Optimal dense coding and quantum phase transition in Ising-XXZ diamond chain. (English) Zbl 07482578
Summary: We theoretically propose a dense coding scheme based on an infinite spin-1/2 Ising-XXZ diamond chain, where the Heisenberg spins dimer can be considered as a quantum channel. Using the transfer-matrix approach, we can obtain the analytical expression of the optimal dense coding capacity \(\chi\). The effects of anisotropy, external magnetic field, and temperature on \(\chi\) in the diamond-like chain are discussed, respectively. It is found that \(\chi\) is decayed with increasing the temperature, while the valid dense coding (\(\chi > 1\)) can be carried out by tuning the anisotropy parameter. Additionally, a certain external magnetic field can stimulate the enhancement of dense coding capacity. In an infinite spin-1/2 Ising-XXZ diamond chain, it has been shown that there exist two kinds of quantum phase transitions (QPTs) in zero-temperature phase diagram, i.e., one is that the ground state of system changes from the unentangled ferrimagnetic state to the entangled frustrated state and the other is from the entangled frustrated state to the unentangled ferromagnetic state. Here, we propose that optimal dense coding capacity \(\chi\) can be regarded as a new detector of QPTs in this diamond-like chain, and the relationship between \(\chi\) and QPTs is well established.
MSC:
| 82-XX | Statistical mechanics, structure of matter |
Keywords:
optimal dense coding; Ising-XXZ diamond chain; transfer-matrix approach; quantum phase transitionReferences:
| [1] | Nielson, M. A., Quantum Computation and Quantum Information (2000), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1049.81015 |
| [2] | Watrous, J., The Theory of Quantum Information (2018), Cambridge University Press: Cambridge University Press UK · Zbl 1393.81004 |
| [3] | Holevo, A., Quantum Systems, Channels, Information: A Mathematical Introduction (2012), De Gruyter: De Gruyter Berlin · Zbl 1332.81003 |
| [4] | Scarani, V.; Bechmann-Pasquinucci, H.; Cerf, N. J.; Dušek, M.; Lütkenhaus, N.; Peev, M., The security of practical quantum key distribution, Rev. Modern Phys., 81, 3, 1302-1345 (2009) |
| [5] | Bennett, C. H.; Wiesner, S. J., Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states, Phys. Rev. Lett., 69, 20, 2881-2884 (1992) · Zbl 0968.81506 |
| [6] | Bennett, C. H.; Brassard, G.; Crepeau, C.; Jozsa, R.; Peres, A.; Wootters, W. K., Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett., 70, 13, 1895-1899 (1993) · Zbl 1051.81505 |
| [7] | Bennett, C. H.; Shor, P. W.; Smolin, J. A.; Thapliyal, A. V., Entanglement-assisted classical capacity of noisy quantum channels, Phys. Rev. Lett., 83, 15, 3081-3084 (1999) |
| [8] | Bowen, G., Classical information capacity of superdense coding, Phys. Rev. A, 63, 2, Article 022302 pp. (2001) |
| [9] | Hausladen, P.; Jozsa, R.; Schumacher, B.; Westmoreland, M.; Wootters, W. K., Classical information capacity of a quantum channel, Phys. Rev. A, 54, 3, 1869-1876 (1996) |
| [10] | Hao, J.-C.; Li, C.-F.; Guo, G.-C., Controlled dense coding using the Greenberger-Horne-Zeilinger state, Phys. Rev. A, 63, 5, Article 054301 pp. (2001) |
| [11] | Liu, X. S.; Long, G. L.; Tong, D. M.; Li, F., General scheme for superdense coding between multiparties, Phys. Rev. A, 65, 2, Article 022304 pp. (2002) |
| [12] | Laurenza, R.; Lupo, C.; Lloyd, S.; Pirandola, S., Dense coding capacity of a quantum channel, Phys. Rev. Res., 2, 2, Article 023023 pp. (2020) |
| [13] | Mattle, K.; Weinfurter, H.; Kwiat, P. G.; Zeilinger, A., Dense coding in experimental quantum communication, Phys. Rev. Lett., 76, 25, 4656-4659 (1996) |
| [14] | Li, X.; Pan, Q.; Jing, J.; Zhang, J.; Xie, C.; Peng, K., Quantum dense coding exploiting a bright Einstein-Podolsky-Rosen beam, Phys. Rev. Lett., 76, 4, Article 047904 pp. (2002) |
| [15] | Fang, X.; Zhu, X.; Feng, M.; Mao, X.; Du, F., Experimental implementation of dense coding using nuclear magnetic resonance, Phys. Rev. A, 61, 2, Article 022307 pp. (2000) |
| [16] | Schaetz, T.; Barrett, M. D.; Leibfried, D.; Chiaverini, J.; Britton, J.; Itano, W. M.; Jost, J. D.; Langer, C.; Wineland, D. J., Quantum dense coding with atomic qubits, Phys. Rev. Lett., 93, 4, Article 040505 pp. (2004) |
| [17] | Zhang, W.; Ding, D.-S.; Sheng, Y.-B.; Zhou, L.; Shi, B.-S.; Guo, G.-C., Quantum secure direct communication with quantum memory, Phys. Rev. Lett., 118, 22, Article 220501 pp. (2017) |
| [18] | Williams, B. P.; Sadlier, R. J.; Humble, T. S., Superdense coding over optical fiber links with complete bell-state measurements, Phys. Rev. Lett., 118, 5, Article 050501 pp. (2017) |
| [19] | Barreiro, J. T.; Wei, T.-C.; Kwiat, P. G., Beating the channel capacity limit for linear photonic superdense coding, Nat. Phys., 4, 282-286 (2008) |
| [20] | Schuck, C.; Huber, G.; Kurtsiefer, C.; Weinfurter, H., Complete deterministic linear optics bell state analysis, Phys. Rev. Lett., 96, 19, Article 190501 pp. (2006) |
| [21] | Barenco, A.; Ekert, A. K., Dense coding based on quantum entanglement, J. Modern Opt., 42, 6, 1253-1259 (1995) |
| [22] | Bose, S.; Plenio, M. B.; Vedral, V., Mixed state dense coding and its relation to entanglement measures, J. Modern Opt., 47, 2-3, 291-310 (2000) |
| [23] | Hiroshima, T., Optimal dense coding with mixed state entanglement, J. Phys. A: Math. Gen., 34, 35, 6907-6912 (2001), stacks.iop.org/JPhysA/34/6907 · Zbl 0988.81026 |
| [24] | Arnesen, M. C.; Bose, S.; Vedral, V., Natural thermal and magnetic entanglement in the 1D heisenberg model, Phys. Rev. Lett., 87, 1, Article 017901 pp. (2001) |
| [25] | Ghosh, S.; Chanda, T.; Sen(De), A., Enhancement in the performance of a quantum battery by ordered and disordered interactions, Phys. Rev. A, 101, 3, Article 032115 pp. (2020) |
| [26] | Wang, Z.; Wu, W.; Wang, J., Steady-state entanglement and coherence of two coupled qubits in equilibrium and nonequilibrium environments, Phys. Rev. A, 99, 4, Article 042320 pp. (2019) |
| [27] | Mehran, E.; Mahdavifar, S.; Jafari, R., Induced effects of the Dzyaloshinskii-Moriya interaction on the thermal entanglement in spin-1/2 Heisenberg chains, Phys. Rev. A, 89, 4, Article 042306 pp. (2014) |
| [28] | Militello, B.; Messina, A., Genuine tripartite entanglement in a spin-star network at thermal equilibrium, Phys. Rev. A, 83, 4, Article 042305 pp. (2011) |
| [29] | Sahling, S.; Remenyi, G.; Paulsen, C.; Monceau, P.; Saligrama, V.; Marin, C.; Revcolevschi, A.; Regnault, L. P.; Raymond, S.; Lorenzo, J. E., Experimental realization of long-distance entanglement between spins in antiferromagnetic quantum spin chains, Nat. Phys., 11, 255-260 (2015) |
| [30] | Fortes, R.; Rigolin, G., Probabilistic quantum teleportation via thermal entanglement, Phys. Rev. A, 96, 2, Article 022315 pp. (2017) |
| [31] | Sun, Y.; Chen, Y.; Chen, H., Thermal entanglement in the two-qubit Heisenberg XY model under a nonuniform external magnetic field, Phys. Rev. A, 68, 4, Article 044301 pp. (2003) |
| [32] | Kamta, G. L.; Starace, A. F., Anisotropy and magnetic field effects on the entanglement of a two qubit heisenberg XY chain, Phys. Rev. Lett., 88, 10, Article 107901 pp. (2002) |
| [33] | Zhang, G.f.; Li, S.; Liang, J., Thermal entanglement in Spin-1 biparticle system, Opt. Commun., 245, 1-6, 457-463 (2005) |
| [34] | Wang, X., Entanglement in the quantum Heisenberg XY model, Phys. Rev. A, 64, 1, Article 012313 pp. (2001) |
| [35] | Zhang, G.-F., Effects of anisotropy on optimal dense coding, Phys. Scr., 79, 1, Article 015001 pp. (2009) · Zbl 1160.81357 |
| [36] | Qiu, L.; Wang, A. M.; Ma, X. S., Optimal dense coding with thermal entangled states, Physica A, 383, 2, 325-330 (2007) |
| [37] | Alécio, R. C.; Strecka, J.; Lyra, M. L., Thermodynamic behavior and enhanced magnetocaloric effect in a frustrated spin-1/2 Ising-Heisenberg triangular tube, J. Magn. Magn. Mater., 451, 218-225 (2018) |
| [38] | Gao, K.; Xu, Y.-L.; Kong, X.-M.; Liu, Z.-Q., Thermal quantum correlations and quantum phase transitions in Ising-XXZ diamond chain, Physica A, 429, 10-16 (2015) · Zbl 1400.82144 |
| [39] | Rojas, O., Geometrically frustrated Ising-Heisenberg spin model on expanded Kagomé lattice, J. Magn. Magn. Mater., 473, 442-448 (2019) |
| [40] | Kikuchia, H.; Fujiia, Y.; Chibaa, M.; Mitsudob, S.; Idehara, T., Magnetic properties of the frustrated diamond chain compound Cu3(CO3)2(OH)2, Physica B, 329-333, 967-968 (2003) |
| [41] | Kikuchi, H.; Fujii, Y.; Chiba, M.; Mitsudo, S.; Idehara, T.; Tonegawa, T.; Okamoto, K.; Sakai, T.; Kuwai, T.; Ohta, H., Experimental observation of the1/3 magnetization plateau in the diamond-chain compound Cu3(CO3)2(OH)2, Phys. Rev. Lett., 96, 22, Article 227201 pp. (2005) |
| [42] | Jascur, M.; Strecka, J., Spin frustration in an exactly solvable Ising-Heisenberg diamond chain, J. Magn. Magn. Mater., 272-276, 984-986 (2004) |
| [43] | Čanová, L.; Strečka, J.; Jaščur, M., Geometric frustration in the class of exactly solvable Ising-Heisenberg diamond chains, J. Phys.: Condens. Matter, 18, 20, 4967-4984 (2006) |
| [44] | Strečka, J.; Čanová, L.; Lučivjanský, T.; Jaščur, M., Multiple frustration-induced plateaus in a magnetization process of the mixed spin-1/2 and spin-3/2 Ising-Heisenberg diamond chain, J. Phys.: Conf. Ser., 145, Article 012058 pp. (2009) |
| [45] | Rojas, O.; Rojas, M.; Ananikian, N. S.; de Souza, S. M., Thermal entanglement in an exactly solvable Ising-XXZ diamond chain structure, Phys. Rev. A, 86, 4, Article 042330 pp. (2012) |
| [46] | Canova, L.; Strecka, J.; Jascur, M., Geometric frustration in the class of exactly solvable Ising-Heisenberg diamond chains, J. Phys: Condens. Matter, 18, 4967-4984 (2006) |
| [47] | Rojas, O.; de Souza, S. M.; Ohanyan, V.; Khurshudyan, M., Exactly solvable mixed-spin Ising-Heisenberg diamond chain with biquadratic interactions and single-ion anisotropy, Phys. Rev. B, 83, 9, Article 094430 pp. (2011) |
| [48] | Rojas, O.; de Souza, S. M., Spinless fermion model on diamond chain, Phys. Lett. A, 375, 1295-1299 (2011) · Zbl 1242.82013 |
| [49] | Zheng, Y.; Mao, Z.; Zhou, B., Thermal quantum correlations of a spin-1/2 Ising-Heisenberg diamond chain with Dzyaloshinskii-Moriya interaction, Chin. Phys. B, 27, 9, Article 090306 pp. (2018) |
| [50] | Rojas, M.; de Souza, S. M.; Rojas, O., Entangled state teleportation through a couple of quantum channels composed of XXZ dimers in an Ising-XXZ diamond chain, Ann. Physics, 377, 506-517 (2017) · Zbl 1368.81056 |
| [51] | Osterloh, A.; Amico, L.; Falci, G.; Fazio, R., Scaling of entanglement close to a quantum phase transition, Nature, 416, 608-610 (2002) |
| [52] | Osborne, T. J.; Nielsen, M. A., Entanglement in a simple quantum phase transition, Phys. Rev. A, 66, 3, Article 032110 pp. (2002) |
| [53] | de Oliveira, T. R.; Rigolin, G.; de Oliveira, M. C.; Miranda, E., Multipartite entanglement signature of quantum phase transitions, Phys. Rev. Lett., 97, 17, Article 170401 pp. (2006) |
| [54] | Wu, L.-A.; Sarandy, M. S.; Lidar, D. A., Quantum phase transitions and bipartite entanglement, Phys. Rev. Lett., 93, 25, Article 250404 pp. (2004) |
| [55] | de Oliveira, T. R.; Rigolin, G.; de Oliveira, M. C., Genuine multipartite entanglement in quantum phase transitions, Phys. Rev. A, 73, 1 (2007), 010305(R) |
| [56] | de Oliveira, T. R.; Rigolin, G.; de Oliveira, M. C.; Miranda, E., Symmetry-breaking effects upon bipartite and multipartite entanglement in the XY model, Phys. Rev. A, 77, 3, Article 032325 pp. (2008) |
| [57] | Bao, J.; Guo, B.; Cheng, H.-G.; Zhou, M.; Fu, J.; Deng, Y.-C.; Sun, Z.-Y., Multipartite nonlocality in the Lipkin-Meshkov-Glick model, Phys. Rev. A, 101, 1, Article 012110 pp. (2020) |
| [58] | Sachdev, S., Quantum Phase Transitions (2000), Cambridge University Press: Cambridge University Press Cambridge · Zbl 1008.82016 |
| [59] | Dillenschneider, R., Quantum discord and quantum phase transition in spin chains, Phys. Rev. B, 78, 22, Article 224413 pp. (2008) |
| [60] | Werlang, T.; Trippe, C.; Ribeiro, G. A.P.; Rigolin, G., Quantum correlations in spin chains at finite temperatures and quantum phase transitions, Phys. Rev. Lett., 105, 9, Article 095702 pp. (2010) |
| [61] | Li, Y.-C.; Lin, H.-Q., Thermal quantum and classical correlations and entanglement in the XY spin model with three-spin interaction, Phys. Rev. A, 83, 5, Article 052323 pp. (2011) |
| [62] | Li, Y. C.; Zhang, J.; Lin, H.-Q., Quantum coherence spectrum and quantum phase transitions, Phys. Rev. B, 101, 11, Article 115142 pp. (2020) |
| [63] | Hu, M.-L.; Gao, Y.-Y.; Fan, H., Steered quantum coherence as a signature of quantum phase transitions in spin chains, Phys. Rev. A, 101, 3, Article 032305 pp. (2020) |
| [64] | Mao, R.; Dai, Y.-W.; Cho, S. Y.; Zhou, H.-Q., Quantum coherence and spin nematic to nematic quantum phase transitions in biquadratic spin-1 and spin-2 XY chains with rhombic single-ion anisotropy, Phys. Rev. B, 103, 1, Article 014446 pp. (2021) |
| [65] | Mirmasoudi, F.; Ahadpour, S., Application quantum renormalization group to optimal dense coding in transverse Ising model, Physica A, 515, 232-239 (2019) · Zbl 1514.82085 |
| [66] | Baxter, R. J., Exactly Solved Models in Statistical Mechanics (1982), Academic Press: Academic Press New York · Zbl 0538.60093 |
| [67] | Holevo, A. S., Some estimates for the amount of information transmittable by a quantum communications channel, Probl. Inf. Transm., 9, 3, 3-11 (1973) · Zbl 0317.94003 |
| [68] | Holevo, A. S., Information theory and coding theory on capacity of a quantum communications channel, Probl. Inf. Transm., 15, 4, 247-253 (1979) · Zbl 0449.94010 |
| [69] | Holevo, A. S., The capacity of the quantum channel with general signal states, IEEE Trans. Inform. Theory, 44, 1, 269-273 (1998) · Zbl 0897.94008 |
| [70] | Schumacher, B.; Westmoreland, M. D., Sending classical information via noisy quantum channels, Phys. Rev. A, 56, 1, 131-138 (1997) |
| [71] | Wootters, W. K., Entanglement of formation of an arbitrary state of two qubits, Phys. Rev. Lett., 80, 10, 2245-2248 (1997) · Zbl 1368.81047 |
| [72] | Ollivier, H.; Zurek, W. H., Quantum discord: A measure of the quantumness of correlations, Phys. Rev. Lett., 88, 1, Article 017901 pp. (2001) · Zbl 1255.81071 |
| [73] | Henderson, L.; Vedral, V., Classical, quantum and total correlations, J. Phys. A: Math. Gen., 34, 35, 6899-6905 (2001) · Zbl 0988.81023 |
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