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We derive bounds on general quantum error correcting codes against the displacement noise channel.
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Jessie MacWilliams · 1963
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“The MacWilliams Identities for Nonlinear Codes”
F.. MacWilliams, N… Sloane and J.-M. Goethals · 1972
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“Bounds for Unrestricted Codes, by Linear Programming”
P. Delsarte · 1972
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“A Krawtchouk Polynomial Addition Theorem and Wreath Products of Symmetric Groups”
Charles. Dunkl · 1976
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“New Upper Bounds on the Rate of a Code via the Delsarte-MacWilliams Inequalities”
R. McEliece, E. Rodemich, H. Rumsey and L. Welch · 1977
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“On Bounds for Packings on a Sphere and in Space”
G.A. Kabatiansky and V.. Levenshtein · 1978
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“On Bounds for Packings in N-Dimensional Euclidean Space”
V.. Levenshtein · 1979
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J.. Van · 1982
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“An Introduction to Group Representations and Orthogonal Polynomials”
Dennis Stanton · 1990
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“The Entanglement Fidelity and Quantum Error Correction”
M.. Nielsen · 1996
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Benjamin Schumacher · 1996
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Peter Shor and Raymond Laflamme · 1997
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“Stabilizer Codes and Quantum Error Correction”, 1997
Daniel Gottesman · 1997
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“The Sphere Packing Problem.”
N… Sloane · 1998
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“Upper Bounds on the Size of Quantum Codes”
A. Ashikhmin and S. Litsyu · 1999
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“Sphere Packings, Lattices and Groups” 290
J.. Conway and N… Sloane · 1999
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“Special Functions”, Encyclopedia of Mathematics and Its Applications
George. Andrews, Richard Askey and Ranjan Roy · 1999
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“Quantum Shadow Enumerators”
E.M. Rains · 1999
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“A Theory of Quantum Error-Correcting Codes”
Emanuel Knill and Raymond Laflamme · 2000
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A.E. Ashikhmin, A.M. Barg, E. Knill and S.N. Litsyn · 2000
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Daniel Gottesman, Alexei Kitaev and John Preskill · 2001
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Henry Cohn and Yufei Zhao · 2002
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“Methods in Theoretical Quantum Optics”
Stephen. Barnett and Paul. Radmore · 2002
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Henry Cohn and Noam Elkies · 2003
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Baptiste Royer, Shraddha Singh and S.. Girvin · 2020
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Takaya Matsuura, Hayata Yamasaki and Masato Koashi · 2020
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“Bosonic Coding: Introduction and Use Cases”, 2022
Victor. Albert · 2022
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“Gottesman-Kitaev-Preskill Codes: A Lattice Perspective”
Jonathan Conrad, Jens Eisert and Francesco Arzani · 2022
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“Table of Integrals, Series, and Products”
I.. Gradshteyn and I.. Ryzhik · 2022
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“Linear Programming Bounds for Approximate Quantum Error Correction Over Arbitrary Quantum Channels”
Yingkai Ouyang and Ching-Yi Lai · 2022
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A.. Scott · 2004
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A. Schrijver · 2005
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Henry Cohn and Abhinav Kumar · 2009
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“Semidefinite Programming, Harmonic Analysis and Coding Theory”
Christine Bachoc · 2010
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Christian Weedbrook et al · 2012
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Alexei Ashikhmin · 2014
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“Three-Point Bounds for Sphere Packing”
Henry Cohn, David de Laat and Andrew Salmon · 2022
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“From Sphere Packing to Fourier Interpolation”
Henry Cohn · 2023
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“Advances in Bosonic Quantum Error Correction with Gottesman-Kitaev-Preskill Codes: Theory, Engineering and Applications”
Anthony. Brady et al · 2023
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“A Quantum Analog of Delsarte’s Linear Programming Bounds”, 2023
Rui Okada · 2023
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“Shor–Laflamme Distributions of Graph States and Noise Robustness of Entanglement”
Daniel Miller et al · 2023
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Ansgar. Burchards, Steven. Flammia and Jonathan Conrad · 2024
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Jonathan Conrad, Jens Eisert and Jean-Pierre Seifert · 2024
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“SDP Bounds on Quantum Codes”
Gerardès Munné, Andrew Nemec and Felix Huber · 2024
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“Experimental Measurement and a Physical Interpretation of Quantum Shadow Enumerators”
Daniel Miller et al · 2024
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“Invariant Theory and Magic State Distillation”
Amolak Kalra and Shiroman Prakash · 2025
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Barbara. Terhal, Jonathan Conrad and Christophe Vuillot · 2058
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