{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:19:08Z","timestamp":1760242748003,"version":"build-2065373602"},"reference-count":64,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2016,5,27]],"date-time":"2016-05-27T00:00:00Z","timestamp":1464307200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We develop a novel method for multiphoton controllable transport between remote resonators. Specifically, an auxiliary resonator is used to control the coherent long-range coupling of two spatially separated resonators, mediated by a coupled-resonator chain of arbitrary length. In this manner, an arbitrary multiphoton quantum state can be either transmitted through or reflected off the intermediate chain on demand, with very high fidelity. We find, on using a time-independent perturbative treatment, that quantum information leakage of an arbitrary Fock state is limited by two upper bounds, one for the transmitted case and the other for the reflected case. In principle, the two upper bounds can be made arbitrarily small, which is confirmed by numerical simulations.<\/jats:p>","DOI":"10.3390\/e18060179","type":"journal-article","created":{"date-parts":[[2016,5,27]],"date-time":"2016-05-27T10:25:03Z","timestamp":1464344703000},"page":"179","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multiphoton Controllable Transport between Remote Resonators"],"prefix":"10.3390","volume":"18","author":[{"given":"Wei","family":"Qin","sequence":"first","affiliation":[{"name":"School of Physics, Beijing Institute of Technology, Beijing 100081, China"},{"name":"Center for Emergent Matter Science (CEMS), The Institute of Physical and Chemical Research (RIKEN), Wako-shi, Saitama 351-0198, Japan"}]},{"given":"Guilu","family":"Long","sequence":"additional","affiliation":[{"name":"State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics, Tsinghua University, Beijing 100084, China"},{"name":"Tsinghua National Laboratory for Information Science and Technology, Tsinghua University, Beijing 100084, China"}]}],"member":"1968","published-online":{"date-parts":[[2016,5,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"575","DOI":"10.1038\/37539","article-title":"Experimental quantum teleportation","volume":"390","author":"Bouwmeester","year":"1997","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"4733","DOI":"10.1103\/PhysRevLett.84.4733","article-title":"Entangled state quantum cryptography: Eavesdropping on the ekert protocol","volume":"84","author":"Naik","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4737","DOI":"10.1103\/PhysRevLett.84.4737","article-title":"Quantum cryptography using entangled photons in energy-time bell states","volume":"84","author":"Tittel","year":"2000","journal-title":"Phys. Rev. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1038\/35106500","article-title":"Long-distance quantum communication with atomic ensembles and linear optics","volume":"414","author":"Duan","year":"2001","journal-title":"Nature"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Deng, F.G., Long, G.L., and Liu, X.S. (2003). Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block. Phys. Rev. A, 68.","DOI":"10.1103\/PhysRevA.68.042317"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"618","DOI":"10.1007\/s11434-010-4336-4","article-title":"An error-free protocol for quantum entanglement distribution in long-distance quantum communication","volume":"56","author":"Salemian","year":"2011","journal-title":"Chin. Sci. Bull."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1238","DOI":"10.1007\/s11433-014-5461-x","article-title":"Quantum secure direct dialogue using Einstein-Podolsky-Rosen pairs","volume":"57","author":"Zheng","year":"2014","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Zhang, J.F., Long, G.L., Zhang, W., Deng, Z.W., Liu, W.Z., and Lu, Z.H. (2005). Simulation of Heisenberg XY interactions and realization of a perfect state transfer in spin chains using liquid nuclear magnetic resonance. Phys. Rev. A, 72.","DOI":"10.1103\/PhysRevA.72.012331"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Feng, G.R., Xu, G.F., and Long, G.L. (2013). Experimental realization of nonadiabatic holonomic quantum computation. Phys. Rev. Lett., 110.","DOI":"10.1103\/PhysRevLett.110.190501"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1126\/science.1131871","article-title":"Coherent dynamics of coupled electron and nuclear spin qubits in diamond","volume":"314","author":"Childress","year":"2006","journal-title":"Science"},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Zagoskin, A.M., Johansson, J.R., Ashhab, S., and Nori, F. (2007). Quantum information processing using frequency control of impurity spins in diamond. Phys. Rev. B, 76.","DOI":"10.1103\/PhysRevB.76.014122"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Bermudez, A., Jelezko, F., Plenio, M.B., and Retzker, A. (2011). Electron-mediated nuclear-spin interactions between distant nitrogen-vacancy centers. Phys. Rev. Lett., 107.","DOI":"10.1103\/PhysRevLett.107.150503"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yao, N.Y., Jiang, L., Gorshkov, A.V., Maurer, P.C., Giedke, G., Cirac, J.I., and Lukin, M.D. (2012). Scalable architecture for a room temperature solid-state quantum information processor. Nat. Commun., 3.","DOI":"10.1038\/ncomms1788"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"2920","DOI":"10.1007\/s11434-013-5967-z","article-title":"Optimizing ultrasensitive single electron magnetometer based on nitrogen-vacancy center in diamond","volume":"58","author":"Wang","year":"2013","journal-title":"Chin. Sci. Bull."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2013.02.001","article-title":"The nitrogen-vacancy colour centre in diamond","volume":"528","author":"Doherty","year":"2013","journal-title":"Phys. Rep."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Liu, Y.X., Wei, L.F., Tsai, J.S., and Nori, F. (2006). Controllable coupling between flux qubits. Phys. Rev. Lett., 96.","DOI":"10.1103\/PhysRevLett.96.067003"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"723","DOI":"10.1126\/science.1141324","article-title":"Quantum coherent tunable coupling of superconducting qubits","volume":"316","author":"Niskanen","year":"2007","journal-title":"Science"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Ashhab, S., Niskanen, A.O., Harrabi, K., Nakamura, Y., Picot, T., De Groot, P.C., Harmans, C.J.P.M., Mooij, J.E., and Nori, F. (2008). Interqubit coupling mediated by a high-excitation-energy quantum object. Phys. Rev. B, 77.","DOI":"10.1103\/PhysRevB.77.014510"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Xiong, W., Jin, D.Y., Jing, J., Lam, C.H., and You, J.Q. (2015). Controllable coupling between a nanomechanical resonator and a coplanar-waveguide resonator via a superconducting flux qubit. Phys. Rev. A, 92.","DOI":"10.1103\/PhysRevA.92.032318"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1038\/nature06124","article-title":"Coherent quantum state storage and transfer between two phase qubits via a resonant cavity","volume":"449","author":"Park","year":"2007","journal-title":"Nature"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1038\/nature06184","article-title":"Coupling superconducting qubits via a cavity bus","volume":"449","author":"Majer","year":"2007","journal-title":"Nature"},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Zhou, L., Gong, Z.R., Liu, Y.X., Sun, C.P., and Nori, F. (2008). Controllable scattering of a single photon inside a one-dimensional resonator waveguide. Phys. Rev. Lett., 101.","DOI":"10.1103\/PhysRevLett.101.100501"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Nataf, P., and Ciuti, C. (2011). Protected quantum computation with multiple resonators in ultrastrong coupling circuit QED. Phys. Rev. Lett., 107.","DOI":"10.1103\/PhysRevLett.107.190402"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Yang, C.P., Su, Q.P., and Nori, F. (2013). Entanglement generation and quantum information transfer between spatially-separated qubits in different cavities. New J. Phys., 15.","DOI":"10.1088\/1367-2630\/15\/11\/115003"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1038\/nature01371","article-title":"Ultra-high-Q toroid microcavity on a chip","volume":"421","author":"Armani","year":"2003","journal-title":"Natrue"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"394","DOI":"10.1038\/nphys2927","article-title":"Parity-time-symmetric whispering-gallery microcavities","volume":"10","author":"Peng","year":"2014","journal-title":"Nat. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"328","DOI":"10.1126\/science.1258004","article-title":"Loss-induced suppression and revival of lasing","volume":"346","author":"Peng","year":"2014","journal-title":"Science"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Jing, H., \u00d6zdemir, \u015e.K., Lu, X.Y., Zhang, J., Yang, L., and Nori, F. (2014). PT-Symmetric phonon laser. Phys. Rev. Lett., 113.","DOI":"10.1103\/PhysRevLett.113.053604"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"083017","DOI":"10.1088\/1367-2630\/15\/8\/083017","article-title":"Robust-to-loss entanglement generation using a quantum plasmonic nanoparticle array","volume":"15","author":"Lee","year":"2013","journal-title":"New J. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"3221","DOI":"10.1103\/PhysRevLett.78.3221","article-title":"Quantum state transfer and entanglement distribution among distant nodes in a quantum network","volume":"78","author":"Cirac","year":"1997","journal-title":"Phys. Rev. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Serafini, A., Mancini, S., and Bose, S. (2006). Distributed quantum computation via optical fibers. Phys. Rev. Lett., 96.","DOI":"10.1103\/PhysRevLett.96.010503"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1023","DOI":"10.1038\/nature07127","article-title":"The quantum internet","volume":"453","author":"Kimble","year":"2008","journal-title":"Nature"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1002\/lpor.200810046","article-title":"Quantum many-body phenomena in coupled cavity arrays","volume":"2","author":"Hartmann","year":"2008","journal-title":"Laser Photonics Rev."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"907","DOI":"10.1038\/nphys2063","article-title":"Robust optical delay lines with topological protection","volume":"7","author":"Hafezi","year":"2011","journal-title":"Nat. Phys."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"153","DOI":"10.1103\/RevModPhys.86.153","article-title":"Quantum simulation","volume":"86","author":"Georgescu","year":"2014","journal-title":"Rev. Mod. Phys."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1038\/nphoton.2015.57","article-title":"Quantum many-body models with cold atoms coupled to photonic crystals","volume":"9","author":"Douglas","year":"2015","journal-title":"Nat. Photonics"},{"key":"ref_37","doi-asserted-by":"crossref","unstructured":"Wang, Z.H., Li, Y., Zhou, D.L., Sun, C.P., and Zhang, P. (2012). Single-photon scattering on a strongly dressed atom. Phys. Rev. A, 86.","DOI":"10.1103\/PhysRevA.86.023824"},{"key":"ref_38","doi-asserted-by":"crossref","unstructured":"Zhou, L., Yang, L.P., Li, Y., and Sun, C.P. (2013). Quantum routing of single photons with a cyclic three-level system. Phys. Rev. Lett., 111.","DOI":"10.1103\/PhysRevLett.111.103604"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Lombardo, F., Ciccarello, F., and Palma, G.M. (2014). Photon localization versus population trapping in a coupled-cavity array. Phys. Rev. A, 89.","DOI":"10.1103\/PhysRevA.89.053826"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"024202","DOI":"10.1088\/1674-1056\/23\/2\/024202","article-title":"Single photon transport properties in coupled cavity arrays nonlocally coupled to a two-level atom in the presence of dissipation","volume":"23","author":"Hai","year":"2014","journal-title":"Chin. Phys. B"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"22955","DOI":"10.1364\/OE.23.022955","article-title":"T-shaped single-photon router","volume":"23","author":"Lu","year":"2015","journal-title":"Opt. Express"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1234","DOI":"10.1007\/s11433-010-4014-1","article-title":"Photonic Feshbach resonance","volume":"53","author":"Xu","year":"2010","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Zhu, W., Wang, Z.H., and Zhou, D.L. (2014). Multimode effects in cavity QED based on a one-dimensional cavity array. Phys. Rev. A, 90.","DOI":"10.1103\/PhysRevA.90.043828"},{"key":"ref_44","doi-asserted-by":"crossref","unstructured":"Qin, W., and Nori, F. (2016). Controllable single-photon transport between remote coupled-cavity arrays. Phys. Rev. A, 93.","DOI":"10.1103\/PhysRevA.93.032337"},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Longo, P., Schmitteckert, P., and Busch, K. (2010). Few-photon transport in low-dimensional systems: interaction-induced radiation trapping. Phys. Rev. Lett., 104.","DOI":"10.1103\/PhysRevLett.104.023602"},{"key":"ref_46","doi-asserted-by":"crossref","unstructured":"Longo, P., Schmitteckert, P., and Busch, K. (2011). Few-photon transport in low-dimensional systems. Phys. Rev. A, 83.","DOI":"10.1103\/PhysRevA.83.063828"},{"key":"ref_47","doi-asserted-by":"crossref","unstructured":"Roy, D. (2010). Few-photon optical diode. Phys. Rev. B, 81.","DOI":"10.1103\/PhysRevB.81.155117"},{"key":"ref_48","doi-asserted-by":"crossref","unstructured":"Roy, D. (2011). Two-Photon scattering by a driven three-level emitter in a one-dimensional waveguide and electromagnetically induced transparency. Phys. Rev. Lett., 106.","DOI":"10.1103\/PhysRevLett.106.053601"},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Shi, T., Chang, D.E., and Cirac, J.I. (2015). Multiphoton-scattering theory and generalized master equations. Phys. Rev. A, 92.","DOI":"10.1103\/PhysRevA.92.053834"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1712","DOI":"10.1007\/s11433-014-5551-9","article-title":"Universal quantum computation with qudits","volume":"57","author":"Luo","year":"2014","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"ref_51","doi-asserted-by":"crossref","unstructured":"Qin, W., Wang, C., Cao, Y., and Long, G.L. (2014). Multiphoton quantum communication in quantum networks. Phys. Rev. A, 89.","DOI":"10.1103\/PhysRevA.89.062314"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"2829","DOI":"10.1007\/s11434-014-0443-y","article-title":"Efficient generation of NOON states on two microwave-photon resonators","volume":"59","author":"Hua","year":"2014","journal-title":"Chin. Sci. Bull."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"407","DOI":"10.1016\/0003-4916(61)90115-4","article-title":"Two soluble models of an antiferromagnetic chain","volume":"16","author":"Lieb","year":"1961","journal-title":"Ann. Phys."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Christandl, M., Datta, N., Ekert, A., and Landahl, A.J. (2004). Perfect state transfer in quantum spin networks. Phys. Rev. Lett., 92.","DOI":"10.1103\/PhysRevLett.92.187902"},{"key":"ref_55","doi-asserted-by":"crossref","unstructured":"Yao, N.Y., Jiang, L., Gorshkov, A.V., Gong, Z.-X., Zhai, A., Duan, L.-M., and Lukin, M.D. (2011). Robust quantum state transfer in random unpolarized spin chains. Phys. Rev. Lett., 106.","DOI":"10.1103\/PhysRevLett.106.040505"},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1038\/nature07136","article-title":"Generation of Fock states in a superconducting quantum circuit","volume":"454","author":"Hofheinz","year":"2008","journal-title":"Nature"},{"key":"ref_57","unstructured":"In order to plot the transmission and reflection infidelities, we numerically perform the exact diagonalization of the coupling matrix A, and then calculate these infidelities according to Equations (26) and (27), and the definitions of such infidelities. The upper bounds, however, are straightforwardly plotted according to Equations (47) and (54). In addition, we plot these quantities at a specific evolution time, \n        \n          \n            \n              t\n              =\n              \u03c4\n              \u2261\n              \u03c0\n              \/\n              \n                2\n              \n              \n                g\n                z\n              \n            \n          \n        \n      , to make the quantum state of either the transmitted or reflected photons remain unchanged"},{"key":"ref_58","doi-asserted-by":"crossref","unstructured":"Bose, S. (2003). Quantum communication through an unmodulated spin chain. Phys. Rev. Lett., 91.","DOI":"10.1103\/PhysRevLett.91.207901"},{"key":"ref_59","doi-asserted-by":"crossref","unstructured":"Liu, Y., and Zhou, D.L. (2014). Optimized quantum state transfer through an XY spin chain. Phys. Rev. A, 89.","DOI":"10.1103\/PhysRevA.89.062331"},{"key":"ref_60","doi-asserted-by":"crossref","first-page":"040305","DOI":"10.1088\/1674-1056\/24\/4\/040305","article-title":"High-dimensional quantum state transfer in a noisy network environment","volume":"24","author":"Qin","year":"2015","journal-title":"Chin. Phys. B"},{"key":"ref_61","doi-asserted-by":"crossref","unstructured":"Qin, W., Wang, C., and Zhang, X.D. (2015). Protected quantum-state transfer in decoherence-free subspaces. Phys. Rev. A, 91.","DOI":"10.1103\/PhysRevA.91.042303"},{"key":"ref_62","doi-asserted-by":"crossref","unstructured":"Fukuhara, T., Hild, S., Zeiher, J., Schau\u00df, P., Bloch, I., Endres, M., and Gross, C. (2015). Spatially resolved detection of a spin-entanglement wave in a bose-hubbard chain. Phys. Rev. Lett., 115.","DOI":"10.1103\/PhysRevLett.115.035302"},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"7111","DOI":"10.1088\/0305-4470\/34\/35\/335","article-title":"Induced measures in the space of mixed quantum states","volume":"34","author":"Sommers","year":"2001","journal-title":"J. Phys. A Math. Gen."},{"key":"ref_64","doi-asserted-by":"crossref","unstructured":"Yang, Z., Gao, M., and Qin, W. (2015). Transfer of high-dimensional quantum state through an XXZ-Heisenberg quantum spin chain. Int. J. Mod. Phys. 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