For a quantum channel of additive Gaussian noise with loss, in the general case of
n copies input, we show that up to first order perturbation, any non-Gaussian perturbation to the product thermal state input has a less quantum information transmission rate when the input energy tend to infinitive.
The quantum capacity of thermal noise channel (which is addressed as Gaussian quantum channel before) is studied, it turns out to be the maximum of the coherent information of a single use of the channel. The quantum capacity is achieved when the input state is a thermal noise state with infinitive energy. The capacity is achievable with quantum error-correction code. The quantum capacities of thermal noise channels with damping or amplification are also given. One of the most important issues of classical information theory is the Shannon formula, which is the capacity of an additive white Gaussian noise channel. It is achieved when the input is a Gaussian noise source with power constrain [1] [2]. C = log2 (1 + S), (1)
The quantum capacity of the bosonic thermal attenuator, which is given by the regularization of its coherent information, is unknown. The seminal work of Holevo and Werner established in 1999 the standard one-use lower bound obtained from input thermal states. We first prove that this long-standing lower bound is the exact supremum over all single-mode Gaussian states and then show that, crucially, a non-Gaussian state can do better. As a consequence, we prove positivity of the quantum capacity in a parameter region where the channel is not antidegradable, yet its coherent information optimized over single-mode Gaussian states vanishes. For example, with one thermal photon in the environment and at transmissivity
η=0.8, the coherent information is non-positive for every single-mode Gaussian input. We give an explicit rank-two non-Gaussian state, supported on only six Fock levels, whose coherent information is certified to be at least
4.7×10−4 qubits per channel use. This short witness is far from numerically optimal: a numerical optimization over fixed non-Gaussian families reaches at least
8.4×10−3 qubits per channel use at the same point. More generally, at
ν=1, using non-Gaussian inputs we certify positivity of the coherent information, and therefore of the quantum capacity, down to
η=0.7841; by contrast, the channel is antidegradable, and hence has zero quantum capacity, for
η≤0.75. Overall, our work identifies new high-noise regimes in which bosonic quantum communication is possible.
We present an algorithm for calculation of the Gaussian classical capacity of a quantum bosonic memory channel with additive Gaussian noise. The algorithm, restricted to Gaussian input states, is applicable to all channels with noise correlations obeying certain conditions and works in the full input energy domain, beyond previous treatments of this problem. As an illustration, we study the optimal input states and capacity of a quantum memory channel with Gauss-Markov noise [J. Sch\"afer, Phys. Rev. A 80, 062313 (2009)]. We evaluate the enhancement of the transmission rate when using these optimal entangled input states by comparison with a product coherent-state encoding and find out that such a simple coherent-state encoding achieves not less than 90
of the capacity.
We study the transmission of classical information via optical Gaussian channels with a classical additive noise under the physical assumption of a finite input energy including the energy of classical signal (modulation) and the energy spent on squeezing the quantum states carrying information. Multiple uses of a certain class of memory channels with correlated noise is equivalent to one use of parallel independent channels generally with a phase-dependent noise. The calculation of the channels capacity implies finding the optimal distribution of the input energy between the channels. Above a certain input energy threshold, the optimal energy distribution is given by a solution known in the case of classical channels as water-filling. Below the threshold, the optimal distribution of the input energy depends on the noise spectrum and on the input energy level, so that the channels fall into three different classes: the first class corresponds to very noisy channels excluded from information transmission, the second class is composed of channels in which only one quadrature (q or p) is modulated and the third class corresponds to the water-filling solution. Although the non-modulated quadrature in the channels of the second class is not used for information transmission, a part of the input energy is used for the squeezing the quantum state which is a purely quantum effect. We present a complete solution to this problem for one mode and analyze the influence of the noise phase dependence on the capacity. Contrary to our intuition, in the highly phase-dependent noise limit, there exists a universal value of the capacity which neither depends on the input energy nor on the value of noise temperature. In addition, similarly to the case of lossy channels for weak thermal contribution of the noise, there exists an optimal squeezing of the noise, which maximizes the capacity.