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:2402.13194 · IEEE International Symposium on Information Theory (ISIT)

Quantum Wiretap Channel Coding Assisted by Noisy Correlation

Minglai Cai, Andreas Winter

Published Jul 7, 2024• 2 citations
arXivHTMLPDF

Abstract

We consider the private classical capacity of a quantum wiretap channel, where the users (sender Alice, receiver Bob, and eavesdropper Eve) have access to the resource of a shared quantum state, additionally to their channel inputs and outputs. An extreme case is maximal entanglement or a secret key between Alice and Bob, both of which would allow for one-time padding the message. But here both the wiretap channel and the shared state are general. In the other extreme case that the state is trivial, we recover the wiretap channel and its private capacity [N. Cai, A. Winter and R. W. Yeung, Probl. Inform. Transm. 40(4):318-336, 2004]. We show how to use the given resource state to build a code for secret classical communication. Our main result is a lower bound on the assisted private capacity, which asymptotically meets the multi-letter converse and which encompasses all sorts of previous results as special cases.

DOI
10.1109/isit57864.2024.10619364

Related papers

One-Shot Private Classical Capacity of Quantum Wiretap Channel: Based on one-shot quantum covering lemma

Jaikumar Radhakrishnan, Sen, Pranab, Naqueeb Ahmad Warsi

In this work we study the problem of communication over the quantum wiretap channel. For this channel there are three parties Alice (sender), Bob (legitimate receiver) and Eve (eavesdropper). We obtain upper and lower bounds on the amount of information Alice can communicate to Bob such that Eve gets to know as little information as possible about the transmitted messages. Our bounds are in terms of quantum hypothesis testing divergence and smooth max quantum relative entropy. To obtain our result we prove a one-shot version of the quantum covering lemma along with operator Chernoff bound for non-square matrices.

arXiv:1703.01932•Mar 6, 2017•14 citations

Entanglement-assisted private communication over quantum broadcast channels

Haoyu Qi, Kunal Sharma, Mark M. Wilde

Abstract We consider entanglement-assisted (EA) private communication over a quantum broadcast channel, in which there is a single sender and multiple receivers. We divide the receivers into two sets: the decoding set and the malicious set. The decoding set and the malicious set can either be disjoint or can have a finite intersection. For simplicity, we say that a single party Bob has access to the decoding set and another party Eve has access to the malicious set, and both Eve and Bob have access to the pre-shared entanglement with Alice. The goal of the task is for Alice to communicate classical information reliably to Bob and securely against Eve, and Bob can take advantage of pre-shared entanglement with Alice. In this framework, we establish a lower bound on the one-shot EA private capacity. When there exists a quantum channel mapping the state of the decoding set to the state of the malicious set, such a broadcast channel is said to be degraded. We establish an upper bound on the one-shot EA private capacity in terms of smoothed min- and max-entropies for such channels. In the limit of a large number of independent channel uses, we prove that the EA private capacity of a degraded quantum broadcast channel is given by a single-letter formula. Finally, we consider two specific examples of degraded broadcast channels and find their capacities. In the first example, we consider the scenario in which one part of Bob’s laboratory is compromised by Eve. We show that the capacity for this protocol is given by the conditional quantum mutual information of a quantum broadcast channel, and so we thus provide an operational interpretation to the dynamic counterpart of the conditional quantum mutual information. In the second example, Eve and Bob have access to mutually exclusive sets of outputs of a broadcast channel.

arXiv:1803.03976•Journal of Physics A Mathematical and Theoretical•Jul 26, 2018•29 citations

Wiretap Channels With Causal State Information: Strong Secrecy

Te Sun Han, Masahide Sasaki

The coding problem for wiretap channels with causal channel state information available at the encoder and/or the decoder is studied under the strong secrecy criterion. This problem consists of two aspects: one is due to wiretap channel coding and the other is due to one-time pad cipher based on the secret key agreement between Alice and Bob using the channel state information. These two aspects are closely related to each other and give rise to an intriguing tradeoff between exploiting the state to boost secret-message rates versus extracting cryptographic key to improve secrecy capabilities. This issue has yet to be understood how to optimally reconcile the two. We newly devised the “iterative” forward-backward coding scheme, combining wiretap channel coding and secret-key-agreement-based one-time pad cipher. We then established reasonable lower bounds of the secrecy capacity for wiretap channels with causal channel state information available only at the encoder (Theorem 1), which can be easily extended to general cases with various kinds of correlated channel state information at the encoder (Alice), decoder (Bob), and wiretapper (Eve). In particular, for degraded wiretap channels, we give the secret-message (secret-key) capacity bounds (Theorems 2, 4, and 5).

arXiv:1708.00422•IEEE Transactions on Information Theory•Jun 27, 2019•22 citations

Quantum One-Time Pad in the Presence of an Eavesdropper

Fernando G. S. L. Brandão, Jonathan Oppenheim

A classical one-time pad allows two parties to send private messages over a public classical channel-an eavesdropper who intercepts the communication learns nothing about the message. A quantum one-time pad is a shared quantum state which allows two parties to send private messages or private quantum states over a public quantum channel. If the eavesdropper intercepts the quantum communication she learns nothing about the message. In the classical case, a one-time pad can be created using shared and partially private correlations. Here we consider the quantum case in the presence of an eavesdropper, and find the single-letter formula for the rate at which the two parties can send messages using a general quantum state as a quantum one-time pad. Surprisingly, the formula coincides with the distillable entanglement assisted by a symmetric channel, an important quantity in quantum information theory, but which lacked a clear operational meaning.

arXiv:1004.3328•Physical Review Letters•Jan 27, 2012•29 citations

Private Classical Communication

Mark M. Wilde

We have now seen in Chapters 20–22 how Alice can communicate classical or quantum information to Bob, perhaps even with the help of shared entanglement. One might argue that these communication tasks are the most fundamental tasks in quantum Shannon theory, given that they have furthered our understanding of the nature of information transmission over quantum channels. However, when discussing the communication of classical information, we made no stipulation as to whether this classical information should be public, so that any third party might have partial or full access to it, or private, so that no third party has access. This chapter establishes the private classical capacity theorem, which gives the maximum rate at which Alice can communicate classical information privately to Bob without anyone else in the universe knowing what she sent to him. A variation of the information-processing task corresponding to this theorem was one of the earliest studied in quantum information theory, with the Bennett– Brassard-84 quantum key distribution protocol being the first proposed protocol for exploiting quantum mechanics to establish a shared secret key between two parties. The private classical capacity theorem is important for quantum key distribution because it establishes the maximum rate at which two parties can generate a shared secret key. Another equally important, but less obvious utility of private classical communication is in establishing a protocol for quantum communication at the coherent information rate. Section 22.2 demonstrated a somewhat roundabout way of arriving at the conclusion that it is possible to communicate quantum information reliably at the coherent information rate—recall that we “coherified” the entanglement-assisted classical capacity theorem and then exploited the coherent communication identity and catalytic use of entanglement. Establishing achievability of the coherent information rate via private classical coding is another way of arriving at the same result, with the added benefit that the resulting protocol does not require the catalytic use of entanglement. The intuition for quantum communication via privacy arises from the nocloning theorem. Suppose that Alice is able to communicate private classical messages to Bob, so that the channel's environment (Eve) is not able to distinguish which message Alice is transmitting to Bob.

Cambridge University Press eBooks•Nov 2, 2016•2 citations

Additivity in Classical-Quantum Wiretap Channels

Arkin Tikku, Joseph M. Renes, Mario Berta

Due to Csiszár and Körner, the capacity of classical wiretap channels has a single-letter characterization in terms of the private information. For quantum wiretap channels, however, it is known that regularization of the private information is necessary to reach the capacity. Here we study hybrid classical-quantum wiretap channels in order to resolve how much quantumness is needed to witness non-additivity phenomena in Shannon information theory. For wiretap channels with quantum inputs but classical outputs, we prove that the characterization of the capacity in terms of the private information stays single-letter. Hence, entangled input states are of no asymptotic advantage in this setting. For wiretap channels with classical inputs, we show by means of explicit examples that the private information already becomes non-additive when either one of the two receivers becomes quantum (with the other receiver staying classical). This gives non-additivity examples that are not caused by entanglement and illustrates that in the wiretap model quantum adversaries are strictly different from classical adversaries.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2020•0 citations
We consider the private classical capacity of a quantum wiretap channel, where the users (sender Alice, receiver Bob, and eavesdropper Eve) have access to the resource of a shared quantum state, additionally to their channel inputs and outputs. An extreme case is maximal entanglement or a secret key between Alice and Bob, both of which would allow for one-time padding the message. But here both the wiretap channel and the shared state are general. In the other extreme case that the state is trivial, we recover the wiretap channel and its private capacity [N. Cai, A. Winter and R. W. Yeung, Probl. Inform. Transm. 40(4):318-336, 2004]. We show how to use the given resource state to build a code for secret classical communication. Our main result is a lower bound on the assisted private capacity, which asymptotically meets the multi-letter converse and which encompasses all sorts of previous results as special cases.
In this work we study the problem of communication over the quantum wiretap channel. For this channel there are three parties Alice (sender), Bob (legitimate receiver) and Eve (eavesdropper). We obtain upper and lower bounds on the amount of information Alice can communicate to Bob such that Eve gets to know as little information as possible about the transmitted messages. Our bounds are in terms of quantum hypothesis testing divergence and smooth max quantum relative entropy. To obtain our result we prove a one-shot version of the quantum covering lemma along with operator Chernoff bound for non-square matrices.
Abstract We consider entanglement-assisted (EA) private communication over a quantum broadcast channel, in which there is a single sender and multiple receivers. We divide the receivers into two sets: the decoding set and the malicious set. The decoding set and the malicious set can either be disjoint or can have a finite intersection. For simplicity, we say that a single party Bob has access to the decoding set and another party Eve has access to the malicious set, and both Eve and Bob have access to the pre-shared entanglement with Alice. The goal of the task is for Alice to communicate classical information reliably to Bob and securely against Eve, and Bob can take advantage of pre-shared entanglement with Alice. In this framework, we establish a lower bound on the one-shot EA private capacity. When there exists a quantum channel mapping the state of the decoding set to the state of the malicious set, such a broadcast channel is said to be degraded. We establish an upper bound on the one-shot EA private capacity in terms of smoothed min- and max-entropies for such channels. In the limit of a large number of independent channel uses, we prove that the EA private capacity of a degraded quantum broadcast channel is given by a single-letter formula. Finally, we consider two specific examples of degraded broadcast channels and find their capacities. In the first example, we consider the scenario in which one part of Bob’s laboratory is compromised by Eve. We show that the capacity for this protocol is given by the conditional quantum mutual information of a quantum broadcast channel, and so we thus provide an operational interpretation to the dynamic counterpart of the conditional quantum mutual information. In the second example, Eve and Bob have access to mutually exclusive sets of outputs of a broadcast channel.
The coding problem for wiretap channels with causal channel state information available at the encoder and/or the decoder is studied under the strong secrecy criterion. This problem consists of two aspects: one is due to wiretap channel coding and the other is due to one-time pad cipher based on the secret key agreement between Alice and Bob using the channel state information. These two aspects are closely related to each other and give rise to an intriguing tradeoff between exploiting the state to boost secret-message rates versus extracting cryptographic key to improve secrecy capabilities. This issue has yet to be understood how to optimally reconcile the two. We newly devised the “iterative” forward-backward coding scheme, combining wiretap channel coding and secret-key-agreement-based one-time pad cipher. We then established reasonable lower bounds of the secrecy capacity for wiretap channels with causal channel state information available only at the encoder (Theorem 1), which can be easily extended to general cases with various kinds of correlated channel state information at the encoder (Alice), decoder (Bob), and wiretapper (Eve). In particular, for degraded wiretap channels, we give the secret-message (secret-key) capacity bounds (Theorems 2, 4, and 5).
A classical one-time pad allows two parties to send private messages over a public classical channel-an eavesdropper who intercepts the communication learns nothing about the message. A quantum one-time pad is a shared quantum state which allows two parties to send private messages or private quantum states over a public quantum channel. If the eavesdropper intercepts the quantum communication she learns nothing about the message. In the classical case, a one-time pad can be created using shared and partially private correlations. Here we consider the quantum case in the presence of an eavesdropper, and find the single-letter formula for the rate at which the two parties can send messages using a general quantum state as a quantum one-time pad. Surprisingly, the formula coincides with the distillable entanglement assisted by a symmetric channel, an important quantity in quantum information theory, but which lacked a clear operational meaning.
We have now seen in Chapters 20–22 how Alice can communicate classical or quantum information to Bob, perhaps even with the help of shared entanglement. One might argue that these communication tasks are the most fundamental tasks in quantum Shannon theory, given that they have furthered our understanding of the nature of information transmission over quantum channels. However, when discussing the communication of classical information, we made no stipulation as to whether this classical information should be public, so that any third party might have partial or full access to it, or private, so that no third party has access. This chapter establishes the private classical capacity theorem, which gives the maximum rate at which Alice can communicate classical information privately to Bob without anyone else in the universe knowing what she sent to him. A variation of the information-processing task corresponding to this theorem was one of the earliest studied in quantum information theory, with the Bennett– Brassard-84 quantum key distribution protocol being the first proposed protocol for exploiting quantum mechanics to establish a shared secret key between two parties. The private classical capacity theorem is important for quantum key distribution because it establishes the maximum rate at which two parties can generate a shared secret key. Another equally important, but less obvious utility of private classical communication is in establishing a protocol for quantum communication at the coherent information rate. Section 22.2 demonstrated a somewhat roundabout way of arriving at the conclusion that it is possible to communicate quantum information reliably at the coherent information rate—recall that we “coherified” the entanglement-assisted classical capacity theorem and then exploited the coherent communication identity and catalytic use of entanglement. Establishing achievability of the coherent information rate via private classical coding is another way of arriving at the same result, with the added benefit that the resulting protocol does not require the catalytic use of entanglement. The intuition for quantum communication via privacy arises from the nocloning theorem. Suppose that Alice is able to communicate private classical messages to Bob, so that the channel's environment (Eve) is not able to distinguish which message Alice is transmitting to Bob.
Due to Csiszár and Körner, the capacity of classical wiretap channels has a single-letter characterization in terms of the private information. For quantum wiretap channels, however, it is known that regularization of the private information is necessary to reach the capacity. Here we study hybrid classical-quantum wiretap channels in order to resolve how much quantumness is needed to witness non-additivity phenomena in Shannon information theory. For wiretap channels with quantum inputs but classical outputs, we prove that the characterization of the capacity in terms of the private information stays single-letter. Hence, entangled input states are of no asymptotic advantage in this setting. For wiretap channels with classical inputs, we show by means of explicit examples that the private information already becomes non-additive when either one of the two receivers becomes quantum (with the other receiver staying classical). This gives non-additivity examples that are not caused by entanglement and illustrates that in the wiretap model quantum adversaries are strictly different from classical adversaries.