Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2202.02069 · IEEE Computer Security Foundations Workshop (CSFW)

Beware of Greeks bearing entanglement? Quantum covert channels, information flow and non-local games

David Mestel

Published Aug 1, 2022• 0 citations
arXivHTMLPDF

Abstract

Can quantum entanglement increase the capacity of (classical) covert channels? To one familiar with Holevo's Theorem it is tempting to think that the answer is obviously no. However, in this work we show: quantum entanglement can in fact increase the capacity of a classical covert channel, in the presence of an active adversary; on the other hand, a zero-capacity channel is not improved by entanglement, so entanglement cannot create ‘purely quantum’ covert channels; the problem of determining the capacity of a given channel in the presence of entanglement is undecidable; but there is an algorithm to bound the entangled capacity of a channel from above, adapted from the semi-definite hierarchy from the theory of non-local games, whose close connection to channel capacity is at the core of all of our results.

DOI
10.1109/csf54842.2022.9919683

Related papers

Covert Entanglement Generation and Secrecy

Ohad Kimelfeld, Boulat A. Bash, Uzi Pereg

We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission itself remains undetectable. The entanglement dimension follows a square root law (SRL) in the covert setting, i.e., $O\left( {\sqrt n } \right)$ 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.

IEEE Information Theory Workshop (ITW)•Sep 29, 2025•2 citations

Quantum entanglement in non-local games, graph parameters and zero-error information theory

Scarpa, Giannicola

We study quantum entanglement and some of its applications in graph theory and zero-error information theory. In Chapter 1 we introduce entanglement and other fundamental concepts of quantum theory. In Chapter 2 we address the question of how much quantum correlations generated by entanglement can deviate from classical predictions. We focus on non-local games: experiments in which two players are separated and forbidden to communicate, and have to collaborate to accomplish a task. We give two games exhibiting quantum-classical separations close to optimal. Remarkably, our results in theoretical physics are inspired by theoretical computer science. Chapter 3 is dedicated to the study of quantum graph parameters. Well-known quantities such as the chromatic number and the independence number of a graph can be interpreted as parameters for non-local games. A definition of quantum graph parameters follows from this fact. We contribute to the field in a number of ways. Among other results, we find a surprising characterization of the quantum chromatic number that relates to the Kochen-Specker theorem, a result in the foundations of quantum mechanics. In Chapter 4, we move to zero-error information theory. We study the zero error capacity of a classical noisy channel when the sender and the receiver can use quantum entanglement. We initiate the study of the source problem and source-channel problem with entanglement and we find channels and sources that exhibit a strong divergence in quantum and classical behaviours. To do that, we use results in combinatorics, linear algebra, optimization and number theory.

•Jan 1, 2013•3 citations

Quantum Entanglement Assistance Improves the Capacity and Activates the Zero-Error Capacity of Classical Channels with Causal CSIT

Yuhang Yao, Syed A. Jafar

For classical point-to-point channels, it has been shown by Bennett et al. that quantum entanglement assistance cannot improve their capacity, and by Cubitt et al. that entanglement assistance cannot activate (increase from zero to non-zero) their zero-error capacity. In contrast, we show that for classical point-to-point channels with causal CSIT (channel state information at the transmitter), quantum entanglement assistance can in some cases improve their capacity, and in some cases activate their zero-error capacity.

quant-pharXiv:2603.20416•Mar 24, 2026•0 citations

Covert Entanglement Generation and Secrecy

Ohad Kimelfeld, Boulat A. Bash, Uzi Pereg

We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission itself remains undetectable. The entanglement dimension follows a square root law (SRL) in the covert setting, i.e., $O(\sqrt{n})$ 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.

arXiv:2503.21002•IEEE Transactions on Information Theory•Apr 30, 2026•0 citations

On the undecidability of quantum channel capacities

Archishna Bhattacharyya, Arthur Mehta, Yuming Zhao

An important distinction in our understanding of capacities of classical versus quantum channels is marked by the following question: is there an algorithm which can compute (or even efficiently compute) the capacity? While there is overwhelming evidence suggesting that quantum channel capacities may be uncomputable, a formal proof of any such statement is elusive. We initiate the study of the hardness of computing quantum channel capacities. We show that, for a general quantum channel, it is QMA-hard to compute its quantum capacity, and that the entanglement-assisted zero-error capacity under some restrictions is uncomputable; indicative of the fact that quantum channel capacities may generally be undecidable.

quant-pharXiv:2601.22471•Feb 2, 2026•0 citations

Improving Zero-Error Classical Communication with Entanglement

Toby S. Cubitt, Debbie Leung, William Matthews +1 more

Given one or more uses of a classical channel, only a certain number of messages can be transmitted with zero probability of error. The study of this number and its asymptotic behavior constitutes the field of classical zero-error information theory. We show that, given a single use of certain classical channels, entangled states of a system shared by the sender and receiver can be used to increase the number of (classical) messages which can be sent without error. In particular, we show how to construct such a channel based on any proof of the Kochen-Specker theorem. We investigate the connection to pseudotelepathy games. The use of generalized nonsignaling correlations to assist in this task is also considered. In this case, an elegant theory results and, remarkably, it is sometimes possible to transmit information with zero error using a channel with no unassisted zero-error capacity.

arXiv:0911.5300•Physical Review Letters•Jun 8, 2010•145 citations
Can quantum entanglement increase the capacity of (classical) covert channels? To one familiar with Holevo's Theorem it is tempting to think that the answer is obviously no. However, in this work we show: quantum entanglement can in fact increase the capacity of a classical covert channel, in the presence of an active adversary; on the other hand, a zero-capacity channel is not improved by entanglement, so entanglement cannot create ‘purely quantum’ covert channels; the problem of determining the capacity of a given channel in the presence of entanglement is undecidable; but there is an algorithm to bound the entangled capacity of a channel from above, adapted from the semi-definite hierarchy from the theory of non-local games, whose close connection to channel capacity is at the core of all of our results.
We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission itself remains undetectable. The entanglement dimension follows a square root law (SRL) in the covert setting, i.e., O(n)O\left( {\sqrt n } \right)O(n​) 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.
We study quantum entanglement and some of its applications in graph theory and zero-error information theory. In Chapter 1 we introduce entanglement and other fundamental concepts of quantum theory. In Chapter 2 we address the question of how much quantum correlations generated by entanglement can deviate from classical predictions. We focus on non-local games: experiments in which two players are separated and forbidden to communicate, and have to collaborate to accomplish a task. We give two games exhibiting quantum-classical separations close to optimal. Remarkably, our results in theoretical physics are inspired by theoretical computer science. Chapter 3 is dedicated to the study of quantum graph parameters. Well-known quantities such as the chromatic number and the independence number of a graph can be interpreted as parameters for non-local games. A definition of quantum graph parameters follows from this fact. We contribute to the field in a number of ways. Among other results, we find a surprising characterization of the quantum chromatic number that relates to the Kochen-Specker theorem, a result in the foundations of quantum mechanics. In Chapter 4, we move to zero-error information theory. We study the zero error capacity of a classical noisy channel when the sender and the receiver can use quantum entanglement. We initiate the study of the source problem and source-channel problem with entanglement and we find channels and sources that exhibit a strong divergence in quantum and classical behaviours. To do that, we use results in combinatorics, linear algebra, optimization and number theory.
For classical point-to-point channels, it has been shown by Bennett et al. that quantum entanglement assistance cannot improve their capacity, and by Cubitt et al. that entanglement assistance cannot activate (increase from zero to non-zero) their zero-error capacity. In contrast, we show that for classical point-to-point channels with causal CSIT (channel state information at the transmitter), quantum entanglement assistance can in some cases improve their capacity, and in some cases activate their zero-error capacity.
We determine the covert capacity for entanglement generation over a noisy quantum channel. While secrecy guarantees that the transmitted information remains inaccessible to an adversary, covert communication ensures that the transmission itself remains undetectable. The entanglement dimension follows a square root law (SRL) in the covert setting, i.e., O(n)O(\sqrt{n})O(n​) Einstein-Podolsky-Rosen (EPR) pairs can be distributed covertly and reliably over nnn 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.
An important distinction in our understanding of capacities of classical versus quantum channels is marked by the following question: is there an algorithm which can compute (or even efficiently compute) the capacity? While there is overwhelming evidence suggesting that quantum channel capacities may be uncomputable, a formal proof of any such statement is elusive. We initiate the study of the hardness of computing quantum channel capacities. We show that, for a general quantum channel, it is QMA-hard to compute its quantum capacity, and that the entanglement-assisted zero-error capacity under some restrictions is uncomputable; indicative of the fact that quantum channel capacities may generally be undecidable.
Given one or more uses of a classical channel, only a certain number of messages can be transmitted with zero probability of error. The study of this number and its asymptotic behavior constitutes the field of classical zero-error information theory. We show that, given a single use of certain classical channels, entangled states of a system shared by the sender and receiver can be used to increase the number of (classical) messages which can be sent without error. In particular, we show how to construct such a channel based on any proof of the Kochen-Specker theorem. We investigate the connection to pseudotelepathy games. The use of generalized nonsignaling correlations to assist in this task is also considered. In this case, an elegant theory results and, remarkably, it is sometimes possible to transmit information with zero error using a channel with no unassisted zero-error capacity.