Abstract
We investigate the entanglement properties of the two magnon states and explicate conditions under which, the two magnon state becomes useful for several quantum communication protocols. We systematically study the temporal behaviour of concurrence to find out the effect of exchange interaction on entanglement. The two magnon state, which is potentially realizable in quantum dots using Heisenberg exchange interaction, is found to be suitable for carrying out deterministic teleportation of an arbitrary two qubit composite system. Further, conditions for which the channel capacity reaches “Holevo bound”, allowing four classical bits to be transmitted through two qubits are derived. Later, an unconventional protocol is given to demonstrate that this state can be used for sharing of a two qubit entangled state among two parties.
Similar content being viewed by others
References
Schrödinger E.: Discussion of probability relations between separated systems. Proc. Camb. Philos. Soc. 31, 555–563 (1935)
Einstein A., Podolsky B., Rosen N.: Can quantum-mechanical description of physical reality be considered complete?. Phys. Rev. 47, 777 (1935)
Nielsen M.A., Chuang I.L.: Quantum Computation and Quantum Information. Cambridge University Press, Cambridge (2006)
Vedral V.: Introduction to Quantum Information Science. Oxford University Press, Oxford (2006)
Bose S.: Quantum communication through an unmodulated spin chain. Phys. Rev. Lett. 91, 207901 (2003)
Rao, D.D.B., Ghosh, S., Panigrahi, P.K.: Generation of entangled channels for perfect teleportation using multielectron quantum dots. Phys. Rev. A 78, 042328 (2008) and references therein
DiVincenzo D.P., Bacon D., Kempe J., Burkard G., Whaley K.B.: Universal quantum computation with the exchange interaction. Nature 408, 339–342 (2004)
Arnesen M., Bose S., Vedral V.: Natural thermal and magnetic entanglement in the 1D Heisenberg model. Phys. Rev. Lett. 87, 017901 (2001)
Raussendorf R., Briegel H.J.: A one-way quantum computer. Phys. Rev. Lett. 86, 5188–5191 (2001)
Briegel H.J., Raussendorf R.: Persistent entanglement in arrays of interacting particles. Phys. Rev. Lett. 86, 910–913 (2001)
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, 1895–1899 (1993)
Muralidharan, S., Panigrahi, P.K.: Perfect teleportation, quantum-state sharing, and superdense coding through a genuinely entangled five-qubit state. Phys. Rev. A 77,032321 (2008) and references therein
Bennett C.H., Wiesner S.J.: Communication via one-and two-particle operators on Einstein–Podolsky–Rosen states. Phys. Rev. Lett. 69, 2881–2884 (1992)
Zheng S.B.: High-speed geometric quantum phase gates for trapped ions in thermal motion. Phys. Rev. A 74, 054303 (2006)
Agrawal P., Pati A.K.: Perfect teleportation and superdense coding with W states. Phys. Rev. A 74, 062320 (2006)
Oguchi T.: Theory of two-magnon bound states in the Heisenberg Ferro- and antiferromagnet. J. Phys. Soc. Jpn. 31, 394–402 (1971)
Mattis D.C.: The Theory of Magnetism I: Statics and Dynamics. Springer, Berlin (1981)
Gorbachev V.N., Trubilko A.I., Rodichkina A.A., Zhiliba A.I.: Can the states of the W-class be suitable for teleportation?. Phys. Lett. A 314, 267–271 (2003)
Verstraete F., Dehaene J., Moor B.D., Verschelde H.: Four qubits can be entangled in nine different ways. Phys. Rev. A 65, 052112 (2002)
Dur W., Vidal G., Cirac J.I.: Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000)
Wang X.W., Shan Y.G., Xia L.X., Lu M.W.: Dense coding and teleportation with one-dimensional cluster states. Phys. Lett. A 364, 7–11 (2007)
Wang Y., Su X., Shen H., Tan A., Xie C., Peng K.: Toward demonstrating controlled-X operation based on continuous-variable four-partite cluster states and quantum teleporters. Phys. Rev. A 81, 022311 (2010)
Petta R., Johnson A.C., Taylor J.M., Laird E.A., Yacoby A., Lukin M.D., Marcus C.M., Hanson M.P., Gossard A.C.: Coherent manipulation of coupled electron spins in semiconductor quantum dots. Science 309, 2180 (2005)
Schliemann J., Khaetskii A., Loss D.: Electron spin dynamics in quantum dots and related nanostructures due to hyperfine interaction with nuclei. J. Phys. Condens. Matter 15, 1809 (2003)
Ashoori R.C.: Electrons in artificial atoms. Nature 379, 413–419 (1996)
Laird E.A., Petta J.R., Johnson A.C., Marcus C.M., Yacoby A., Hanson M.P., Gossard A.C.: Effect of exchange interaction on spin dephasing in a double quantum dot. Phys. Rev. Lett. 97, 056801 (2006)
Schmidt E.: Zur Theorie der linearen und nichtlinearen Integralgleichungen. Mathematische Annalen 63, 433–476 (1906)
Wu E., Zhang X.-A.: Dynamics of pairwise entanglement in the three-qubit Heisenberg XX spin chain. Int. J. Quant. Info. 8, 1447–1458 (2009)
Wootters W.K.: Entanglement of formation of an arbitrary state of two qubits. Phys. Rev. Lett. 80, 2245–2248 (1998)
O’Connor K.M., Wootters W.K.: Entangled rings. Phys. Rev. A 63, 052302 (2001)
Brus D., Ariano G.M.D., Lewenstein M., Macchiavello C., Sen(De) A., Sen U.: Distributed quantum dense coding. Phys. Rev. Lett. 93, 210501 (2004)
Hillery M., Buzek V., Berthiaume A.: Quantum secret sharing. Phys. Rev. A 59, 1829 (1999)
Bandyopadhyay S.: Phys. Rev. A 62, 012308 (2000)
Tittel W., Zbinden H., Gisin N.: Experimental demonstration of quantum secret sharing. Phys. Rev. A 63, 042301 (2001)
Schmid C., Trojek P., Bourennane M., Kurtsiefer C., Z̆ukowski M.: Experimental single qubit quantum secret sharing. Phys. Rev. Lett. 95, 230505 (2005)
Muralidharan S., Panigrahi P.K.: Quantum-information splitting using multipartite cluster states. Phys. Rev. A 78, 062333 (2008)
Choudhury S., Muralidharan S., Panigrahi P.K.: Quantum teleportation and state sharing using a genuinely entangled six-qubit state. J. Phys. A Math. Theor. 42, 115303 (2009)
Muralidharan S., Karumanchi, S., Srikanth, R., Panigrahi, P.K.: In how many ways can quantum information be split? arXiv:quant-ph/0907.3532v1 (2009)
Rao D.D.B., Panigrahi P.K., Mitra C.: Teleportation in the presence of common bath decoherence at the transmitting station. Phys. Rev. A 78, 022336 (2008)
Kiesel N., Schmid C., Toth G., Solano E., Weinfurter H.: Experimental observation of four-photon entangled Dicke state with high fidelity. Phys. Rev. Lett. 98, 063604 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Prasath, E.S., Muralidharan, S., Mitra, C. et al. Multipartite entangled magnon states as quantum communication channels. Quantum Inf Process 11, 397–410 (2012). https://doi.org/10.1007/s11128-011-0252-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11128-011-0252-z