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.
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.
In this paper, we investigate the additivity phenomenon in the quantum dynamic capacity region of a quantum channel for trading the resources of classical communication, quantum communication, and entanglement. Understanding such an additivity property is important if we want to optimally use a quantum channel for general communication purposes. However, in a lot of cases, the channel one will be using only has an additive single or double resource capacity region, and it is largely unknown if this could lead to a strictly superadditive double or triple resource capacity region, respectively. For example, if a channel has additive classical and quantum capacities, can the classical-quantum capacity region be strictly superadditive? In this paper, we answer such questions affirmatively. We give proof-of-principle requirements for these channels to exist. In most cases, we can provide an explicit construction of these quantum channels. The existence of these superadditive phenomena is surprising in contrast to the result that the additivity of both classical-entanglement and classical-quantum capacity regions imply the additivity of the triple resource capacity region for a given channel.
The classical capacity of quantum channels is the tight upper bound for the transmission rate of classical information. This is a quantum counterpart of the foundational notion of the channel capacity introduced by Shannon. Bosonic Gaussian quantum channels provide a good model for optical communications. In order to properly define the classical capacity for these quantum systems, an energy constraint at the channel input is necessary, as in the classical case. A further restriction to Gaussian input ensembles defines the Gaussian (classical) capacity, which can be studied analytically. It also provides a lower bound on the classical capacity and moreover, it is conjectured to coincide with the classical capacity. Therefore, the Gaussian capacity is a useful and important notion in quantum information theory. Recently, we have shown that the study of both the classical and Gaussian capacity of an arbitrary single mode Gaussian quantum channel can be reduced to the study of a particular fiducial channel. In this work we consider the Gaussian capacity of the fiducial channel, discuss its additivity and analyze its dependence on the channel parameters. In addition, we extend previously obtained results on the optimal channel environment to the single mode fiducial channel. In particular, we show that the optimal channel environment for the lossy, amplification, and phase conjugating channels is given by a pure quantum state if its energy is constrained.
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.
Quantum communication channels differ from their classical counterparts because their capacities can be superadditive. The principle of monogamy of entanglement suggests that superadditive improvements in the transmission capacity of a channel should reduce the amount of information loss to the environment. We challenge this intuition by demonstrating that the coherent and private information of a channel and its complement can be simultaneously superadditive for arbitrarily many channel uses. To quantify the limits of this effect, we consider the notion of max (resp. total) private information of a channel, which represents the maximum (resp. sum) of the private information of the channel itself and its complement, and study its relationship with the coherent information of the individual direct and complementary channels. We show that these quantities can obey different interleaving sequences of inequalities for a varying number of channel uses.
Abstract A brief general review is presented of the theory of information transmission capacities of quantum communication channels, which is a development of the classical Shannon theory. Unlike a classical communication channel, a quantum channel is characterised by a whole set of different capacities, which depend on the type of transmitted information (classical or quantum) and on additional resources used during transmission. The main characteristics of a quantum channel are considered: classical capacity, capacity assisted by entanglement between the channel input and output, quantum capacity and secret classical capacity. The unique role of the quantum entanglement property, which manifests itself, in particular, in a nonclassical phenomenon of capacity superadditivity, is emphasised.
We study classical capacity regions of quantum Gaussian multiple access channels (MAC). In classical variants of such channels, whilst some capacity superadditivity-type effects such as the so called water filling effect may be achieved, a fundamental classical additivity law can still be identified, viz. adding resources to one sender is never advantageous to other senders in sending their respective information to the receiver. Here, we show that quantum resources allow violation of this law, by providing an illustrative scheme of an experimentally feasible Gaussian MAC.