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:2603.29987

Strong converse bounds on the classical identification capacity of the qubit depolarizing channel

Liuhang Ye, Bjarne Bergh, Nilanjana Datta

quant-phSubmitted Mar 31, 2026• Announced Apr 1, 2026• 0 citations
arXivHTMLPDF

Abstract

A strong converse bound for the classical identification capacity of a quantum channel is an upper bound on the asymptotic identification rate of classical messages sent through the channel, such that, above this rate, the probability of an identification error necessarily converges to one. Converse bounds for identification are notoriously difficult to obtain for fully quantum channels. The only previously known converse bound, due to Atif, Pradhan and Winter [Int.~J.~Quantum Inf.~22(5):2440013, 2024], has the unsatisfactory feature of remaining strictly positive even for a completely noisy channel, for which identification is clearly impossible. We derive strong (and hence also weak) converse bounds, for the qubit depolarizing channel with noise parameter $p$, that vanish as $p\to 1$, thereby yielding the correct behavior in the completely noisy limit. Moreover, in the setting of simultaneous classical identification under the constraint of complete product measurements, our converse bound matches the corresponding achievability bound, and establishes that in this case the identification capacity equals the classical capacity of the channel.

Comments
28 pages, 1 figure

Related papers

The entanglement-assisted transmission capacity is a strong converse bound for identification

Satvik Singh

Classical identification via a noisy channel is a communication task in which the receiver is not required to reconstruct the full transmitted message, but only to decide whether it coincides with a message of interest. This relaxation allows the number of identifiable messages to grow doubly exponentially with the blocklength. For quantum channels, the resulting (doubly exponential) identification capacity $C_{\mathrm{ID}}$ can strictly exceed the ordinary (exponential) transmission capacity $C$. In this paper, we prove that the entanglement-assisted transmission capacity $C_E$ is a strong converse bound for this task: $C_{\mathrm{ID}}\leq C_E$. For sufficiently low-noise channels, this bound can also be achieved via the Hayden-Winter (quantum) identification + fingerprinting codes. This yields an exact characterization $C_{\mathrm{ID}}=C_E$ of identification capacity for such channels. However, for general channels, we prove that this upper bound can be strict. We exhibit an explicit family of transpose-depolarizing channels for which $C_{\mathrm{ID}}<C_E$. As a consequence, we also obtain the first example of strict superadditivity of the identification capacity $C_{\mathrm{ID}}$.

quant-pharXiv:2608.11000•Aug 12, 2026•0 citations

Gaussian mean width strong converse bound on the classical identification capacity of quantum channels

Satvik Singh

We establish a single-letter and efficiently computable strong converse bound on the classical identification capacity of quantum channels. By equipping the $n$-fold channel output space with a product state-weighted $σ$-Euclidean geometry, we allow trace-distance separation constraints for identification codes to be controlled by Euclidean covering estimates. Using Sudakov's inequality, we bound the covering numbers of the $n$-fold channel outputs via their Gaussian mean widths in the weighted geometry, whose exponential growth in $n$ is governed by the operator norm of a single-letter positive operator. Upon optimizing over all weighing states $σ$, this yields a strong converse bound on the identification capacity of the channel, which also admits a semidefinite representation. Our method improves the best known converse bounds on the identification capacity of several important examples, such as depolarizing, Pauli, erasure, and amplitude damping channels. We also discuss extensions of this method to more general Euclidean geometries on the output space.

quant-pharXiv:2606.05032•Jun 4, 2026•0 citations

The Classical Capacity of Additive Quantum Queue-Channels

Prabha Mandayam, Krishna Jagannathan, Avhishek Chatterjee

We consider a setting where a stream of qubits is processed sequentially. We derive fundamental limits on the rate at which classical information can be transmitted using qubits that decohere as they wait to be processed. Specifically, we model the sequential processing of qubits using a single server queue, and derive expressions for the classical capacity of such a quantum `queue-channel.' Focusing on two important noise models, namely the erasure channel and the depolarizing channel, we obtain explicit single-letter capacity formulas in terms of the stationary waiting time of qubits in the queue. Our capacity proof also implies that a `classical' coding/decoding strategy is optimal, i.e., an encoder which uses only orthogonal product states, and a decoder which measures in a fixed product basis, are sufficient to achieve the classical capacity of both queue-channels. Our proof technique for the converse theorem generalizes readily - in particular, whenever the underlying quantum noise channel is additive, we can obtain a single-letter upper bound on the classical capacity of the corresponding quantum queue-channel. More broadly, our work begins to quantitatively address the impact of decoherence on the performance limits of quantum information processing systems.

arXiv:1906.01356•IEEE Journal on Selected Areas in Information Theory•Aug 1, 2020•16 citations

Achievable Identification Rates in Noisy Bosonic Broadcast Channels

Zuhra Amiri, Janis Nötzel

Identification in quantum communication enables receivers to verify the presence of a message without decoding its entire content. While identification capacity has been explored for classical and finite-dimensional quantum channels, its behaviour in bosonic systems remains less understood. This work analyses identification over noisy bosonic broadcast channels using coherent states. We derive achievable identification rate regions while ensuring error probabilities remain bounded, even in an infinite-dimensional setting. Our approach leverages quantum hypothesis testing and approximates the infinite sender alphabet with discrete subsets to maintain power constraints.

quant-pharXiv:2512.01833•Globecom•Dec 2, 2025•0 citations

Pursuing the Fundamental Limits for Quantum Communication

Xin Wang

The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information coherently. In this paper, we derive single-letter upper bounds on the quantum and private capacities of quantum channels. The quantum capacity of a quantum channel is always no larger than the quantum capacity of its extended channels, since the extensions of the channel can be considered as assistance from the environment. By optimizing the parametrized extended channels with specific structures such as the flag structure, we obtain new upper bounds on the quantum capacity of the original quantum channel. Furthermore, we extend our approach to estimating the fundamental limits of private communication and one-way entanglement distillation. As notable applications, we establish improved upper bounds to the quantum and private capacities for fundamental quantum channels of interest in quantum information, some of which are also the sources of noise in superconducting quantum computing. In particular, our upper bounds on the quantum capacities of the depolarizing channel and the generalized amplitude damping channel are strictly better than previously best-known bounds for certain regimes.

arXiv:1912.00931•IEEE Transactions on Information Theory•Mar 24, 2021•22 citations

Convergence Properties of Good Quantum Codes for Classical Communication

Alptug Aytekin, Mohamed Nomeir, Lei Hu +1 more

An important part of the information theory folklore had been about the output statistics of codes that achieve the capacity and how the empirical distributions compare to the output distributions induced by the optimal input in the channel capacity problem. Results for a variety of such empirical output distributions of good codes have been known in the literature, such as the comparison of the output distribution of the code to the optimal output distribution in vanishing and non-vanishing error probability cases. Motivated by these, we aim to achieve similar results for the quantum codes that are used for classical communication, that is the setting in which the classical messages are communicated through quantum codewords that pass through a noisy quantum channel. We first show the uniqueness of the optimal output distribution, to be able to talk more concretely about the optimal output distribution. Then, we extend the vanishing error probability results to the quantum case, by using techniques that are close in spirit to the classical case. We also extend non-vanishing error probability results to the quantum case on block codes, by using the second-order converses for such codes based on hypercontractivity results for the quantum generalized depolarizing semi-groups.

cs.ITCross-listedarXiv:2601.11498•IEEE International Symposium on Information Theory (ISIT)•Jan 19, 2026•1 citation
A strong converse bound for the classical identification capacity of a quantum channel is an upper bound on the asymptotic identification rate of classical messages sent through the channel, such that, above this rate, the probability of an identification error necessarily converges to one. Converse bounds for identification are notoriously difficult to obtain for fully quantum channels. The only previously known converse bound, due to Atif, Pradhan and Winter [Int.~J.~Quantum Inf.~22(5):2440013, 2024], has the unsatisfactory feature of remaining strictly positive even for a completely noisy channel, for which identification is clearly impossible. We derive strong (and hence also weak) converse bounds, for the qubit depolarizing channel with noise parameter ppp, that vanish as p→1p\to 1p→1, thereby yielding the correct behavior in the completely noisy limit. Moreover, in the setting of simultaneous classical identification under the constraint of complete product measurements, our converse bound matches the corresponding achievability bound, and establishes that in this case the identification capacity equals the classical capacity of the channel.
Classical identification via a noisy channel is a communication task in which the receiver is not required to reconstruct the full transmitted message, but only to decide whether it coincides with a message of interest. This relaxation allows the number of identifiable messages to grow doubly exponentially with the blocklength. For quantum channels, the resulting (doubly exponential) identification capacity CIDC_{\mathrm{ID}}CID​ can strictly exceed the ordinary (exponential) transmission capacity CCC. In this paper, we prove that the entanglement-assisted transmission capacity CEC_ECE​ is a strong converse bound for this task: CID≤CEC_{\mathrm{ID}}\leq C_ECID​≤CE​. For sufficiently low-noise channels, this bound can also be achieved via the Hayden-Winter (quantum) identification + fingerprinting codes. This yields an exact characterization CID=CEC_{\mathrm{ID}}=C_ECID​=CE​ of identification capacity for such channels. However, for general channels, we prove that this upper bound can be strict. We exhibit an explicit family of transpose-depolarizing channels for which CID<CEC_{\mathrm{ID}}<C_ECID​<CE​. As a consequence, we also obtain the first example of strict superadditivity of the identification capacity CIDC_{\mathrm{ID}}CID​.
We establish a single-letter and efficiently computable strong converse bound on the classical identification capacity of quantum channels. By equipping the nnn-fold channel output space with a product state-weighted σσσ-Euclidean geometry, we allow trace-distance separation constraints for identification codes to be controlled by Euclidean covering estimates. Using Sudakov's inequality, we bound the covering numbers of the nnn-fold channel outputs via their Gaussian mean widths in the weighted geometry, whose exponential growth in nnn is governed by the operator norm of a single-letter positive operator. Upon optimizing over all weighing states σσσ, this yields a strong converse bound on the identification capacity of the channel, which also admits a semidefinite representation. Our method improves the best known converse bounds on the identification capacity of several important examples, such as depolarizing, Pauli, erasure, and amplitude damping channels. We also discuss extensions of this method to more general Euclidean geometries on the output space.
We consider a setting where a stream of qubits is processed sequentially. We derive fundamental limits on the rate at which classical information can be transmitted using qubits that decohere as they wait to be processed. Specifically, we model the sequential processing of qubits using a single server queue, and derive expressions for the classical capacity of such a quantum `queue-channel.' Focusing on two important noise models, namely the erasure channel and the depolarizing channel, we obtain explicit single-letter capacity formulas in terms of the stationary waiting time of qubits in the queue. Our capacity proof also implies that a `classical' coding/decoding strategy is optimal, i.e., an encoder which uses only orthogonal product states, and a decoder which measures in a fixed product basis, are sufficient to achieve the classical capacity of both queue-channels. Our proof technique for the converse theorem generalizes readily - in particular, whenever the underlying quantum noise channel is additive, we can obtain a single-letter upper bound on the classical capacity of the corresponding quantum queue-channel. More broadly, our work begins to quantitatively address the impact of decoherence on the performance limits of quantum information processing systems.
Identification in quantum communication enables receivers to verify the presence of a message without decoding its entire content. While identification capacity has been explored for classical and finite-dimensional quantum channels, its behaviour in bosonic systems remains less understood. This work analyses identification over noisy bosonic broadcast channels using coherent states. We derive achievable identification rate regions while ensuring error probabilities remain bounded, even in an infinite-dimensional setting. Our approach leverages quantum hypothesis testing and approximates the infinite sender alphabet with discrete subsets to maintain power constraints.
The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information coherently. In this paper, we derive single-letter upper bounds on the quantum and private capacities of quantum channels. The quantum capacity of a quantum channel is always no larger than the quantum capacity of its extended channels, since the extensions of the channel can be considered as assistance from the environment. By optimizing the parametrized extended channels with specific structures such as the flag structure, we obtain new upper bounds on the quantum capacity of the original quantum channel. Furthermore, we extend our approach to estimating the fundamental limits of private communication and one-way entanglement distillation. As notable applications, we establish improved upper bounds to the quantum and private capacities for fundamental quantum channels of interest in quantum information, some of which are also the sources of noise in superconducting quantum computing. In particular, our upper bounds on the quantum capacities of the depolarizing channel and the generalized amplitude damping channel are strictly better than previously best-known bounds for certain regimes.
An important part of the information theory folklore had been about the output statistics of codes that achieve the capacity and how the empirical distributions compare to the output distributions induced by the optimal input in the channel capacity problem. Results for a variety of such empirical output distributions of good codes have been known in the literature, such as the comparison of the output distribution of the code to the optimal output distribution in vanishing and non-vanishing error probability cases. Motivated by these, we aim to achieve similar results for the quantum codes that are used for classical communication, that is the setting in which the classical messages are communicated through quantum codewords that pass through a noisy quantum channel. We first show the uniqueness of the optimal output distribution, to be able to talk more concretely about the optimal output distribution. Then, we extend the vanishing error probability results to the quantum case, by using techniques that are close in spirit to the classical case. We also extend non-vanishing error probability results to the quantum case on block codes, by using the second-order converses for such codes based on hypercontractivity results for the quantum generalized depolarizing semi-groups.