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Covert Quantum Communication Over Bosonic Channels and Covert Quantum Computing

Evan J. D. Anderson

Published Jan 1, 2025• 0 citations
OpenAlex

Abstract

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: $M(n)\propto\sqrt{n}$ 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 $\mathcal{O}(\sqrt{n})$ 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 $\mathcal{O}(\sqrt{n})$ 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.

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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: $\propto\sqrt{n}$ 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.

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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:$\propto\sqrt{n}$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.

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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 MMM 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)∝nM(n)\propto\sqrt{n}M(n)∝n​ qubits can be transmitted covertly and reliably over nnn 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)\mathcal{O}(\sqrt{n})O(n​) spectator qubits bordering the circuit provide detection information to an adversary, where nnn 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)\mathcal{O}(\sqrt{n})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 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\propto\sqrt{n}∝n​ qubits can be transmitted covertly and reliably over nnn 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:∝n\propto\sqrt{n}∝n​qubits can be transmitted covertly and reliably overnnnuses 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 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 L_{\text{sec }}Lsec ​. 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:LEGnL_{\text{EG}} \sqrt{n}LEG​n​entangled bits (ebits) can be generated covertly and reliably overnnnuses of a bosonic channel. We report a single-letter expression for optimalLEGL_{\text{EG}}LEG​as 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 an arbitrary quantum channel. Covert communication conceals the transmissions in the channel noise, ensuring that an adversary is unable to detect their presence. We show the achievability of a square root law (SRL) for quantum covert communication similar to that for classical:M(n)nM(n) \sqrt{n}M(n)n​qubits can be transmitted covertly and reliably overnnnuses of a general quantum channel. We lower boundM(n)M (n)M(n)with and without assistance from a two-way covert classical channel. In the former case, we quantify the number of classical covert bits sufficient for our protocol.
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)L\sqrt{n} + o(\sqrt{n})Ln​+o(n​) bits can be reliably transmitted covertly over nnn uses of the channel where LLL is the channel-dependent covert capacity. We derive a single-letter expression for LLL and show that the required pre-shared secret key also scales as n\sqrt{n}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-EAL_{\text{no-EA}}Lno-EA​, and show that the required pre-shared classical secret key scales as n\sqrt{n}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 LEAnlog⁡n+o(nlog⁡n)L_{\text{EA}} \sqrt{n} \log n + o(\sqrt{n} \log n)LEA​n​logn+o(n​logn), 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.
As quantum computers become available through multi-tenant cloud platforms, ensuring privacy against adversaries sharing the same quantum processing unit becomes critical. We introduce and explore \emph{covert quantum computing}, a new concept that ensures an adversary with access to all other quantum computational units (QCUs) of a quantum computer cannot detect computation on the subset that they cannot access. Analogous to covert communication, we employ information theory. However, since here the adversary controls the systems used for detection, we require a richer framework for covertness analysis that accounts for the use of quantum memories and adaptive operations. Thus, we adopt the \emph{quantum-strategy} framework used in quantum game theory and memory channel discrimination. Current quantum computers use planar graph circuit layouts and typically assume nearest-neighbor crosstalk. We derive discrete isoperimetric inequalities to show that, for an nnn-qubit circuit under this model, only O(n)\mathcal{O}(\sqrt{n})O(n​) border qubits provide detection information to the adversary. We then explore this scaling law on IQM's 54-qubit \emph{Emerald} processor and IBM's 156-qubit \emph{ibm\_fez} machine employing the Heron 2 architecture. We implement Ramsey experiments on qubits not used in computation, and detect nearest-neighbor crosstalk, as expected. However, we also observe long-range coupling effects beyond the border qubits, revealing a side channel that the adversary can exploit. We hypothesize that this long-range crosstalk is induced by leakage from the drive and control lines. Beyond weakening covertness, it exposes co-tenants to both adversarial and unintended crosstalk and degrades circuits that span spatially distributed qubits, motivating further work on spatial isolation and crosstalk characterization.