universal asymmetric covariant quantum cloning circuits for qubit entanglement manipulation. Phys Rev A, 2010, 81: 032323
- 12
Wootters W K. Entanglement of formation of an arbitrary state of two qubits. Phys Rev Lett, 1998, 80: 2245–2248
- 13
Ollivier H, Zurek W H. Quantum discord: a measure of the quantumness of correlations. Phys Rev Lett, 2002, 88: 017901
- 14
Knill E, Laflamme R. Power of one bit of quantum information. Phys Rev Lett, 1998, 81: 5672–5675
- 15
Datta A, Shaji A, Caves C M. Quantum discord and the power of one qubit. Phys Rev Lett, 2008, 100: 050502
- 16
Coffman V, Kundu J, Wootters W K. Distributed entanglement. Phys Rev A, 2000, 61: 052306
- 17
Verstraete F, Dehaene J, De Moor B, et al. Four qubits can be entangled in nine different ways. Phys Rev A, 2002, 65: 052112
- 18
Osterloh A, Siewert J. Constructing N-qubit entanglement monotones from antilinear operators. Phys Rev A, 2005, 72: 012337
- 19
Ren X J, Jiang W, Zhou X, et al. Permutation-invariant monotones for multipartite entanglement characterization. Phys Rev A, 2008, 78: 012343
- 20
Ren X J, Fan H. Quantum circuits for asymmetric 1 → n quantum cloning. Quantum Inf Comput, 2015, 15: 914–922
- 21
Ali M, Rau A R P, Alber G. Quantum discord for two-qubit X states. Phys Rev A, 2010, 81: 042105
- 22
Chen Q, Zhang C, Yu S, et al. Quantum discord of two-qubit X states. Phys Rev A, 2011, 84: 042313
- 23
Ou Y C, Fan H. Bounds on negativity of superpositions. Phys Rev A, 2007, 76: 022320
- 24
Yu C S, Yi X X, Song H S. Concurrence of superpositions. Phys Rev A, 2007, 75: 022332
- 25
Song W, Liu N L, Chen Z B. Bounds on the multipartite entanglement of superpositions. Phys Rev A, 2007, 76: 054303
- 26
Parashar P, Rana S. Entanglement and discord of the superposition of Greenberger-Horne-Zeilinger states. Phys Rev A, 2011, 83: 032301
Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant No. U1204114).
Author information
Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Ren, X. Quantum correlations generation and distribution in a universal covariant quantum cloning circuit. Sci. China Inf. Sci. 60, 122501 (2017). https://doi.org/10.1007/s11432-016-0569-2
Received:
Accepted:
Published:
Keywords
- quantum information
- quantum correlation
- quantum discord
- universal covariant quantum cloning circuit
- genuine multipartite quantum correlation