Polarization of Quantum Channels using Cliffordbased Channel Combining
Abstract
We provide a purely quantum version of polar codes, achieving the symmetric coherent information of any qubitinput quantum channel. Our scheme relies on a recursive channel combining and splitting construction, where a twoqubit gate randomly chosen from the Clifford group is used to combine two singlequbit channels. The inputs to the synthesized bad channels are frozen by preshared EPR pairs between the sender and the receiver, so our scheme is entanglement assisted. We further show that quantum polarization can be achieved by choosing the channel combining Clifford operator randomly, from a much smaller subset of only nine twoqubit Clifford gates. Subsequently, we show that a Pauli channel polarizes if and only if a specific classical channel over a foursymbol input set polarizes. We exploit this equivalence to prove fast polarization for Pauli channels, and to devise an efficient successive cancellation based decoding algorithm for such channels. Finally, we present a code construction based on chaining several quantum polar codes, which is shown to require a rate of preshared entanglement that vanishes asymptotically.
 Publication:

arXiv eprints
 Pub Date:
 April 2019
 arXiv:
 arXiv:1904.04713
 Bibcode:
 2019arXiv190404713D
 Keywords:

 Quantum Physics
 EPrint:
 38 pages, 6 figures