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Quantum error correction (QEC) is an essential concept for any quantum information processing device.
Linear transformations which preserve hermitian and positive semidefiniet operations
John de Pillis · 1967
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Completely positive linear maps on complex matrices
Man-Duen Choi · 1975
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States, Effects, and Operations: Fundamental Notions of Quantum Theory
K. Kraus · 1983
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Matrix Analysis
Roger A. Horn and Charles R. Johnson · 1985
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Fidelity for mixed quantum states
Richard Jozsa · 1994
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Scheme for reducing decoherence in quantum computer memory
Peter W. Shor · 1995
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Mixed state entanglement and quantum error correction
C. H. Bennett, D. P. DiVincenzo, J. A. Smolin, and K. W. Wootters · 1996
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Good quantum error-correcting codes exist
A. R. Calderbank and Peter W. Shor · 1996
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Fault-tolerant error correction with efficient quantum codes
D.P. DiVincenzo and P. W. Shor · 1996
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Class of quantum error-correcting codes saturating the quantum Hamming bound
D. Gottesman · 1996
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Perfect quantum error correction code
R. Laflamme, C. Miquel, J.-P. Paz, and W. H. Zurek · 1996
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Sending entanglement through noisy quantum channels
Benjamin Schumacher · 1996
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Fault-tolerant quantum computation
P. W. Shor · 1996
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Error correcting codes in quantum theory
A. M. Steane · 1996
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Semidefinite programming
Lieven Vandenberghe and Stephen Boyd · 1996
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Quantum error correction and orthogonal geometry
A. R. Calderbank, E. M. Rains, P. W. Shor, and N. J. A. Sloane · 1997
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Stabilizer Codes and Quantum Error Correction
Daniel Gottesman · 1997
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Quantum computations: algorithms and error correction
A. Y. Kitaev · 1997
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Quantum error correction with imperfect gates
A. Y. Kitaev · 1997
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Theory of quantum error-correcting codes
E. Knill and R. Laflamme · 1997
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Approximate quantum error correction can lead to better codes
D. W. Leung, M. A. Nielsen, I. L. Chuang, and Y. Yamamoto · 1997
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Quantum error correction via codes over GF(4)
A. R. Calderbank, E. M Rains, P. W. Shor, and N. J. A. Sloane · 1998
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Theory of fault-tolerant quantum computation
D. Gottesman · 1998
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Mixed-quantum-state detection with inconclusive results
Yonina C. Eldar · 2003
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A semidefinite programming approach to optimal unambiguous discrimination of quantum states
Yonina C. Eldar · 2003
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Robust procedures for converting among Lindblad, Kraus and matrix representations of quantum dynamical semigroups
Timothy F. Havel · 2003
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Capacities of quantum channels and how to find them
Peter W. Shor · 2003
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Operator-schmidt decompositions and the fourier transform, with applications to the operator-schmidt numbers of unitaries
Jon Tyson · 2003
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Convex Optimization
Stephen Boyd and Lieven Vandenberghe · 2004
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Carlton M. Caves · 1999
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An introduction to quantum error correction
Daniel Gottesman · 2000
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Quantum Computation and Quantum Information
Michael A. Nielsen and Isaac L. Chuang · 2000
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Optimal nonuniversally covariant cloning
G. M. D’Ariano and P. Lo Presti · 2001
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A semidefinite program for distillable entanglement
E. M. Rains · 2001
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Optimizing completely positive maps using semidefinite programming
Koenraad Audenaert and Bart De Moor · 2002
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Separable multipartite mixed states: Operational asymptotically necessary and sufficient conditions
Fernando G. S. L. Brandao and Reinaldo O. Vianna · 2004
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Optimal quantum detectors for unambiguous detection of mixed states
Yonina C. Eldar, Mihailo Stojnic, and Babak Hassibi · 2004
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Detecting multipartite entanglement
A. C. Doherty, Pablo A. Parrilo, and Federico M. Spedalieri · 2005
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Iterative optimization of error correcting codes
M. Reimpell and R. F. Werner · 2005
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Supobtimal quantum-error-correcting procedure based on semidefinite programming
Naoki Yamamoto, Shinji Hara, and Koji Tsumura · 2005
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Quantum error corretion via convex optimization, 2006
Robert L. Kosut and Daniel A. Lidar · 2006
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Comment on “Optimum quantum error recovery using semidefinite programming”, 2006
M. Reimpell, R. F. Werner, and K. Audenaert · 2006
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Quantum algorithms for the ordered search problem via semidefinite programming
Andrew M. Childs, Andrew J. Landahl, and Pablo A. Parrilo · 2007
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Near-optimal channel-adapted quantum error recovery for high dimensional channels
Andrew S. Fletcher, Peter W. Shor, and Moe Z. Win · 2007
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Optimum quantum error recovery using semidefinite programming
Andrew S. Fletcher, Peter W. Shor, and Moe Z. Win · 2007
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