Covert quantum communication is usually analyzed under idealized assumptions that channel parameters, such as transmissivity and background noise, are perfectly known and constant. In realistic optical links, including satellite, fiber, and free-space systems, these parameters vary because of environmental fluctuations, calibration noise, and estimation errors. We study covert quantum communication over compound quantum optical channels with bounded uncertainty in both transmissivity and thermal noise, and derive guarantees that hold for all admissible channel realizations. We develop a robust framework for certifying both covertness and reliability under uncertainty. A central finding is that robustness cannot be obtained by simply inserting worst-case parameter values into known-channel bounds: the channel realizations that are most adverse for covertness and reliability generally occur at different corners of the uncertainty set. This creates a fundamental trade-off in secure system design. We derive a closed-form lower bound on the worst-case guaranteed number of covert qubits that can be transmitted reliably, identify a sharp feasibility boundary beyond which the guaranteed payload drops to zero, and quantify the security penalty caused by uncertainty. We validate the covertness term with QuTiP simulations of a four-mode bosonic model and combine it with an analytical reliability bound to evaluate the robust payload. Our results move covert quantum communication from nominal perfect-knowledge analysis to certified worst-case operation under uncertainty.
Covert quantum communication is usually analyzed under idealized assumptions that channel parameters, such as transmissivity and background noise, are perfectly known and constant. In realistic optical links, including satellite, fiber, and free-space systems, these parameters vary because of environmental fluctuations, calibration noise, and estimation errors. We study covert quantum communication over compound quantum optical channels with bounded uncertainty in both transmissivity and thermal noise, and derive guarantees that hold for all admissible channel realizations. We develop a robust framework for certifying both covertness and reliability under uncertainty. A central finding is that robustness cannot be obtained by simply inserting worst-case parameter values into known-channel bounds: the channel realizations that are most adverse for covertness and reliability generally occur at different corners of the uncertainty set. This creates a fundamental trade-off in secure system design. We derive a closed-form lower bound on the worst-case guaranteed number of covert qubits that can be transmitted reliably, identify a sharp feasibility boundary beyond which the guaranteed payload drops to zero, and quantify the security penalty caused by uncertainty. We validate the covertness term with QuTiP simulations of a four-mode bosonic model and combine it with an analytical reliability bound to evaluate the robust payload. Our results move covert quantum communication from nominal perfect-knowledge analysis to certified worst-case operation under uncertainty.
Covert quantum communication (CQC) seeks to hide not only message content but also the existence of communication. Existing CQC models usually assume deterministic or worst-case channel conditions, which are difficult to justify in realistic free-space optical and quantum links affected by turbulence, fluctuating background radiance, and stochastic detector noise. We propose a stochastic risk-aware optimization framework for CQC under uncertain physical-layer conditions. By modeling transmissivity and background noise as random variables, we express covertness and reliability guarantees through chance constraints with explicit outage budgets εcov and εrel. This recasts CQC design as a risk-calibrated resource-allocation problem balancing throughput, covertness, reliability, and communication privacy. We derive quantile-based reformulations of the outage constraints, characterize feasible operating regions under stochastic uncertainty, and introduce a complementary risk-adjusted utility formulation to expose throughput-risk trade-offs. The analysis reveals that modest relaxations in acceptable covertness-outage risk can yield large throughput gains, while aggressive optimization may break covertness outside sparse-transmission regimes. Monte Carlo results under log-normal fading and stochastic thermal noise show that the framework expands feasible operating regions, improves covert throughput by more than an order of magnitude, and identifies degradation boundaries beyond which covert operation becomes unreliable. These results move CQC closer to realistic secure quantum networking for free-space, satellite, and low-probability-of-detection applications.
We explore covert communication of qubits over the lossy thermal-noise bosonic channel, which is a quantum-mechanical model of many practical channels, including optical. Covert communication ensures that an adversary is unable to detect the presence of transmissions, which are concealed in channel noise. We show a \emph{square root law} (SRL) for quantum covert communication similar to that for classical: ∝n qubits can be transmitted covertly and reliably over n uses of an optical channel. Our achievability proof uses photonic dual-rail qubit encoding, which has been proposed for long-range repeater-based quantum communication and entanglement distribution. Our converse employs prior covert signal power limit results and adapts well-known methods to upper bound quantum capacity of optical channels. Finally, we believe that the gap between our lower and upper bounds for the number of reliable covert qubits can be mitigated by improving the quantum error correction codes and quantum channel capacity bounds.
We explore covert communication of qubits over the lossy thermal-noise bosonic channel, which is a quantum-mechanical model of many practical channels, including optical. Covert communication ensures that an adversary is unable to detect the presence of transmissions, which are concealed in channel noise. We show a square root law (SRL) for quantum covert communication similar to that for classical:∝nqubits can be transmitted covertly and reliably overnuses of an optical channel. Our achievability proof uses photonic dual-rail qubit encoding, which has been proposed for long-range repeater-based quantum communication and entanglement distribution. Our converse employs prior covert signal power limit results and adapts well-known methods to upper bound quantum capacity of optical channels. Finally, we believe that the gap between our lower and upper bounds for the number of reliable covert qubits can be mitigated by improving the quantum error correction codes and quantum channel capacity bounds.
This dissertation explores covertness in two quantum settings: communication and computing. Covert communication refers to transmitting over a channel such that an adversary cannot detect the presence of the transmission, whereas covert quantum computing refers to running computations on a quantum computer that are undetectable by an adversary who is also using the same device. Although these problems arise from different physical phenomena, they share the common goal of preventing an adversary from detecting their operation. We begin by presenting the preliminaries and mathematical tools from quantum information theory required for covert analysis of communication over quantum channels and covert quantum computing. We then proceed to explore covert communication over the lossy thermal-noise bosonic channel, a quantum-mechanical model of many practical channels, including optical ones. First, we characterize the covert capacity region of the degraded lossy thermal-noise bosonic broadcast channel. We extend prior work on degraded bosonic broadcast channels to incorporate photon loss to an adversarial environment. We derive the classical capacity region and the covert capacity for the two-receiver case, and extend them to M receivers. We demonstrate that coherent-state encoding achieves these capacities and establish that time-division is optimal in the covert regime. These results rely on a strong minimum entropy output conjecture, a direct result of the entropy photon-number inequality (EPnI) conjecture. Building on covert communication, we develop a system construction for reliable transmission of covert qubits over an arbitrary quantum channel using single- and dual-rail encodings. We apply this construction to the lossy thermal-noise bosonic channel, thereby deriving achievable rates. We further explore the impact of access to a two-way classical communication link. While a tight upper bound remains an open problem, we provide a converse upper bound by decomposing the channel into a concatenation of a pure-loss channel and a quantum-limited amplifier and discarding the former. These bounds demonstrate a \emph{square root law} (SRL) for covert quantum communication similar to that for classical: M(n)∝n qubits can be transmitted covertly and reliably over n uses of the channel. We conjecture that the gap between our lower and upper bounds on the number of reliable covert qubits can be reduced by improving quantum error-correction codes and quantum channel capacity bounds. We then shift our focus to \emph{covert quantum computing}, introducing and formalizing a setting in which an adversary attempts to detect whether computation is occurring on a shared quantum processing unit (QPU) by monitoring a subset of the qubits or qumodes. For superconducting architectures with a nearest-neighbor crosstalk noise model and planar qubit topologies, a circuit remains covert by inserting idle qubits between the qubits running the computation and the remaining qubits on the QPU. Using discrete isoperimetric inequalities, we show that a circuit placement exists such that only O(n) spectator qubits bordering the circuit provide detection information to an adversary, where n is the number of qubits used for computation. Thus, in this setting, the cost of maintaining covertness while also maintaining reliability of the computation is an additional O(n) idle border qubits. We experimentally explore this model on IQM's Emerald processor, using Ramsey experiments on the adversary's qubits to detect gate operations. While nearest-neighbor crosstalk was detected as expected, long-range coupling effects were also observed beyond the border qubits, identifying a side channel that an adversary can exploit for detection. Finally, we discuss the outlook, future research directions, and open problems.
We establish the fundamental limits of covert communication over quantum channels, focusing on both finite-dimensional classical-quantum (CQ) channels and the infinite-dimen\-sional lossy thermal-noise bosonic channel. For general memoryless CQ channels, we characterize when covert communication is possible and prove a square root law (SRL): at most Ln+o(n) bits can be reliably transmitted covertly over n uses of the channel where L is the channel-dependent covert capacity. We derive a single-letter expression for L and show that the required pre-shared secret key also scales as n under mild conditions. We also identify and characterize corner cases where either constant-rate or zero-rate covert communication is possible. For the bosonic channel, we prove that the SRL holds and derive exact covert capacities under different resource assumptions. In particular, we show that the covert secrecy and covert entanglement generation capacities both equal the covert classical capacity without entanglement-assistance, Lno-EA, and show that the required pre-shared classical secret key scales as n. We also find that quadrature phase-shift keying (QPSK) achieves the optimal covert capacity, outperforming binary modulation in contrast to the classical channel setting. When Alice and Bob instead share entanglement, the covert classical capacity improves to LEAnlogn+o(nlogn), though this scaling is sensitive to noise in the entangled resource. Finally, we propose a practical covert transceiver and simulate its performance compared to recently experimentally-tested transceivers under realistic conditions.
Quantum-secure covert communication is an emerging technology crucial for secure transmission in hostile environments. However, existing studies primarily focus on single-transmitter scenarios, leaving a gap in the research on multi-user settings. This paper investigates the fundamental limits of quantum-secure covert communications over lossy bosonic random access channels with Gaussian thermal noise in view of realistic communication systems. The square root law is first established in the scenario where only randomly activated covert users exist. We then demonstrate that the square root law can be surpassed with the assistance of randomly activated overt users in quantum communication system, enabling covert users to transmitO(N)bits of information overNchannel uses, provided that the mean photon numbers of all users reaching the detecting end are equal. To prove this, a recursive upper bound is developed on the trace distance (TD) to measure the detection probability of the warden, which is tighter than the traditional quantum relative entropy measurement. However, if the mean photon number of any covert user deviates from the above condition, its covert capacity will degrade toO(N)bits, whereas the capacities of other users will remain atO(N)bits. This result is derived by exploiting the iterative relationship of the upper bound of TD and introducing a two-step detection strategy for the warden to handle random user activation uncertainty. Numerical experiments validate the theoretical findings, confirming the performance of covert transmission in both scenarios.