Approximate Quantum Error Correction

X iv :q ua nt -p h/ 01 12 10 6v 1 1 8 D ec 2 00 1 Approximate quantum error correction Benjamin Schumacher and Michael D. Westmoreland February 1, 2008 Department of Physics, Kenyon College, Gambier, OH 43022 USA Department of Mathematical Sciences, Denison University, Granville, OH 43023 USA Abstract The errors that arise in a quantum channel can be corrected perfectly if and only if the channel does not decrease the coherent information of the input state. We show that, if the loss of coherent information is small, then approximate quantum error correction is possible. 1 Perfect quantum error correction The problem of quantum information transfer via a channel can be cast as the problem of sending quantum entanglement using the channel [1]. Suppose R and Q are subsystems of a composite quantum system initially in a pure entangled state ∣