Quantum Capacity and Coding

Noboru Watanabe

Markus Grassl, Zhengfeng Ji, Zhaohui Wei +1 more

The quantum-channel capacity gives the ultimate limit for the rate at which quantum data can be reliably transmitted through a noisy quantum channel. Degradable quantum channels are among the few channels whose quantum capacities are known. Given the quantum capacity of a degradable channel, it remains challenging to find a practical coding scheme which approaches capacity. Here we discuss code designs for the detected-jump channel, a degradable channel with practical relevance describing the physics of spontaneous decay of atoms with detected photon emission. We show that this channel can be used to simulate a binary classical channel with both erasures and bit flips. The capacity of the simulated classical channel gives a lower bound on the quantum capacity of the detected-jump channel. When the jump probability is small, it almost equals the quantum capacity. Hence using a classical capacity-approaching code for the simulated classical channel yields a quantum code which approaches the quantum capacity of the detected-jump channel.

François Chapeau‐Blondeau

Graeme Smith, John A. Smolin

A striking feature of quantum error correcting codes is that they can sometimes be used to correct more errors than they can uniquely identify. Indeed, such degenerate codes are known to outperform all non-degenerate codes for very noisy quantum channels. As a result, rather than being chosen randomly according to some i.i.d. distribution, capacity achieving quantum codes must be chosen in a highly structured fashion. While there is no systematic understanding of how to design such codes, I will describe our best understanding of the problem. I will also briefly discuss a single-letter upper bound on the quantum capacity and its relation to the capacitypsilas possible additivity.

Vlatko Vedral

Shogo Usami, Tsuyoshi Sasaki Usuda, Ichi Takumi +2 more

Analytical solution of mutual information by square-root measurement for binary linear code is given. Applying the solution, we show properties of superadditivity in capacity by BCH codes with codeword length 15 and 31. Furthermore, we refer to codes almost achieving the quantum channel capacity.