Polarization of Quantum Channels Using Clifford-Based Channel Combining

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