We show that covert secret key expansion is possible using a public authenticated classical channel and a quantum channel largely under control of an adversary, which we precisely define. We also prove a converse result showing that, under the golden standard of quantum key distribution by which the adversary completely controls the quantum channel, no covert key generation is possible. We propose a protocol based on pulse-position modulation and multi-level coding that allows one to use traditional quantum key distribution (QKD) protocols while ensuring covertness, in the sense that no statistical test by the adversary can detect the presence of communication better than a random guess. When run over a bosonic channel, our protocol can leverage existing discrete-modulated continuous variable protocols. Since existing techniques to bound Eve's information do not directly apply, we develop a new bound that results in positive throughput for a range of channel parameters.
We show that covert secret key expansion is possible using a public authenticated classical channel and a quantum channel largely under control of an adversary, which we precisely define. We also prove a converse result showing that, under the golden standard of quantum key distribution by which the adversary completely controls the quantum channel, no covert key generation is possible. We propose a protocol based on pulse-position modulation and multi-level coding that allows one to use traditional quantum key distribution (QKD) protocols while ensuring covertness, in the sense that no statistical test by the adversary can detect the presence of communication better than a random guess. When run over a bosonic channel, our protocol can leverage existing discrete-modulated continuous variable protocols. Since existing techniques to bound Eve's information do not directly apply, we develop a new bound that results in positive throughput for a range of channel parameters.
We propose a protocol based on pulse-position modulation and multi-level coding that allows one to bootstrap traditional quantum key distribution protocols while ensuring covertness, in the sense that no statistical test by the adversary can detect the presence of communication over the quantum channel better than a random guess. When run over a bosonic channel, our protocol can leverage existing discrete-modulated continuous-variable protocols. Since existing techniques to bound Eve's information do not directly apply, we develop a new bound that results in positive, although very low, throughput for a range of channel parameters. The analysis of the protocol performance shows that covert secret key expansion is possible using a public authenticated classical channel and a quantum channel largely but not fully under the control of an adversary, which we precisely define. We also establish a converse result showing that, under the golden standard of quantum key distribution, by which the adversary completely controls the quantum channel, no covert key generation is possible.
We show that covert secret key expansion is possible against a restricted class of coherent attacks, which we characterize. Specifically, we propose a protocol based on pulse-position modulation and multi-level coding that allows one to use traditional quantum key distribution (QKD) protocols while ensuring covertness, in the sense that no statistical test by the adversary can detect the presence of communication better than a random guess. Covertness holds as long as there exists some noise in the channel that is not under the control of the adversary, which we model as a quantum channel preceding the adversary's apparatus.
Covert and secret quantum key distribution aims at generating information-theoretically secret bits between distant legitimate parties in a manner that remains provably undetectable by an adversary. We propose a framework in which to precisely define and analyze such an operation, and we show that covert and secret key expansion is possible. For fixed and known classical-quantum wiretap channels, we develop and analyze protocols based on forward and reverse reconciliation. The crux of our approach is the use of information reconciliation and privacy amplification techniques that are able to process the sparse signals required for covert operation and the Shannon entropy of which scales as the square root of their length. In particular, our results show that the coordination required between legitimate parties to achieve covert communication can be achieved with a negligible number of secret key bits.
We consider an enhanced measure of security for a quantum key distribution protocol, in which we require that the adversary not only obtains no information about the key but also remains unaware that a key generation protocol has been executed. When the adversary applies the same quantum channel independently to each transmitted quantum state, akin to a collective attack in the quantum key distribution literature, we propose a protocol that achieves covert and secret key expansion under mild restrictions. A crucial component of the protocol is a covert estimation stage, which is then combined with universal channel coding for reliability and resolvability in the covert regime.
We extend covert communication to the quantum regime by showing that covert quantum communication is possible over optical channels with noise arising either from the environment or from the sender's lab. In particular, we show that sequences of qubits can be transmitted covertly by using both a single photon and a coherent state encoding. We study the possibility of performing covert quantum key distribution (QKD) and show that positive key rates and covertness can be achieved simultaneously. Covert communication requires a secret key between the sender and receiver, which raises the problem of how this key can be regenerated covertly. We show that covert QKD consumes more secret bits than it can generate and propose instead a hybrid protocol for covert key regeneration that uses pseudorandom number generators (PRNGs) together with covert QKD to regenerate secret keys. The security of the new key is guaranteed by QKD while the security of the covert communication is at least as strong as the security of the PRNG.
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.