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We introduce a general operational characterization of information-preserving structures (IPS) -- encompassing noiseless subsystems, decoherence-free subspaces, pointer bases, and error-correcting codes -- by demonstrating that they are isometric to fixed points of unital quantum processes.
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“Initialization-free” DFS/NS, introduced in A. Shabani and D. A. Lidar, Phys. Rev. A 72
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A. Granas and J. Dugundji, Fixed Point Theory (Springer, New York, 2003)
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An isometry is a 1:1 distance-preserving map; the relevant distance here is the 1-norm, ‖ A ‖ 1 = tr | A | ||A||_{1}=\mbox{tr}|A|
Cited in the paper.
R. Blume-Kohout, H. K. Ng, D. Poulin, and L. Viola, in preparation
Cited in the paper.
For example, processes that preserve a 1-qubit DFS and a 4-state pointer basis have identical eigenvalues ( { 1 , 1 , 1 , 1 , x 1 , x 2 , … } \{1,1,1,1,x_{1},x_{2},\ldots\} , | x j | < 1 |x_{j}|<1 ), but different IPS shape (respectively, { 2 } \{2\} and { 1 , 1 , 1 , 1 } \{1,1,1,1\} )
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Our “unitarily noiseless” differs from that in D. W. Kribs, R. Laflamme, D. Poulin, and M. Lesosky, Quantum Inf. Comp. 6
2006
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C. Beny, A. Kempf, and D. W. Kribs, Phys. Rev. Lett. 98
2007
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