Activation of quantum capacity is a surprising phenomenon according to which the quantum capacity of a certain channel may increase by combining it with another channel with zero quantum capacity. Superactivation describes an even more particular occurrence, in which both channels have zero quantum capacity, but their composition has a nonvanishing one. We investigate these effects for all single-mode phase-insensitive Gaussian channels, which include thermal attenuators and amplifiers, assisted by a two-mode positive-partial-transpose channel. Our result shows that activation phenomena are special but not uncommon. We can reveal superactivation in a broad range of thermal attenuator channels, even when the transmissivity is quite low, or the thermal noise is high. This means that we can transmit quantum information reliably through very noisy Gaussian channels with the help of another Gaussian channel, whose quantum capacity is also zero. We further show that no superactivation is possible for entanglement-breaking Gaussian channels in physically relevant circumstances by proving the nonactivation property of the coherent information of bosonic entanglement-breaking channels with finite input energy.
There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises, including squeezing or even non-Gaussian cases. We introduce new upper bounds on the energy-constrained quantum capacity of those channels by using the conditional quantum entropy power inequality. Also, we obtain lower bounds for the same channels by means of Gaussian optimizer with fixed input entropy. They give narrow bounds when the transmissivity is near unity and the energy of input state is low.
There have been several upper bounds on the quantum capacity of the single-mode Gaussian channels with thermal noise, such as thermal attenuator and amplifier. We consider a class of attenuator and amplifier with more general noises, including squeezing or even non-Gaussian noises. We derive upper bounds the energy-constrained quantum capacity of those channels by using the quantum conditional entropy power inequality. Also, we obtain lower bounds for the same channels by means of Gaussian optimizer with fixed input entropy. They give narrow bounds when the transmissivity is near unity and the energy of input state is low.
Thermal attenuator channels model the decoherence of quantum systems interacting with a thermal bath, e.g., a two-level system subject to thermal noise and an electromagnetic signal traveling through a fiber or in free-space. Hence determining the quantum capacity of these channels is an outstanding open problem for quantum computation and communication. Here we derive several upper bounds on the quantum capacity of qubit and bosonic thermal attenuators. We introduce an extended version of such channels which is degradable and hence has a single-letter quantum capacity, bounding that of the original thermal attenuators. Another bound for bosonic attenuators is given by the bottleneck inequality applied to a particular channel decomposition. With respect to previously known bounds we report better results in a broad range of attenuation and noise: we can now approximate the quantum capacity up to a negligible uncertainty for most practical applications, e.g., for low thermal noise.
We determine the exact quantum communication and entanglement-distribution capacities of three fundamental bosonic channels, namely thermal loss, thermal amplification and additive Gaussian noise, assisted by operations that completely preserve positive partial transpose (PPT). These operations are more powerful than local operations and classical communication (LOCC), but cannot generate distillable entanglement on their own. For thermal loss, the unconstrained capacity coincides with the Pirandola-Laurenza-Ottaviani-Banchi (PLOB) bound throughout the non-entanglement-breaking regime. The corresponding upper bounds are also attained for thermal amplification and additive noise. We extend these results to energy-constrained communication, establishing exact capacities for all three channels at every prescribed mean input energy. Our results solve a class of bosonic capacity problems under PPT assistance and establish exact benchmarks for determining whether the same communication rates can be achieved via LOCC alone.
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.