EPR pairs can be distributed covertly and reliably over n channel uses. We begin with covert communication of classical information under a secrecy constraint. We then leverage this result to construct a coding scheme for covert entanglement generation. Consequently, the covert entanglement-generation capacity is the same as for classical information without secrecy, albeit our scheme employs a larger key.

DOI: 10.1109/itw62417.2025.11240442

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arXiv:2503.21002IEEE Transactions on Information TheoryApr 30, 20260 citations

Covert Entanglement Generation Over Bosonic Channels

Evan J. D. Anderson, Michael S. Bullock, Ohad Kimelfeld +4 more

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 capacity $L_{\text{sec }}$ . 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: $L_{\text{EG}} \sqrt{n}$ entangled bits (ebits) can be generated covertly and reliably over $n$ uses of a bosonic channel. We report a single-letter expression for optimal $L_{\text{EG}}$ 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 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 capacity$L_{\text{sec }}$. 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:$L_{\text{EG}} \sqrt{n}$entangled bits (ebits) can be generated covertly and reliably over$n$uses of a bosonic channel. We report a single-letter expression for optimal$L_{\text{EG}}$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.

IEEE International Conference on Quantum Computing and Engineering (QCE)Aug 30, 20250 citations

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Michael S. Bullock

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 $L\sqrt{n} + o(\sqrt{n})$ 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 $\sqrt{n}$ 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, $L_{\text{no-EA}}$ , and show that the required pre-shared classical secret key scales as $\sqrt{n}$ . 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 $L_{\text{EA}} \sqrt{n} \log n + o(\sqrt{n} \log n)$ , 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.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 $L\sqrt{n} + o(\sqrt{n})$ 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 $\sqrt{n}$ 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, $L_{\text{no-EA}}$, and show that the required pre-shared classical secret key scales as $\sqrt{n}$. 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 $L_{\text{EA}} \sqrt{n} \log n + o(\sqrt{n} \log n)$, 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.

Jan 1, 20250 citations

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Azadeh Sheikholeslami, Boulat A. Bash, Don Towsley +2 more

Recently, the fundamental limits of covert, i.e., reliable-yet-undetectable, communication have been established for general memoryless channels and for lossy-noisy bosonic (quantum) channels with a quantum-limited adversary. The key import of these results was the square-root law (SRL) for covert communication, which states that O(√n) covert bits, but no more, can be reliably transmitted over n channel uses with O(√n) bits of secret pre-shared between communicating parties. Here we prove the achievability of the SRL for a general memoryless classical-quantum channel, showing that SRL covert communication is achievable over any quantum communication channel with a product-state transmission strategy. We leave open the converse, which, if proven, would show that even using entangled transmissions and entangling measurements, the SRL for covert communication cannot be surpassed over an arbitrary quantum channel.Recently, the fundamental limits of covert, i.e., reliable-yet-undetectable, communication have been established for general memoryless channels and for lossy-noisy bosonic (quantum) channels with a quantum-limited adversary. The key import of these results was the square-root law (SRL) for covert communication, which states that O(√n) covert bits, but no more, can be reliably transmitted over n channel uses with O(√n) bits of secret pre-shared between communicating parties. Here we prove the achievability of the SRL for a general memoryless classical-quantum channel, showing that SRL covert communication is achievable over any quantum communication channel with a product-state transmission strategy. We leave open the converse, which, if proven, would show that even using entangled transmissions and entangling measurements, the SRL for covert communication cannot be surpassed over an arbitrary quantum channel.

IEEE International Symposium on Information Theory (ISIT)Jul 1, 201653 citations

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Fundamental Limits of Covert Communication Over Classical-Quantum Channels

Michael S. Bullock, Azadeh Sheikholeslami, Mehrdad Tahmasbi +3 more

We investigate covert communication over general memoryless classical-quantum channels with fixed finite-size input alphabets. We show that the square root law (SRL) governs covert communication in this setting when product a ofninput states is used: $L_{\mathrm { SRL}}\sqrt {n}+o(\sqrt {n})$ covert bits (but no more) can be reliably transmitted innuses of classical-quantum channel, where $L_{\mathrm { SRL}}\gt 0$ is a channel-dependent constant that we callcovert capacity. We also show that ensuring covertness requires $J_{\mathrm { SRL}}\sqrt {n}+o(\sqrt {n})$ bits secret key shared by the communicating parties prior to transmission, where $J_{\mathrm { SRL}}\geq 0$ is a channel-dependent constant. We assume a quantum-powerful adversary that can perform an arbitrary joint (entangling) measurement on allnchannel uses. We determine the single-letter expressions for $L_{\mathrm { SRL}}$ and $J_{\mathrm { SRL}}$ , and establish conditions when $J_{\mathrm { SRL}}=0$ (i.e., no pre-shared secret key is needed). Finally, we evaluate scenarios where covert communication is not governed by the SRL.We investigate covert communication over general memoryless classical-quantum channels with fixed finite-size input alphabets. We show that the square root law (SRL) governs covert communication in this setting when product a ofninput states is used:$L_{\mathrm { SRL}}\sqrt {n}+o(\sqrt {n})$covert bits (but no more) can be reliably transmitted innuses of classical-quantum channel, where$L_{\mathrm { SRL}}\gt 0$is a channel-dependent constant that we callcovert capacity. We also show that ensuring covertness requires$J_{\mathrm { SRL}}\sqrt {n}+o(\sqrt {n})$bits secret key shared by the communicating parties prior to transmission, where$J_{\mathrm { SRL}}\geq 0$is a channel-dependent constant. We assume a quantum-powerful adversary that can perform an arbitrary joint (entangling) measurement on allnchannel uses. We determine the single-letter expressions for$L_{\mathrm { SRL}}$and$J_{\mathrm { SRL}}$, and establish conditions when$J_{\mathrm { SRL}}=0$(i.e., no pre-shared secret key is needed). Finally, we evaluate scenarios where covert communication is not governed by the SRL.

arXiv:1601.06826IEEE Transactions on Information TheoryFeb 13, 202510 citations

O\left( {\sqrt n } \right)

O(\sqrt{n})

Einstein-Podolsky-Rosen (EPR) pairs can be distributed covertly and reliably over

n

channel uses. We begin with covert communication of classical information under a secrecy constraint. We then leverage this result to construct a coding scheme for covert entanglement generation. Single-letter expressions are derived for the covert key-assisted and unassisted secrecy capacities, as well as for the covert entanglement-generation capacity.

L_{\text{sec }}

. 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:

L_{\text{EG}} \sqrt{n}

entangled bits (ebits) can be generated covertly and reliably over

n

uses of a bosonic channel. We report a single-letter expression for optimal

L_{\text{EG}}

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.

L\sqrt{n} + o(\sqrt{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

\sqrt{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,

L_{\text{no-EA}}

, and show that the required pre-shared classical secret key scales as

\sqrt{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

L_{\text{EA}} \sqrt{n} \log n + o(\sqrt{n} \log n)

, 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.

L_{\rm EG}\sqrt{n}

entangled bits (ebits) can be generated covertly and reliably over

n

uses of a bosonic channel. We report a single-letter expression for optimal

L_{\rm EG}

as well as an achievable method. We additionally analyze the performance of covert entanglement generation using single- and dual-rail photonic qubits, which may be more practical for physical implementation.

L_{\mathrm { SRL}}\sqrt {n}+o(\sqrt {n})

covert bits (but no more) can be reliably transmitted innuses of classical-quantum channel, where

L_{\mathrm { SRL}}\gt 0

is a channel-dependent constant that we callcovert capacity. We also show that ensuring covertness requires

J_{\mathrm { SRL}}\sqrt {n}+o(\sqrt {n})

bits secret key shared by the communicating parties prior to transmission, where

J_{\mathrm { SRL}}\geq 0

is a channel-dependent constant. We assume a quantum-powerful adversary that can perform an arbitrary joint (entangling) measurement on allnchannel uses. We determine the single-letter expressions for

L_{\mathrm { SRL}}

and

J_{\mathrm { SRL}}

, and establish conditions when

J_{\mathrm { SRL}}=0

(i.e., no pre-shared secret key is needed). Finally, we evaluate scenarios where covert communication is not governed by the SRL.