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arXiv · quant-ph/9706064

Information-theoretic approach to quantum error correction and reversible measurement

M. A. Nielsen·Carlton M. Caves·Benjamin Schumacher·Howard Barnum
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Abstract

Quantum operations provide a general description of the state changes allowed by quantum mechanics. The reversal of quantum operations is important for quantum error-correcting codes, teleportation, and reversing quantum measurements. We derive information-theoretic conditions and equivalent algebraic conditions that are necessary and sufficient for a general quantum operation to be reversible. We analyze the thermodynamic cost of error correction and show that error correction can be regarded as a kind of ``Maxwell demon,'' for which there is an entropy cost associated with information obtained from measurements performed during error correction. A prescription for thermodynamically efficient error correction is given.

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M. A. Nielsen, Carlton M. Caves, Benjamin Schumacher, Howard Barnum. 1997-06-30. Information-theoretic approach to quantum error correction and reversible measurement. https://doi.org/10.1098/rspa.1998.0160

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