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arXiv:quant-ph/9705043 · Physics Letters A

A demonstration of superadditivity in the classical capacity of a quantum channel

Masahide Sasaki, Kentaro Kato, Masayuki Izutsu, Osamu Hirota

Published Dec 1, 1997• 32 citations
arXivHTMLPDF
DOI
10.1016/s0375-9601(97)00740-8

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Finding the optimal encoding strategies can be challenging for communication using quantum channels, as classical and quantum capacities may be superadditive. Entanglement assistance can often simplify this task, as the entanglement-assisted classical capacity for any channel is additive, making entanglement across channel uses unnecessary. If the entanglement assistance is limited, the picture is much more unclear. Suppose the classical capacity is superadditive, then the classical capacity with limited entanglement assistance could retain superadditivity by continuity arguments. If the classical capacity is additive, it is unknown if superadditivity can still be developed with limited entanglement assistance. We show this is possible, by providing an example. We construct a channel for which the classical capacity is additive, but that with limited entanglement assistance can be superadditive. This shows entanglement plays a weird role in communication, and we still understand very little about it.
The amount of information transmissible through a communications channel is determined by the noise characteristics of the channel and by the quantities of available transmission resources. In classical information theory, the amount of transmissible information can be increased twice at most when the transmission resource is doubled for fixed noise characteristics. In quantum information theory, however, the amount of information transmitted can increase even more than twice. We present a proof-of-principle demonstration of this superadditivity of classical capacity of a quantum channel by using the ternary symmetric states of a single photon, and by event selection from a weak coherent light source. We also show how the superadditive coding gain, even in a small code length, can boost the communication performance of the conventional coding technique.
We introduce new type of superadditivity for classical capacity of quantum channels, which involves the properties of channels' environment.By imposing different restrictions on the total energy contained in channels' environment we can consider different types of superadditivity.Using lossy bosonic and additive noise quantum channels as examples, we demonstrate that their capacities can be either additive or superadditive depending on the values of channels parameters.The parameters corresponding to transition between the additive and superadditive cases are related with recently found critical and supercritical parameters for Gaussian channels.