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.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:2606.05032Jun 4, 20260 citations

Distance-Bounding Protocols

Stefan A. Brands, David Chaum

Springer eBooksJul 31, 2007805 citations

Discriminating States: The Quantum Chernoff Bound

K. M. R. Audenaert, John Calsamiglia, R. Muñoz-Tapia +4 more

We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the minimal probability of error. This leads to the identification of the quantum Chernoff bound, thereby solving a long-standing open problem. The bound reduces to the classical Chernoff bound when the quantum states under consideration commute. The quantum Chernoff bound is the natural symmetric distance measure between quantum states because of its clear operational meaning and because it does not seem to share some of the undesirable features of other distance measures.We consider the problem of discriminating two different quantum states in the setting of asymptotically many copies, and determine the minimal probability of error. This leads to the identification of the quantum Chernoff bound, thereby solving a long-standing open problem. The bound reduces to the classical Chernoff bound when the quantum states under consideration commute. The quantum Chernoff bound is the natural symmetric distance measure between quantum states because of its clear operational meaning and because it does not seem to share some of the undesirable features of other distance measures.

arXiv:quant-ph/0610027Physical Review LettersApr 17, 2007522 citations

Group Distance Bounding Protocols

Srđjan Čapkun, Karim M. El Defrawy, Gene Tsudik

Lecture notes in computer scienceJan 1, 201114 citations

New directions in the theory of identification via channels

Rudolf Ahlswede, Z. Zhang

Studies two problems in the theory of identification via channels. The first problem concerns the identification via channels with noisy feedback. Whereas for Shannon's transmission problem the capacity of a discrete memoryless channel does not change with feedback, it is known that the identification capacity is affected by feedback. The authors study its dependence on the feedback channel. They prove both, a direct and a converse coding theorem. Although a gap exists between the upper and lower bounds provided by these two theorems, the known result for channels without feedback and the known result for channels with complete feedback, are both special cases of these two new theorems, because in these cases the bounds coincide. The second problem is the identification via wiretap channels. A secrecy identification capacity is defined for the wiretap channel. A "dichotomy theorem" is proved which says that the second-order secrecy identification capacity is the same as Shannon's capacity for the main channel as long as the secrecy transmission capacity of the wiretap channel is not zero, and zero otherwise. Equivalently, one can say that the identification capacity is not lowered by the presence of a wiretapper as long as 1 bit can be transmitted (or identified) correctly with arbitrarily small error probability. This is in strong contrast to the case of transmission.>Studies two problems in the theory of identification via channels. The first problem concerns the identification via channels with noisy feedback. Whereas for Shannon's transmission problem the capacity of a discrete memoryless channel does not change with feedback, it is known that the identification capacity is affected by feedback. The authors study its dependence on the feedback channel. They prove both, a direct and a converse coding theorem. Although a gap exists between the upper and lower bounds provided by these two theorems, the known result for channels without feedback and the known result for channels with complete feedback, are both special cases of these two new theorems, because in these cases the bounds coincide. The second problem is the identification via wiretap channels. A secrecy identification capacity is defined for the wiretap channel. A "dichotomy theorem" is proved which says that the second-order secrecy identification capacity is the same as Shannon's capacity for the main channel as long as the secrecy transmission capacity of the wiretap channel is not zero, and zero otherwise. Equivalently, one can say that the identification capacity is not lowered by the presence of a wiretapper as long as 1 bit can be transmitted (or identified) correctly with arbitrarily small error probability. This is in strong contrast to the case of transmission.>

IEEE Transactions on Information TheoryJul 1, 199570 citations

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.