{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,25]],"date-time":"2026-08-25T13:14:49Z","timestamp":1787663689728,"version":"build-2736575974"},"reference-count":79,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T00:00:00Z","timestamp":1621209600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T00:00:00Z","timestamp":1621209600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["2019R1A2C1006167"],"award-info":[{"award-number":["2019R1A2C1006167"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Grand Information Technology Research Center support program","award":["IITP-2020-0-01462"],"award-info":[{"award-number":["IITP-2020-0-01462"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Sci Rep"],"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We propose a photonic procedure using cross-Kerr nonlinearities (XKNLs) to encode single logical qubit information onto four-photon decoherence-free states. In quantum information processing, a decoherence-free subspace can secure quantum information against collective decoherence. Therefore, we design a procedure employing nonlinear optical gates, which are composed of XKNLs, quantum bus beams, and photon-number-resolving measurements with linear optical devices, to conserve quantum information by encoding quantum information onto four-photon decoherence-free states (single logical qubit information). Based on our analysis in quantifying the affection (photon loss and dephasing) of the decoherence effect, we demonstrate the experimental condition to acquire the reliable procedure of single logical qubit information having the robustness against the decoherence effect.<\/jats:p>","DOI":"10.1038\/s41598-021-89809-w","type":"journal-article","created":{"date-parts":[[2021,5,17]],"date-time":"2021-05-17T10:04:53Z","timestamp":1621245893000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Procedure via cross-Kerr nonlinearities for encoding single logical qubit information onto four-photon decoherence-free states"],"prefix":"10.1038","volume":"11","author":[{"given":"Jino","family":"Heo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Seong-Gon","family":"Choi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,5,17]]},"reference":[{"key":"89809_CR1","doi-asserted-by":"publisher","first-page":"1895","DOI":"10.1103\/PhysRevLett.70.1895","volume":"70","author":"CH Bennett","year":"1993","unstructured":"Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895 (1993).","journal-title":"Phys. Rev. Lett."},{"key":"89809_CR2","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1038\/37539","volume":"390","author":"D Bouwmeester","year":"1997","unstructured":"Bouwmeester, D. et al. Experimental quantum teleportation. Nature 390, 575 (1997).","journal-title":"Nature"},{"key":"89809_CR3","doi-asserted-by":"publisher","first-page":"187902","DOI":"10.1103\/PhysRevLett.89.187902","volume":"89","author":"K Bostrom","year":"2002","unstructured":"Bostrom, K. & Felbinger, F. Deterministic secure direct communication using entanglement. Phys. Rev. Lett. 89, 187902 (2002).","journal-title":"Phys. Rev. Lett."},{"key":"89809_CR4","doi-asserted-by":"publisher","first-page":"042312","DOI":"10.1103\/PhysRevA.65.042312","volume":"65","author":"GH Zeng","year":"2002","unstructured":"Zeng, G. H. & Keitel, C. H. Arbitrated quantum-signature scheme. Phys. Rev. A 65, 042312 (2002).","journal-title":"Phys. Rev. A"},{"key":"89809_CR5","doi-asserted-by":"publisher","first-page":"2137","DOI":"10.1007\/s11128-016-1268-1","volume":"15","author":"X Tan","year":"2016","unstructured":"Tan, X. & Zhang, X. Controlled quantum secure direct communication by entanglement distillation or generalized measurement. Quantum Inf. Process. 15, 2137 (2016).","journal-title":"Quantum Inf. Process."},{"key":"89809_CR6","doi-asserted-by":"publisher","first-page":"3705","DOI":"10.1007\/s10773-020-04626-7","volume":"59","author":"J Heo","year":"2020","unstructured":"Heo, J., Hong, C., Kang, M. S. & Yang, H. J. Scheme for bidirectional quantum teleportation of unknown electron-spin states of quantum dots within single-sided cavities. Int. J. Theor. Phys. 59, 3705 (2020).","journal-title":"Int. J. Theor. Phys."},{"key":"89809_CR7","first-page":"e60","volume":"3","author":"H Du","year":"2021","unstructured":"Du, H., Malaney, R. & Green, J. Satellite-based distribution of hybrid entanglement. Quant. Eng. 3, e60 (2021).","journal-title":"Quant. Eng."},{"key":"89809_CR8","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/j.fmre.2021.01.002","volume":"1","author":"C Wang","year":"2021","unstructured":"Wang, C. Quantum secure direct communication: Intersection of communication and cryptography. Fundam. Res. 1, 91 (2021).","journal-title":"Fundam. Res."},{"key":"89809_CR9","doi-asserted-by":"publisher","first-page":"46","DOI":"10.1016\/j.scib.2016.11.007","volume":"62","author":"FG Deng","year":"2017","unstructured":"Deng, F. G., Ren, B. C. & Li, X. H. Quantum hyperentanglement and its applications in quantum information processing. Sci. Bull. 62, 46 (2017).","journal-title":"Sci. Bull."},{"key":"89809_CR10","doi-asserted-by":"publisher","first-page":"10208","DOI":"10.1038\/s41598-017-09510-9","volume":"7","author":"J Heo","year":"2017","unstructured":"Heo, J. et al. Distribution of hybrid entanglement and hyperentanglement with time-bin for secure quantum channel under noise via weak cross-Kerr nonlinearity. Sci. Rep. 7, 10208 (2017).","journal-title":"Sci. Rep."},{"key":"89809_CR11","doi-asserted-by":"publisher","first-page":"15971","DOI":"10.1038\/ncomms15971","volume":"8","author":"F Steinlechner","year":"2017","unstructured":"Steinlechner, F. et al. Distribution of high-dimensional entanglement via an intra-city free-space link. Nat. Commun. 8, 15971 (2017).","journal-title":"Nat. Commun."},{"key":"89809_CR12","doi-asserted-by":"publisher","first-page":"10151","DOI":"10.1038\/s41598-019-46231-7","volume":"9","author":"J Heo","year":"2019","unstructured":"Heo, J., Hong, C., Choi, S. G. & Hong, J. P. Scheme for generation of three-photon entangled W state assisted by cross-Kerr nonlinearity and quantum dot. Sci. Rep. 9, 10151 (2019).","journal-title":"Sci. Rep."},{"key":"89809_CR13","doi-asserted-by":"publisher","first-page":"023021","DOI":"10.1103\/PhysRevResearch.1.023021","volume":"1","author":"Z Zhang","year":"2019","unstructured":"Zhang, Z., Scully, M. O. & Agarwal, G. S. Quantum entanglement between two magnon modes via Kerr nonlinearity driven far from equilibrium. Phys. Rev. Res. 1, 023021 (2019).","journal-title":"Phys. Rev. Res."},{"key":"89809_CR14","doi-asserted-by":"publisher","first-page":"085104","DOI":"10.1088\/1402-4896\/aba02e","volume":"95","author":"C Hong","year":"2020","unstructured":"Hong, C. et al. Generation of two-photon hybrid-entangled W state with photonic qubit and time-bin via cross-Kerr nonlinearities. Phys. Scr. 95, 085104 (2020).","journal-title":"Phys. Scr."},{"key":"89809_CR15","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1016\/j.scib.2017.06.007","volume":"62","author":"YB Sheng","year":"2017","unstructured":"Sheng, Y. B. & Zhou, L. Distributed secure quantum machine learning. Sci. Bull. 62, 1025\u20131029 (2017).","journal-title":"Sci. Bull."},{"key":"89809_CR16","doi-asserted-by":"publisher","first-page":"6167","DOI":"10.1038\/s41598-019-42662-4","volume":"9","author":"MS Kang","year":"2019","unstructured":"Kang, M. S., Heo, J., Choi, S. G., Moon, S. & Han, S. W. Implementation of SWAP test for two unknown states in photons via cross-Kerr nonlinearities under decoherence effect. Sci. Rep. 9, 6167 (2019).","journal-title":"Sci. Rep."},{"key":"89809_CR17","doi-asserted-by":"publisher","first-page":"022323","DOI":"10.1103\/PhysRevA.100.022323","volume":"100","author":"L Bouten","year":"2019","unstructured":"Bouten, L., Vissers, G. & Schmidt-Kaler, F. \u201cQuantum algorithm for simulating an experiment: Light interference from single ions and their mirror images. Phys. Rev. A 100, 022323 (2019).","journal-title":"Phys. Rev. A"},{"key":"89809_CR18","doi-asserted-by":"publisher","first-page":"31023","DOI":"10.1364\/OE.27.031023","volume":"27","author":"C Hong","year":"2019","unstructured":"Hong, C. et al. Photonic scheme of quantum phase estimation for quantum algorithms via cross-Kerr nonlinearities under decoherence effect. Opt. Express 27, 31023 (2019).","journal-title":"Opt. Express"},{"key":"89809_CR19","doi-asserted-by":"publisher","first-page":"12440","DOI":"10.1038\/s41598-019-48695-z","volume":"9","author":"J Heo","year":"2019","unstructured":"Heo, J., Won, K., Yang, H. J., Hong, J. P. & Choi, S. G. Photonic scheme of discrete quantum Fourier transform for quantum algorithms via quantum dots. Sci. Rep. 9, 12440 (2019).","journal-title":"Sci. Rep."},{"key":"89809_CR20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1038\/s41598-019-56847-4","volume":"10","author":"MS Kang","year":"2020","unstructured":"Kang, M. S., Heo, J., Choi, S. G., Sung, M. & Han, S. W. Optical Fredkin gate assisted by quantum dot within optical cavity under vacuum noise and sideband leakage. Sci. Rep. 10, 1\u201313 (2020).","journal-title":"Sci. Rep."},{"key":"89809_CR21","doi-asserted-by":"publisher","first-page":"85","DOI":"10.1016\/j.fmre.2020.12.001","volume":"1","author":"K Li","year":"2021","unstructured":"Li, K., Yan, P. G. & Cai, Q. Y. Quantum computing and the security of public key cryptography. Fundam. Res. 1, 85 (2021).","journal-title":"Fundam. Res."},{"key":"89809_CR22","first-page":"e58","volume":"3","author":"JY Quan","year":"2021","unstructured":"Quan, J. Y., Li, Q., Liu, C. D., Shi, J. J. & Peng, Y. A simplified verifiable blind quantum computing protocol with quantum input verification. Quant. Eng. 3, e58 (2021).","journal-title":"Quant. Eng."},{"key":"89809_CR23","doi-asserted-by":"publisher","first-page":"R2493","DOI":"10.1103\/PhysRevA.52.R2493","volume":"52","author":"PW Shor","year":"1995","unstructured":"Shor, P. W. Scheme for reducing decoherence in quantum computer memory. Phys. Rev. A 52, R2493 (1995).","journal-title":"Phys. Rev. A"},{"key":"89809_CR24","doi-asserted-by":"publisher","first-page":"2551","DOI":"10.1098\/rspa.1996.0136","volume":"452","author":"A Steane","year":"1996","unstructured":"Steane, A. Multiple-particle interference and quantum error correction. Proc. R. Soc. A 452, 2551 (1996).","journal-title":"Proc. R. Soc. A"},{"key":"89809_CR25","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9781139034807","volume-title":"Quantum Error Correction","author":"D Lidar","year":"2013","unstructured":"Lidar, D. & Brun, T. Quantum Error Correction (Cambridge University Press, 2013)."},{"key":"89809_CR26","doi-asserted-by":"publisher","first-page":"010503","DOI":"10.1103\/PhysRevLett.126.010503","volume":"126","author":"XM Hu","year":"2021","unstructured":"Hu, X. M. et al. Long-distance entanglement purification for quantum communication. Phys. Rev. Lett. 126, 010503 (2021).","journal-title":"Phys. Rev. Lett."},{"key":"89809_CR27","doi-asserted-by":"publisher","first-page":"571","DOI":"10.1364\/OE.409931","volume":"29","author":"PS Yan","year":"2021","unstructured":"Yan, P. S., Zhou, L., Zhong, W. & Sheng, Y. B. Feasible time-bin entanglement purification based on sum-frequency generation. Opt. Express 29, 571 (2021).","journal-title":"Opt. Express"},{"key":"89809_CR28","doi-asserted-by":"publisher","first-page":"9363","DOI":"10.1364\/OE.420348","volume":"29","author":"PS Yan","year":"2021","unstructured":"Yan, P. S., Zhou, L., Zhong, W. & Sheng, Y. B. Feasible measurement-based entanglement purification in linear optics. Opt. Express 29, 9363 (2021).","journal-title":"Opt. Express"},{"key":"89809_CR29","doi-asserted-by":"publisher","first-page":"012307","DOI":"10.1103\/PhysRevA.85.012307","volume":"85","author":"YB Sheng","year":"2012","unstructured":"Sheng, Y. B. et al. Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs. Phys. Rev. A 85, 012307 (2012).","journal-title":"Phys. Rev. A"},{"key":"89809_CR30","doi-asserted-by":"publisher","first-page":"042302","DOI":"10.1103\/PhysRevA.85.042302","volume":"85","author":"YB Sheng","year":"2012","unstructured":"Sheng, Y. B. et al. Efficient two-step entanglement concentration for arbitrary W states. Phys. Rev. A 85, 042302 (2012).","journal-title":"Phys. Rev. A"},{"key":"89809_CR31","doi-asserted-by":"publisher","first-page":"060301","DOI":"10.1007\/s11433-015-5672-9","volume":"58","author":"YB Sheng","year":"2015","unstructured":"Sheng, Y. B. et al. Efficient N-particle W state concentration with different parity check gates. Sci. China Phys. Mech. Astron. 58, 060301 (2015).","journal-title":"Sci. China Phys. Mech. Astron."},{"key":"89809_CR32","doi-asserted-by":"publisher","first-page":"3306","DOI":"10.1103\/PhysRevLett.79.3306","volume":"79","author":"P Zanardi","year":"1997","unstructured":"Zanardi, P. & Rasetti, M. Noiseless quantum codes. Phys. Rev. Lett. 79, 3306 (1997).","journal-title":"Phys. Rev. Lett."},{"key":"89809_CR33","doi-asserted-by":"publisher","first-page":"042307","DOI":"10.1103\/PhysRevA.63.042307","volume":"63","author":"J Kempe","year":"2001","unstructured":"Kempe, J., Bacon, D., Lidar, D. A. & Whaley, K. B. Theory of decoherence-free fault-tolerant universal quantum computation. Phys. Rev. A 63, 042307 (2001).","journal-title":"Phys. Rev. A"},{"key":"89809_CR34","doi-asserted-by":"publisher","first-page":"2059","DOI":"10.1126\/science.1064460","volume":"293","author":"L Viola","year":"2001","unstructured":"Viola, L. et al. Experimental realization of noiseless subsystems for quantum information processing. Science 293, 2059 (2001).","journal-title":"Science"},{"key":"89809_CR35","doi-asserted-by":"publisher","first-page":"7067","DOI":"10.1088\/0305-4470\/34\/35\/331","volume":"34","author":"L Viola","year":"2001","unstructured":"Viola, L., Knill, E. & Laflamme, R. Constructing qubits in physical systems. J. Phys. A 34, 7067 (2001).","journal-title":"J. Phys. A"},{"key":"89809_CR36","doi-asserted-by":"publisher","first-page":"147901","DOI":"10.1103\/PhysRevLett.92.147901","volume":"92","author":"JB Altepeter","year":"2004","unstructured":"Altepeter, J. B., Hadley, P. G., Wendelken, S. M., Berglund, A. J. & Kwiat, P. G. Experimental investigation of a two-qubit decoherence-free subspace. Phys. Rev. Lett. 92, 147901 (2004).","journal-title":"Phys. Rev. Lett."},{"key":"89809_CR37","doi-asserted-by":"publisher","first-page":"1030","DOI":"10.1364\/OL.41.001030","volume":"41","author":"L Dong","year":"2016","unstructured":"Dong, L. et al. Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem. Opt. Lett. 41, 1030 (2016).","journal-title":"Opt. Lett."},{"key":"89809_CR38","doi-asserted-by":"publisher","first-page":"287","DOI":"10.1016\/j.aop.2016.04.022","volume":"371","author":"L Dong","year":"2016","unstructured":"Dong, L. et al. Generation of three-photon polarization-entangled decoherence-free states. Ann. Phys. 371, 287 (2016).","journal-title":"Ann. Phys."},{"key":"89809_CR39","doi-asserted-by":"publisher","first-page":"13843","DOI":"10.1038\/s41598-018-32137-3","volume":"8","author":"J Heo","year":"2018","unstructured":"Heo, J., Kang, M. S., Hong, C. H., Hong, J. P. & Choi, S. G. Preparation of quantum information encoded on three-photon decoherence-free states via cross-Kerr nonlinearities. Sci. Rep. 8, 13843 (2018).","journal-title":"Sci. Rep."},{"key":"89809_CR40","doi-asserted-by":"publisher","first-page":"216","DOI":"10.1007\/s11128-019-2315-5","volume":"18","author":"C Hong","year":"2019","unstructured":"Hong, C., Heo, J., Kang, M. S., Jang, J. & Yang, H. J. Scheme for encoding single logical qubit information into three-photon decoherence-free states assisted by quantum dots. Quantum Inf. Process. 18, 216 (2019).","journal-title":"Quantum Inf. Process."},{"key":"89809_CR41","doi-asserted-by":"publisher","first-page":"135502","DOI":"10.1088\/0953-4075\/43\/13\/135502","volume":"43","author":"XQ Shao","year":"2010","unstructured":"Shao, X. Q., Chen, L., Zhang, S., Zhao, Y. F. & Yeon, K. H. Preparation of three- and four-qubit decoherence-free states via Zeno-like measurements. J. Phys. B 43, 135502 (2010).","journal-title":"J. Phys. B"},{"key":"89809_CR42","doi-asserted-by":"publisher","first-page":"4841","DOI":"10.1007\/s10773-016-3108-6","volume":"55","author":"C Chen","year":"2016","unstructured":"Chen, C. Photonic four-qubit entangled decoherence-free states assisted by cavity-QED system. Int. J Theor. Phys. 55, 4841 (2016).","journal-title":"Int. J Theor. Phys."},{"key":"89809_CR43","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1016\/j.optcom.2015.12.065","volume":"366","author":"YS Zhou","year":"2016","unstructured":"Zhou, Y. S., Li, X., Deng, Y., Li, H. R. & Luo, M. X. Generation of hybrid four-qubit entangled decoherence-free states assisted by the cavity-QED system. Opt. Commun. 366, 397 (2016).","journal-title":"Opt. Commun."},{"key":"89809_CR44","doi-asserted-by":"publisher","first-page":"589","DOI":"10.1007\/s10773-014-2251-1","volume":"54","author":"YB Li","year":"2015","unstructured":"Li, Y. B., Song, T. T., Huang, W. & Zhan, W. W. Fault-tolerant quantum secure direct communication protocol based on decoherence-free states. Int. J Theor. Phys. 54, 589 (2015).","journal-title":"Int. J Theor. Phys."},{"key":"89809_CR45","doi-asserted-by":"publisher","first-page":"38233","DOI":"10.1038\/srep38233","volume":"6","author":"M Wang","year":"2016","unstructured":"Wang, M., Yan, F. & Gao, T. Generation of four-photon polarization entangled decoherence-free states with cross-Kerr nonlinearity. Sci. Rep. 6, 38233 (2016).","journal-title":"Sci. Rep."},{"key":"89809_CR46","doi-asserted-by":"publisher","first-page":"042321","DOI":"10.1103\/PhysRevA.94.042321","volume":"94","author":"XM Xiu","year":"2016","unstructured":"Xiu, X. M. et al. Preparation of four-photon polarization-entangled decoherence-free states employing weak cross-Kerr nonlinearities. Phys. Rev. A 94, 042321 (2016).","journal-title":"Phys. Rev. A"},{"key":"89809_CR47","doi-asserted-by":"publisher","first-page":"195","DOI":"10.1007\/s11128-017-1646-3","volume":"16","author":"M Wang","year":"2017","unstructured":"Wang, M., Yan, F. & Gao, T. Generation of an arbitrary four-photon polarization-entangled decoherence-free state with cross-Kerr nonlinearity. Quantum Inf. Process. 16, 195 (2017).","journal-title":"Quantum Inf. Process."},{"key":"89809_CR48","doi-asserted-by":"publisher","first-page":"15334","DOI":"10.1038\/s41598-020-71072-0","volume":"10","author":"J Heo","year":"2020","unstructured":"Heo, J., Hong, C., Kang, M. S. & Yang, H. J. Encoding scheme using quantum dots for single logical qubit information onto four-photon decoherence-free states. Sci. Rep. 10, 15334 (2020).","journal-title":"Sci. Rep."},{"key":"89809_CR49","doi-asserted-by":"publisher","first-page":"062320","DOI":"10.1103\/PhysRevA.74.062320","volume":"74","author":"P Agrawal","year":"2006","unstructured":"Agrawal, P. & Pati, A. Perfect teleportation and superdense coding with W states. Phys. Rev. A 74, 062320 (2006).","journal-title":"Phys. Rev. A"},{"key":"89809_CR50","doi-asserted-by":"publisher","first-page":"032340","DOI":"10.1103\/PhysRevA.95.032340","volume":"95","author":"J Chen","year":"2017","unstructured":"Chen, J., Zhou, H., Duan, C. & Peng, X. Preparing Greenberger-Horne-Zeilinger and W states on a long-range Ising spin model by global controls. Phys. Rev. A 95, 032340 (2017).","journal-title":"Phys. Rev. A"},{"key":"89809_CR51","doi-asserted-by":"publisher","first-page":"062314","DOI":"10.1103\/PhysRevA.62.062314","volume":"62","author":"W Dur","year":"2000","unstructured":"Dur, W., Vidal, G. & Cirac, J. I. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000).","journal-title":"Phys. Rev. A"},{"key":"89809_CR52","doi-asserted-by":"publisher","first-page":"054301","DOI":"10.1103\/PhysRevA.73.054301","volume":"73","author":"XB Zou","year":"2006","unstructured":"Zou, X. B., Shu, J. & Guo, G. C. Simple scheme for generating four-photon polarization-entangled decoherence-free states using spontaneous parametric down-conversions. Phys. Rev. A 73, 054301 (2006).","journal-title":"Phys. Rev. A"},{"key":"89809_CR53","doi-asserted-by":"publisher","first-page":"042317","DOI":"10.1103\/PhysRevA.77.042317","volume":"77","author":"YX Gong","year":"2008","unstructured":"Gong, Y. X. et al. Generation of arbitrary four-photon polarization-entangled decoherence-free states. Phys. Rev. A 77, 042317 (2008).","journal-title":"Phys. Rev. A"},{"key":"89809_CR54","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1364\/JOSAB.26.000129","volume":"26","author":"Y Xia","year":"2009","unstructured":"Xia, Y., Song, J., Song, H. S. & Zhang, S. Controlled generation of four-photon polarization-entangled decoherence-free states with conventional photon detectors. J. Opt. Soc. Am. B 26, 129 (2009).","journal-title":"J. Opt. Soc. Am. B"},{"key":"89809_CR55","doi-asserted-by":"publisher","first-page":"651","DOI":"10.1007\/s00340-010-3937-6","volume":"99","author":"Y Xia","year":"2010","unstructured":"Xia, Y., Song, J., Yang, Z. B. & Zheng, S. B. Generation of four-photon polarization-entangled decoherence-free states within a network. Appl. Phys. B 99, 651 (2010).","journal-title":"Appl. Phys. B"},{"key":"89809_CR56","doi-asserted-by":"publisher","first-page":"250502","DOI":"10.1103\/PhysRevLett.93.250502","volume":"93","author":"K Nemoto","year":"2004","unstructured":"Nemoto, K. & Munro, W. J. Nearly deterministic linear optical controlled-NOT gate. Phys. Rev. Lett. 93, 250502 (2004).","journal-title":"Phys. Rev. Lett."},{"key":"89809_CR57","doi-asserted-by":"publisher","first-page":"034305","DOI":"10.1103\/PhysRevA.72.034305","volume":"72","author":"H Jeong","year":"2005","unstructured":"Jeong, H. Using weak nonlinearity under decoherence for macroscopic entanglement generation and quantum computation. Phys. Rev. A 72, 034305 (2005).","journal-title":"Phys. Rev. A"},{"key":"89809_CR58","doi-asserted-by":"publisher","first-page":"052320","DOI":"10.1103\/PhysRevA.73.052320","volume":"73","author":"H Jeong","year":"2006","unstructured":"Jeong, H. Quantum computation using weak nonlinearities: Robustness against decoherence. Phys. Rev. A 73, 052320 (2006).","journal-title":"Phys. Rev. A"},{"key":"89809_CR59","doi-asserted-by":"publisher","first-page":"10","DOI":"10.1007\/s11128-017-1560-8","volume":"16","author":"J Heo","year":"2017","unstructured":"Heo, J., Hong, C. H., Yang, H. J., Hong, J. P. & Choi, S. G. Analysis of optical parity gates of generating Bell state for quantum information and secure quantum communication via weak cross-Kerr nonlinearity under decoherence effect. Quantum Inf. Process. 16, 10 (2017).","journal-title":"Quantum Inf. Process."},{"key":"89809_CR60","doi-asserted-by":"publisher","first-page":"022301","DOI":"10.1103\/PhysRevA.79.022301","volume":"79","author":"Q Lin","year":"2009","unstructured":"Lin, Q. & Li, J. Quantum control gates with weak cross-Kerr nonlinearity. Phys. Rev. A 79, 022301 (2009).","journal-title":"Phys. Rev. A"},{"key":"89809_CR61","doi-asserted-by":"publisher","first-page":"052323","DOI":"10.1103\/PhysRevA.79.052323","volume":"79","author":"B He","year":"2009","unstructured":"He, B., Ren, Y. & Bergou, J. A. Creation of high-quality long-distance entanglement with flexible resources. Phys. Rev. A 79, 052323 (2009).","journal-title":"Phys. Rev. A"},{"key":"89809_CR62","doi-asserted-by":"publisher","first-page":"035802","DOI":"10.1103\/PhysRevA.79.035802","volume":"79","author":"B He","year":"2009","unstructured":"He, B., Nadeem, M. & Bergou, J. A. Scheme for generating coherent-state superpositions with realistic cross-Kerr nonlinearity. Phys. Rev. A 79, 035802 (2009).","journal-title":"Phys. Rev. A"},{"key":"89809_CR63","doi-asserted-by":"publisher","first-page":"062338","DOI":"10.1103\/PhysRevA.81.062338","volume":"81","author":"C Wittmann","year":"2010","unstructured":"Wittmann, C., Andersen, U. L., Takeoka, M., Sych, D. & Leuchs, G. Discrimination of binary coherent states using a homodyne detector and a photon number resolving detector. Phys. Rev. A 81, 062338 (2010).","journal-title":"Phys. Rev. A"},{"key":"89809_CR64","doi-asserted-by":"publisher","first-page":"12792","DOI":"10.1038\/srep12792","volume":"5","author":"Q Lin","year":"2015","unstructured":"Lin, Q. & He, B. Highly efficient processing of multi-photon states. Sci. Rep. 5, 12792 (2015).","journal-title":"Sci. Rep."},{"key":"89809_CR65","doi-asserted-by":"publisher","first-page":"060302","DOI":"10.1103\/PhysRevA.74.060302","volume":"74","author":"SD Barrett","year":"2006","unstructured":"Barrett, S. D. & Milburn, G. J. Quantum-information processing via a lossy bus. Phys. Rev. A 74, 060302 (2006).","journal-title":"Phys. Rev. A"},{"key":"89809_CR66","doi-asserted-by":"publisher","first-page":"042310","DOI":"10.1103\/PhysRevA.80.042310","volume":"80","author":"Q Lin","year":"2009","unstructured":"Lin, Q. & He, B. Single-photon logic gates using minimal resources. Phys. Rev. A 80, 042310 (2009).","journal-title":"Phys. Rev. A"},{"key":"89809_CR67","doi-asserted-by":"publisher","first-page":"033819","DOI":"10.1103\/PhysRevA.71.033819","volume":"71","author":"WJ Munro","year":"2005","unstructured":"Munro, W. J., Nemoto, K., Beausoleil, R. G. & Spiller, T. P. High-efficiency quantum-nondemolition single-photon-number-resolving detector. Phys. Rev. A 71, 033819 (2005).","journal-title":"Phys. Rev. A"},{"key":"89809_CR68","doi-asserted-by":"publisher","first-page":"22016","DOI":"10.1038\/srep22016","volume":"6","author":"Q Liu","year":"2016","unstructured":"Liu, Q., Wang, G. Y., Ai, Q., Zhang, M. & Deng, F. G. Complete nondestructive analysis of two-photon six-qubit hyperentangled Bell states assisted by cross-Kerr nonlinearity. Sci. Rep. 6, 22016 (2016).","journal-title":"Sci. Rep."},{"key":"89809_CR69","doi-asserted-by":"publisher","first-page":"013601","DOI":"10.1103\/PhysRevLett.119.013601","volume":"119","author":"LS Costanzo","year":"2017","unstructured":"Costanzo, L. S. et al. Measurement-induced strong Kerr nonlinearity for weak quantum states of light. Phys. Rev. Lett. 119, 013601 (2017).","journal-title":"Phys. Rev. Lett."},{"key":"89809_CR70","doi-asserted-by":"publisher","first-page":"012329","DOI":"10.1103\/PhysRevA.84.012329","volume":"84","author":"Y Hu","year":"2011","unstructured":"Hu, Y., Ge, G. Q., Chen, S., Yang, X. F. & Chen, Y. L. Cross-Kerr-effect induced by coupled Josephson qubits in circuit quantum electrodynamics. Phys. Rev. A 84, 012329 (2011).","journal-title":"Phys. Rev. A"},{"key":"89809_CR71","doi-asserted-by":"publisher","first-page":"052314","DOI":"10.1103\/PhysRevA.95.052314","volume":"95","author":"H Zhang","year":"2017","unstructured":"Zhang, H. & Wang, H. Entanglement concentration of microwave photons based on the Kerr effect in circuit QED. Phys. Rev. A 95, 052314 (2017).","journal-title":"Phys. Rev. A"},{"key":"89809_CR72","doi-asserted-by":"publisher","first-page":"1144","DOI":"10.1109\/JLT.1986.1074837","volume":"4","author":"H Kanamori","year":"1986","unstructured":"Kanamori, H. et al. Transmission characteristics and reliability of pure-silica-core single-mode fibers. J. Lightwave Technol. 4, 1144 (1986).","journal-title":"J. Lightwave Technol."},{"key":"89809_CR73","first-page":"3","volume":"57","author":"K Nagayama","year":"2004","unstructured":"Nagayama, K. et al. Ultra low loss (0.1484dB\/km) pure silica core fiber. SEI Tech. Rev. 57, 3 (2004).","journal-title":"SEI Tech. Rev."},{"key":"89809_CR74","doi-asserted-by":"publisher","first-page":"5132","DOI":"10.1103\/PhysRevA.41.5132","volume":"41","author":"SJD Phoenix","year":"1990","unstructured":"Phoenix, S. J. D. Wave-packet evolution in the damped oscillator. Phys. Rev. A 41, 5132 (1990).","journal-title":"Phys. Rev. A"},{"key":"89809_CR75","doi-asserted-by":"publisher","first-page":"243601","DOI":"10.1103\/PhysRevLett.125.243601","volume":"125","author":"S Sagona-Stophel","year":"2020","unstructured":"Sagona-Stophel, S., Shahrokhshahi, R., Jordaan, B., Namazi, M. & Figueroa, E. Conditional \u03c0-phase shift of single-photon-level pulses at room temperature. Phys. Rev. Lett. 125, 243601 (2020).","journal-title":"Phys. Rev. Lett."},{"key":"89809_CR76","doi-asserted-by":"publisher","first-page":"013808","DOI":"10.1103\/PhysRevA.77.013808","volume":"77","author":"P Kok","year":"2008","unstructured":"Kok, P. Effects of self-phase-modulation on weak nonlinear optical quantum gates. Phys. Rev. A 77, 013808 (2008).","journal-title":"Phys. Rev. A"},{"key":"89809_CR77","doi-asserted-by":"publisher","first-page":"1419","DOI":"10.1103\/PhysRevLett.84.1419","volume":"84","author":"MD Lukin","year":"2000","unstructured":"Lukin, M. D. & Imamo\u011flu, A. Nonlinear optics and quantum entanglement of ultraslow single photons. Phys. Rev. Lett. 84, 1419 (2000).","journal-title":"Phys. Rev. Lett."},{"key":"89809_CR78","doi-asserted-by":"publisher","first-page":"273","DOI":"10.1038\/35095000","volume":"413","author":"MD Lukin","year":"2001","unstructured":"Lukin, M. D. & Imamo\u011flu, A. Controlling photons using electromagnetically induced transparency. Nature 413, 273 (2001).","journal-title":"Nature"},{"key":"89809_CR79","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1103\/RevModPhys.79.135","volume":"79","author":"P Kok","year":"2007","unstructured":"Kok, P. et al. Linear optical quantum computing with photonic qubits. Rev. Mod. Phys. 79, 135 (2007).","journal-title":"Rev. Mod. Phys."}],"container-title":["Scientific Reports"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-89809-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-89809-w","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-89809-w.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,2,2]],"date-time":"2023-02-02T00:09:02Z","timestamp":1675296542000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.nature.com\/articles\/s41598-021-89809-w"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,5,17]]},"references-count":79,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2021,12]]}},"alternative-id":["89809"],"URL":"https:\/\/doi.org\/10.1038\/s41598-021-89809-w","relation":{},"ISSN":["2045-2322"],"issn-type":[{"value":"2045-2322","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,5,17]]},"assertion":[{"value":"4 March 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"30 April 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"17 May 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"10423"}}