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We introduce a linear optical technique that can implement ideal quantum tele-amplification up to the $n^\mathrm{th}$ Fock state, where $n$ can be any positive integer.
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See Supplemental Material at [URL will be inserted by publisher] for the details about the technical proofs for the n n -QS operations, probability of success with improvements, fidelity of output state, comparisons with other NLA protocols, loss-tolerant entanglement distillation analysis, and experimental imperfections analysis, which includes Ref. Scheel 2004 ; Gard et al. 2015 ; Lund et al. 2017 ; Brualdi et al. 1991 ; Percus 2012 ; Ralph and Lund 2009 ; Winnel et al. 2020 ; Tserkis et al. 2019 ; García-Patrón et al. 2009 ; Winnel et al. 2021 ; Reddy et al. 2019 ; Lita et al. 2008 ; Marsili et al. 2013 ; Miller et al. 2003 ; Slussarenko and Pryde 2019 ; Su et al. 2019 ; Xiang et al. 2010 ; Andersen and Ralph 2013
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