Classical capacity of quantum non-Gaussian attenuator and amplifier channels

Abstract

We consider a quantum bosonic channel that couples the input mode via a beam splitter or two-mode squeezer to an environmental mode that is prepared in an arbitrary state. We investigate the classical capacity of this channel, which we call a non-Gaussian attenuator or amplifier channel. If the environment state is thermal, we of course recover a Gaussian phase-covariant channel whose classical capacity is well known. Otherwise, we derive both a lower and an upper bound to the classical capacity of the channel, drawing inspiration from the classical treatment of the capacity of non-Gaussian additive-noise channels. We show that the lower bound to the capacity is always achievable and give examples where the non-Gaussianity of the channel can be exploited so that the communication rate beats the capacity of the Gaussian-equivalent channel (i.e., the channel where the environment state is replaced by a Gaussian state with the same covariance matrix). Finally, our upper bound leads us to formulate and investigate conjectures on the input state that minimizes the output entropy of non-Gaussian attenuator or amplifier channels. Solving these conjectures would be a main step towards accessing the capacity of a large class of non-Gaussian bosonic channels.

17 pages + 1 page of Appendix, 9 figures

References in corpus (15)

• Superadditivity of communication capacity using entangled inputs
• Classical capacity of the lossy bosonic channel: the exact solution
• Ultimate communication capacity of quantum optical channels by solving the Gaussian minimum-entropy conjecture
• Minimum output entropy of bosonic channels: a conjecture
• A solution of the Gaussian optimizer conjecture
• Non-Gaussian operations on bosonic modes of light: Photon-added Gaussian channels
• Exact solution for the quantum and private capacities of bosonic dephasing channels
• Equivalence Relations for the Classical Capacity of Single-Mode Gaussian Quantum channels
• Quantum capacity of bosonic dephasing channel
• Capacity of a bosonic memory channel with Gauss-Markov noise
• Bosonic quantum communication across arbitrarily high loss channels
• Minimum output entropy of a non-Gaussian quantum channel
• Gaussian capacity of the quantum bosonic channel with additive correlated Gaussian noise
• Upper bounds on the quantum capacity for general attenuator and amplifier
• Thinning, photonic beamsplitting, and a general discrete entropy power inequality