×

One-party quantum-error-correcting codes for unbalanced errors: principles and application to quantum dense coding and quantum secure direct communication. (English) Zbl 1194.81055

Summary: We present unbalanced-quantum-error-correcting codes (one-party QECCs) – a novel idea for correcting unbalanced quantum errors. In some quantum communication tasks using entangled pairs, the error distributions between two parts of the pairs are unbalanced, and one party holds the whole entangled pairs at the final stage, and he or she is able to perform joint measurements on the pairs. In this situation the proposed one-party QECCs can improve error correction by allowing a higher-tolerated error rate. We have established the general correspondence between linear classical codes and the one-party QECCs, and we have given the general definition for these types of quantum-error-correcting codes. It has been shown that the one-party QECCs can correct errors as long as the error threshold is not larger than 0.5. They work even for fidelity less than 0.5 as long as it is larger than 0.25. We give several concrete examples of the one-party QECCs. We provide the applications of the one-party QECCs in quantum dense coding, so that it can function in noisy channels. As a result, a large number of quantum secure direct communication protocols based on dense coding are also able to be protected by this new type of one-party QECCs.

MSC:

81P94 Quantum cryptography (quantum-theoretic aspects)
81P70 Quantum coding (general)
94A60 Cryptography
94B05 Linear codes (general theory)
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] DOI: 10.1103/PhysRevA.52.R2493 · doi:10.1103/PhysRevA.52.R2493
[2] DOI: 10.1103/PhysRevA.54.1098 · doi:10.1103/PhysRevA.54.1098
[3] DOI: 10.1098/rspa.1996.0136 · Zbl 0876.94002 · doi:10.1098/rspa.1996.0136
[4] DOI: 10.1109/TIT.2005.862086 · Zbl 1293.94132 · doi:10.1109/TIT.2005.862086
[5] DOI: 10.1109/TIT.2005.851760 · Zbl 1294.94114 · doi:10.1109/TIT.2005.851760
[6] Bennett C. H., Phys. Rev. Lett. 76 pp 772–
[7] DOI: 10.1103/PhysRevLett.77.2818 · doi:10.1103/PhysRevLett.77.2818
[8] DOI: 10.1103/PhysRevA.54.3824 · Zbl 1371.81041 · doi:10.1103/PhysRevA.54.3824
[9] DOI: 10.1126/science.283.5410.2050 · doi:10.1126/science.283.5410.2050
[10] DOI: 10.1103/PhysRevLett.85.441 · doi:10.1103/PhysRevLett.85.441
[11] Lo H.-K., Quant. Inf. Comput. 1 pp 81–
[12] DOI: 10.1109/TIT.2002.807289 · Zbl 1063.94081 · doi:10.1109/TIT.2002.807289
[13] DOI: 10.1103/PhysRevA.66.060302 · doi:10.1103/PhysRevA.66.060302
[14] DOI: 10.1103/PhysRevA.67.012302 · doi:10.1103/PhysRevA.67.012302
[15] DOI: 10.1103/PhysRevA.72.022336 · doi:10.1103/PhysRevA.72.022336
[16] DOI: 10.1103/PhysRevLett.68.3121 · Zbl 0969.94501 · doi:10.1103/PhysRevLett.68.3121
[17] DOI: 10.1103/PhysRevA.65.022304 · doi:10.1103/PhysRevA.65.022304
[18] DOI: 10.1103/PhysRevA.65.032302 · doi:10.1103/PhysRevA.65.032302
[19] DOI: 10.1103/PhysRevLett.89.187902 · doi:10.1103/PhysRevLett.89.187902
[20] DOI: 10.1103/PhysRevA.68.042315 · doi:10.1103/PhysRevA.68.042315
[21] DOI: 10.1103/PhysRevA.68.042317 · doi:10.1103/PhysRevA.68.042317
[22] Cai Q. Y., Chin. Phys. Lett. 21 pp 601–
[23] DOI: 10.1103/PhysRevA.71.044305 · doi:10.1103/PhysRevA.71.044305
[24] DOI: 10.1140/epjb/e2004-00296-4 · doi:10.1140/epjb/e2004-00296-4
[25] DOI: 10.1088/0305-4470/38/25/011 · Zbl 1073.81534 · doi:10.1088/0305-4470/38/25/011
[26] Man Z. X., Chin. Phys. Lett. 22 pp 18–
[27] DOI: 10.1103/PhysRevA.73.022338 · doi:10.1103/PhysRevA.73.022338
[28] DOI: 10.1103/PhysRevA.74.054302 · doi:10.1103/PhysRevA.74.054302
[29] DOI: 10.1103/PhysRevA.73.042305 · doi:10.1103/PhysRevA.73.042305
[30] DOI: 10.1016/j.physleta.2006.05.035 · Zbl 1142.81342 · doi:10.1016/j.physleta.2006.05.035
[31] DOI: 10.1142/S0219749906002304 · Zbl 1110.81059 · doi:10.1142/S0219749906002304
[32] DOI: 10.1142/S0129183106009011 · Zbl 1093.81019 · doi:10.1142/S0129183106009011
[33] Wang H. F., J. Kor. Phys. Soc. 49 pp 459–
[34] Ji X., Chin. Phys. 15 pp 1418–
[35] Cao H. J., Chin. Phys. Lett. 23 pp 290–
[36] Cao H. J., Commun. Theor. Phys. 45 pp 271–
[37] Gao T., Z. Naturforsch. A 59 pp 597–
[38] Gao T., Chin. Phys. 14 pp 893–
[39] Gao T., I Nuovo Cimento B 119 pp 313–
[40] Gao T., J. Phys. A 38 pp 5761C5770–
[41] DOI: 10.1007/s11467-007-0050-3 · doi:10.1007/s11467-007-0050-3
[42] DOI: 10.1016/j.physleta.2005.04.007 · Zbl 1145.81324 · doi:10.1016/j.physleta.2005.04.007
[43] M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, UK, 2000) pp. 472–474. · Zbl 1049.81015
[44] F. J. MacWilliams and N. J. A. Sloane, The Theory of Error-Correcting Codes (Amsterdam, North-Holland, 1977) pp. 557–558.
[45] DOI: 10.1103/PhysRevA.40.4277 · Zbl 1371.81145 · doi:10.1103/PhysRevA.40.4277
[46] DOI: 10.1103/PhysRevA.66.052313 · doi:10.1103/PhysRevA.66.052313
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.