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arXiv:2606.00406

Quantum Simultaneous Information and Power Transfer: Capacity-Power Trade-offs in Discrete and Continuous Channels

Nizar Khalfet, Ioannis Krikidis

Published May 29, 2026• 0 citations
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Abstract

This paper introduces a new framework for quantum simultaneous information and power transfer (QSIPT), enabling the joint use of quantum states for classical information and energy transfer in quantum communication systems. We propose a model in which quantum states simultaneously transmit classical information through a quantum channel and transfer energy to an energy harvesting (EH) receiver. The trade-off between communication rate and harvested energy is characterized by the capacity-power function, defined for both discrete-variable (DV) and continuous-variable (CV) quantum channels. For DV channels, we derive properties of the capacity-power function, providing analytical upper and lower bounds for the amplitude damping channel and an exact closed-form characterization for the quantum erasure channel. For CV channels, we extend the framework by introducing a generalized beam-splitter (BS) receiver with adjustable transmissivity, jointly optimized with a transmitter mean-photon-number budget, splitting the channel output between the information decoder and the EH receiver. We analyze the capacity-power and achievable-rate-power trade-off under various Gaussian encoding schemes, including coherent, squeezed, and thermal states, for both lossy bosonic and additive Gaussian noise channels. Closed-form expressions are derived for coherent-state encoding under the joint photon-number-budget and adjustable-transmissivity formulation; squeezed-state inputs are evaluated numerically. Our results show that, within the considered displaced Gaussian encoding class, coherent states achieve the best capacity-power trade-off, squeezed states do not outperform coherent-state encoding under the phase-insensitive channel and passive receiver architecture, and thermal states enable energy transfer without supporting reliable communication.

DOI
10.48550/arxiv.2606.00406

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This paper introduces a new framework for quantum simultaneous information and power transfer (QSIPT), enabling the joint use of quantum states for classical information and energy transfer in quantum communication systems. We propose a model in which quantum states simultaneously transmit classical information through a quantum channel and transfer energy to an energy harvesting (EH) receiver. The trade-off between communication rate and harvested energy is characterized by the capacity-power function, defined for both discrete-variable (DV) and continuous-variable (CV) quantum channels. For DV channels, we derive properties of the capacity-power function, providing analytical upper and lower bounds for the amplitude damping channel and an exact closed-form characterization for the quantum erasure channel. For CV channels, we extend the framework by introducing a generalized beam-splitter (BS) receiver with adjustable transmissivity, jointly optimized with a transmitter mean-photon-number budget, splitting the channel output between the information decoder and the EH receiver. We analyze the capacity-power and achievable-rate-power trade-off under various Gaussian encoding schemes, including coherent, squeezed, and thermal states, for both lossy bosonic and additive Gaussian noise channels. Closed-form expressions are derived for coherent-state encoding under the joint photon-number-budget and adjustable-transmissivity formulation; squeezed-state inputs are evaluated numerically. Our results show that, within the considered displaced Gaussian encoding class, coherent states achieve the best capacity-power trade-off, squeezed states do not outperform coherent-state encoding under the phase-insensitive channel and passive receiver architecture, and thermal states enable energy transfer without supporting reliable communication.
This paper investigates the capacity-power trade-off in quantum communication channels under energy harvesting (EH) constraints, introducing a novel framework for analyzing the impact of the harvested energy requirements on the achievable channel capacity. We extend the conventional study of quantum channel capacity by incorporating realistic EH models into the analysis for both discrete-variable and continuous-variable quantum channels. Specifically, we explore the amplitude damping channel and quantum erasure channel as representative examples of discrete channels as well as the lossy bosonic channel and additive Gaussian noise channel for the continuous variable case. For each channel, we derive the capacity-power function by solving appropriate optimization problems that balance information transfer and EH requirements. Our results reveal critical insights into the interplay between quantum information transfer and EH constraints, highlighting fundamental trade-offs that are essential for designing an efficient quantum communication systems with EH.
This paper investigates a quantum relay-assisted free-space optical (FSO) communication system in which a decode-and-forward relay is powered by time-switching optical energy harvesting and forwards the decoded information using displaced squeezed signaling (DSS). To obtain a physically con sistent description of turbulence-induced loss for non-classical signaling, each hop is modeled as a pure-loss bosonic chan nel whose random transmissivity follows a truncated Gamma Gamma law, i.e., the Gamma-Gamma irradiance conditioned on the physically admissible range of a transmittance. Under this channel, coherent states remain pure, whereas squeezed states are mapped to mixed Gaussian states. Under Helstrom-optimal detection, the average error of the coherent hop is derived in exact Laplace-series form. For the DSS hop, we derive the output states, a closed-form Gaussian fidelity with rigorous two sided bounds on the Helstrom error, and prove the existence of a loss-aware optimal photon partition. Furthermore, we prove that optimized squeezing preserves both the turbulence-induced diversity order and the leading asymptotic constant of coherent relaying, so that its benefit is a finite-photon-budget effect, and that an interior throughput-optimal harvesting fraction exists. A covariance-preserving benchmark with an exact series representation yields an analytical upper bound on the achievable throughput whose absolute gap vanishes as the relay photon budget grows. Numerical results based on the exact mixed-state Helstrom error quantify the benefit of squeezing and the regime in which it is useful.
Quantum capacity gives the fundamental limit of information transmission through a channel. However, evaluating the quantum capacities of a continuous-variable bosonic quantum channel, as well as finding an optimal code to achieve the optimal information transmission rate, is in general challenging. In this work, we derive the quantum capacity and entanglement-assisted quantum capacity of the bosonic continuous-variable erasure channel when subject to energy constraints. We then construct random codes based on scrambling information within the typical subspace of the encoding state and prove that these codes are asymptotically optimal up to a constant gap. Finally, using our random coding scheme we design a bosonic variation of the Hayden-Preskill protocol and find that information recovery depends on the ratio between the input and output modes. This is in contrast with the conventional discrete-variable scenario which requires only a fixed number of additional output qudits.
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 analog of the capacity-power function, and we 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 we also prove additivity for unentangled and uncorrelated ensembles of input signals for such channels. This implies that we do not need regularized formulas for calculation. We show that 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 geometrically prove that the capacity-power function is piecewise concave, with further support from numerical simulations. Further, we connect channel capacity to 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.
As quantum information systems mature, efficient and coherent transfer of quantum information through noisy channels becomes increasingly important. We examine how passive environment-assisted quantum communication enhances direct quantum information transfer efficiency. A bosonic pure-loss channel, modeled as transmission through a beam splitter with a vacuum input state at the dark port, has zero quantum capacity when transmissivity is below 50%. Quantum communication through the channel can be enhanced by passive environment assistance, achieved via the selection of an appropriate input state for the ancilla port. Although ideal Gottesman-Kitaev-Preskill (GKP) states enable perfect quantum information transmission at arbitrarily small transmissivity, they are challenging to realize experimentally. We therefore explore more experimentally accessible non-Gaussian ancilla states, such as Fock, cat, and squeezed cat states, and numerically determine the optimal encoding and decoding strategies. We also construct analytical schemes that yield high-fidelity transmission and good information rates.
An important problem in quantum information theory is finding the best possible performance of the optical communication channel employing suitable codewords, receiver design, and constellation optimization techniques. Many receiver designs have been studied in the past to discriminate Phase-Shift Keying (PSK) quantum states that are used to encode information before transmitting over the communication channel. Among many types of quantum states, there has been significant work on the use of coherent states for encoding information. Previous work has sought to improve the communication performance in terms of various metrics such as error probability of state discrimination and capacities by employing a number of quantum states such as coherent states and squeezed-displaced states. In this thesis, we provide optimal receiver design employing coherent states and squeezed-displaced states to maximize the mutual information and lower the error probability of state discrimination. In the case of pure coherent states, we derive an alternative channel capacity of phase-shift keying coherent state with a realizable displacement receiver by maximizing mutual information over symbol priors and pre-detection displacement. We find that the capacity is higher than the capacity achieved by maximizing mutual information over symbol prior but with zero displacements. The overall scheme demonstrates designing an improved, yet easy-to-implement receiver for better communication performance by tuning it at different photon number regime. We also explore the use of squeezing operations with a displacement receiver for state discrimination. Our calculation demonstrates that we see no performance improvement in terms of the probability of error of state discrimination or mutual information using displacement receivers when optimal squeezing on the transmitter side is used. In addition, we also study the receiver design scheme for QPSK modulation where squeezing is employed at the receiver side. We find that using the squeezing operation on the receiver side provides an advantage in terms of increased mutual information for the low-photon number regime compared to when no squeezing is used. In the later part of the thesis, we study entanglement-assisted communication using two-mode squeezing vacuum. The use of pre-shared entanglement in entanglement-assisted communication provides a superior alternative to classical communication specifically in the low brightness regime and highly noisy environment. In this thesis, we analyze the performance of a few low-complexity receivers that employ optical parametric amplifiers. In the simulation, we demonstrate that receiver designs with an entanglement-assisted scheme using phase-shift-keying modulation can outperform classical capacities. We describe a newly proposed 2x2 optical hybrid receiver for entanglement-assisted communication whose performance is roughly 10% better in terms of error probability as compared to previously proposed optical parametric amplifier-based receivers. Further, we find that using unequal priors for BPSK provides approximately three times the advantage over equal priors in terms of information rate.