×
Zangi, S. M.; Qiao, Cong-Feng

Robustness of \(2 \times N \times M\) entangled states against qubit loss. (English) Zbl 07409784

Phys. Lett., A 400, Article ID 127322, 6 p. (2021).
Summary: Entanglement in quantum systems is usually degraded by interaction with the environment. From time to time, some parties of a multipartite entangled system may become decoherent with other parties of the system due to the interference with the environment. In this situation, it is interesting to know how much information the residual system would keep on carrying. In this paper, as a starting point for any entangled system, we investigate the property of the \(2 \times N \times M\) state with qubit being disentangled, which is characterized by the measurement of robustness.

Cited in 4 Documents

MSC:

81-XX Quantum theory
82-XX Statistical mechanics, structure of matter

Keywords:

entanglement; robustness; negativity; concurrence
Cite Review PDF
Full Text: DOI arXiv

References:

[1] Einstein, A.; Podolsky, B.; Rosen, N., Phys. Rev., 47, 777 (1935) · Zbl 0012.04201
[2] Arute, F., Quantum supremacy using a programmable superconducting processor, Nature, 574, 505-510 (2019)
[3] Burkhard, G.; Loss, D.; Vincenzo, D. P., Phys. Rev. B, 59, 2070 (1999)
[4] Kane, B. E., Nature (London), 393, 133 (1998)
[5] Vrijen, R., Phys. Rev. A, 62, Article 012306 pp. (2000)
[6] Sorensen, Anders; Molmer, K., Phys. Rev. Lett., 83, 2274 (1999)
[7] Unanyan, R. G.; Shore, B. W.; Bergmann, K., Phys. Rev. A, 63, Article 043405 pp. (2001)
[8] Vidal, G.; Tarrach, R., Phys. Rev. A, 59, 141 (1999)
[9] Lieven, Clarisse, J. Phys. A, Math. Gen., 39, 4239 (2006) · Zbl 1089.81008
[10] Dür, W.; Vidal, G.; Cirac, J. I., Phys. Rev. A, 62, Article 062314 pp. (2000)
[11] Higuchi, A.; Sudbery, A., Phys. Lett. A, 273, 213 (2000) · Zbl 1059.81511
[12] Bell, J. S., Physics, 1, 195 (1964)
[13] Gisin, N.; Bechmann-Pasquinucci, H., Phys. Lett. A, 246, 1-2, 1-6 (1998) · Zbl 0941.81006
[14] Neven, A., Entanglement robustness against particle loss in multiqubit systems, Phys. Rev. A, 98, Article 062335 pp. (2018)
[15] Reich, D. M., Optimal qudit operator bases for efficient characterization of quantum gates, J. Phys. A, Math. Theor., 47, Article 385305 pp. (2014) · Zbl 1298.81011
[16] Cheng, Shuo; Li, Junli; Qiao, Cong-Feng, J. Phys. A, 43, Article 055303 pp. (2010) · Zbl 1186.81019
[17] Li, Junli; Qiao, Cong-Feng, Quantum Inf. Process., 12, 251 (2013) · Zbl 1263.81036
[18] Zangi, S. M.; Li, Jun-Li; Qiao, Cong-Feng, Entanglement classification of four-partite states under the SLOCC, J. Phys. A, Math. Theor., 50, Article 325301 pp. (2017) · Zbl 1372.81025
[19] Li, Jun-Li; Qiao, Cong-Feng, A necessary and sufficient criterion for the separability of quantum state, Sci. Rep., 8, 1442 (2018)
[20] Li, Jun-Li; Qiao, Cong-Feng, Separable decompositions of bipartite mixed states, Quantum Inf. Process., 17, 92 (2018) · Zbl 1395.81040
[21] Horn, R. A.; Johnson, C. R., Matrix Analysis (2013), Cambridge University Press · Zbl 1267.15001
[22] de Vicente, Julio, Separability criteria based on the Bloch representation of density matrices, Quantum Inf. Comput., 7, 624 (2007) · Zbl 1152.81835
[23] Verstraete, F.; Dehaene, J.; De Moor, B., Normal forms and entanglement measures for multipartite quantum state, Phys. Rev. A, 68, Article 012103 pp. (2003)
[24] De Lathauwer, L.; De Moor, B.; Vandewalle, J., A multilinear singular value decomposition, SIAM J. Matrix Anal. Appl., 21, 1253-1278 (2000) · Zbl 0962.15005
[25] Leinaas, J. M.; Myrheim, J.; Ovrum, E., Geometric aspects of entanglement, Phys. Rev. A, 74, Article 012313 pp. (2006)
[26] de Vicente, J. I., Further results on entanglement detection and quantification from the correlation matrix criterion, J. Phys. A, Math. Theor., 41, Article 065309 pp. (2008) · Zbl 1133.81014
[27] Horodecki, P.; Lewenstein, M.; Vidal, G.; Cirac, I., Phys. Rev. A, 62, Article 032310 pp. (2000)
[28] Petz, Dénes
[29] De Nobili, Cristiano; Coser, Andrea; Tonni, Erik
[30] Vidal, G.; Werner, R. F., Computable measure of entanglement, Phys. Rev. A, 65, Article 032314 pp. (2002)
[31] Lee, Soojoon, Phys. Rev. A, 68, Article 062304 pp. (2003)
[32] Wootters, W. K., Phys. Rev. Lett., 80, 2245 (1998) · Zbl 1368.81047
[33] Dür, W., Phys. Rev., 61, Article 062313 pp. (2000)
[34] Horodecki, P., Phys. Lett. A, 232, 333 (1997) · Zbl 1053.81504
[35] Chaves, Rafael; Davidovich, Luiz, Phys. Rev. A, 82, Article 052308 pp. (2010)
[36] Mintert, Florian; Kuś, Marek; Buchleitner, Andreas, Phys. Rev. Lett., 92, Article 167902 pp. (2004)
[37] Bennett, C. H.; DiVinenzo, D. P.; Mor, T.; Shor, P. W.; Smolin, J. A.; Terhal, B. M., Unextendible product bases and bound entanglement, Phys. Rev. Lett., 82, 5385-5388 (1999)
[38] This example is taken from Ref. [22], we recommend [22] and [37] to clarify basic concepts.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.