We develop the capacity region for the bosonic broadcast channel in the presence of thermal noise and photon loss due to the environment. The bosonic channel is a quantum-mechanical description of many practical communication links such as optical, microwave, and radiofrequency. We employ our results to find the capacity region for quantum-secure covert broadcast over such channels and show that time-division is optimal as in the classical covert broadcast scenario. We rely on a strong minimum entropy output conjecture, a direct result of the entropy photon-number inequality (EPnI) conjecture.
We develop the capacity region for the bosonic broadcast channel in the presence of thermal noise and photon loss due to the environment. The bosonic channel is a quantum-mechanical description of many practical communication links such as optical, microwave, and radiofrequency. We employ our results to find the capacity region for quantum-secure covert broadcast over such channels and show that time-division is optimal as in the classical covert broadcast scenario. We rely on a strong minimum entropy output conjecture, a direct result of the entropy photon-number inequality (EPnI) conjecture.
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.
Bosonic channels describe quantum-mechanically many practical communication links such as optical, microwave, and radiofrequency. We investigate the maximum rates for the bosonic multiple access channel (MAC) in the presence of thermal noise added by the environment and when the transmitters utilize Gaussian state inputs. We develop an outer bound for the capacity region for the thermal-noise lossy bosonic MAC. We additionally find that the use of coherent states at the transmitters is capacity-achieving in the limits of high and low mean input photon numbers. Furthermore, we verify that coherent states are capacity-achieving for the sum rate of the channel. In the non-asymptotic regime, when a global mean photon-number constraint is imposed on the transmitters, coherent states are the optimal Gaussian state. Surprisingly however, the use of single-mode squeezed states can increase the capacity over that afforded by coherent state encoding when each transmitter is photon number constrained individually.
We investigate the fundamental limit of quantumsecure covert communication over the lossy thermal noise bosonic channel, the quantum-mechanical mode underlying many practical channels. We assume that the adversary has unlimited quantum information processing capabilities as well as access to all transmitted photons that do not reach the legitimate receiver. Given existence of noise that is uncontrolled by the adversary, the square root law (SRL) governs covert communication: up to c√(n) covert bits can be transmitted reliably in n channel uses. Attempting to surpass this limit results in detection with unity probability as n → ∞. Here we present the expression for c, characterizing the SRL for the bosonic channel. We also prove that discrete-valued coherent state quadrature phase shift keying (QPSK) constellation achieves the optimal c, which is the same as that achieved by a circularly-symmetric complex-valued Gaussian prior on coherent state amplitude. Finally, while binary phase shift keying (BPSK) achieves the Holevo capacity for non-covert bosonic channels in the low received signal-to-noise ratio regime, we show that it is strictly sub-optimal for covert communication.
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.
We explore covert entanglement generation over the lossy thermal-noise bosonic channel, which is a quantummechanical model of many practical settings, including optical, microwave, and radio-frequency (RF) channels. Covert communication ensures that an adversary is unable to detect the presence of transmissions, which are concealed in channel noise. While covert communication of classical bits is well studied, covert quantum communication and entanglement generation remain largely unexplored. Here, we first show that a square root law (SRL) for covert classical secret communication over the lossy thermal-noise bosonic channel, defining the optimal rate and covert capacityLsec . The achievable construction relies on position-based coding, sequential decoding, and quadrature phase-shift keying. Furthermore, we adapt the code used in covert secret communication to show that a square root law (SRL) for covert entanglement generation similar to that for classical:LEGnentangled bits (ebits) can be generated covertly and reliably overnuses of a bosonic channel. We report a single-letter expression for optimalLEGas well as an achievable method. We additionally analyze the performance of covert entanglement generation using single- and dual-rail photonic qubits for varying channel parameters. Despite a performance gap compared to the optimal strategy, these encodings may be more practical for physical implementation.
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.