Landauer's erasure, error correction and entanglement

Classical and quantum error correction are presented in the form of Maxwell's demon and their efficiency analysed from the thermodynamic point of view. We explain how Landauer's principle of information erasure applies to both cases. By then extending this principle to entanglement manipulations we rederive upper bounds on purification procedures, thereby linking the ‘no local increase of entanglement’ principle to the second law of thermodynamics.

[1]  Viola,et al.  Theory of quantum error correction for general noise , 1996, Physical review letters.

[2]  M. Plenio,et al.  Teleportation, entanglement and thermodynamics in the quantum world , 1998 .

[3]  Vlatko Vedral,et al.  Entanglement in Quantum Information Theory , 1998, quant-ph/9804075.

[4]  M. Plenio,et al.  Entanglement measures and purification procedures , 1997, quant-ph/9707035.

[5]  M. Nielsen,et al.  Information-theoretic approach to quantum error correction and reversible measurement , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[6]  H. Lo,et al.  Concentrating entanglement by local actions: Beyond mean values , 1997, quant-ph/9707038.

[7]  S. Lloyd Quantum-mechanical Maxwell’s demon , 1996, quant-ph/9612034.

[8]  E. Knill,et al.  Theory of quantum error-correcting codes , 1996, quant-ph/9604034.

[9]  Anthony J. G. Hey,et al.  Feynman Lectures on Computation , 1996 .

[10]  M. Plenio,et al.  Quantum correlations, local interactions and error correction , 1996, quant-ph/9608030.

[11]  Charles H. Bennett,et al.  Mixed-state entanglement and quantum error correction. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[12]  Charles H. Bennett,et al.  Concentrating partial entanglement by local operations. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[13]  Schumacher,et al.  Quantum coding. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[14]  M. Donald Free energy and the relative entropy , 1987 .

[15]  E. Lubkin,et al.  Keeping the entropy of measurement: Szilard revisited , 1987 .

[16]  Wojciech Hubert Zurek,et al.  Maxwell’s Demon, Szilard’s Engine and Quantum Measurements , 2003, quant-ph/0301076.

[17]  Charles H. Bennett,et al.  The thermodynamics of computation—a review , 1982 .

[18]  L. Szilard On the decrease of entropy in a thermodynamic system by the intervention of intelligent beings. , 1964, Behavioral science.

[19]  R. Landauer,et al.  Irreversibility and heat generation in the computing process , 1961, IBM J. Res. Dev..

[20]  J. Neumann Mathematical Foundations of Quantum Mechanics , 1955 .