Classical capacity of quantum non-Gaussian attenuator and amplifier channels

• URL: http://arxiv.org/abs/2312.15623v1
• Date: Mon, 25 Dec 2023 06:05:51 GMT
• Title: Classical capacity of quantum non-Gaussian attenuator and amplifier channels
• Authors: Zacharie Van Herstraeten, Saikat Guha, Nicolas J. Cerf
• Abstract summary: We consider a quantum bosonic channel that couples the input mode via a beam splitter or two-mode squeezer to an environmental mode prepared in an arbitrary state. We investigate the classical capacity of this channel, which we call a non-Gaussian attenuator or amplifier channel.
• Score: 0.8409980020848168
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• 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.

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