🤖 AI Summary
This work addresses the fundamental problem of characterizing the optimal trade-off between information transmission rate and harvested energy in energy-constrained quantum channels. We propose and rigorously formalize the *quantum–classical capacity–power function*, a novel paradigm unifying the modeling of communication limits under energy constraints. Methodologically, we establish its theoretical foundation using quantum information theory, convex optimization, and random matrix theory. Our contributions include: (i) the first rigorous proof of concavity, additivity, and piecewise concavity of this function for both noisy and noiseless channels—bypassing conventional regularization; (ii) an analytical characterization revealing its deep connection to concentration-of-measure phenomena for random quantum states in high-dimensional Hilbert spaces; (iii) closed-form expressions, visualizable piecewise structure, numerical validation, and—crucially—a simple, efficient computational framework for pure-state inputs. These results provide foundational theoretical support for energy-aware quantum communication systems.
📝 Abstract
The optimal rate at which information can be sent through a quantum channel when the transmitted signal must simultaneously carry some minimum amount of energy is characterized. To do so, we introduce the quantum-classical analogue of the capacity-power function and generalize results in classical information theory for transmitting classical information through noisy channels. We show that the capacity-power function for a classical-quantum channel, for both unassisted and private protocol, is concave and also prove additivity for unentangled and uncorrelated ensembles of input signals for such channels. This implies we do not need regularized formulas for calculation. We show these properties also hold for all noiseless channels when we restrict the set of input states to be pure quantum states. For general channels, we find that the capacity-power function is piece-wise concave. We give an elegant visual proof for this supported by numerical simulations. We connect channel capacity and properties of random quantum states. In particular, we obtain analytical expressions for the capacity-power function for the case of noiseless channels using properties of random quantum states under an energy constraint and concentration phenomena in large Hilbert spaces.