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arXiv:2401.12861 · IEEE International Symposium on Information Theory (ISIT)

Secure Communication with Unreliable Entanglement Assistance

Meir Lederman, Uzi Pereg

Published Jul 7, 2024• 9 citations
arXivHTMLPDF

Abstract

Secure communication is considered with unreliable entanglement assistance, where the adversary may intercept the legitimate receiver's entanglement resource before communication takes place. The communication setting of unreliable assistance, without security aspects, was originally motivated by the extreme photon loss in practical communication systems. The operational principle is to adapt the transmission rate to the availability of entanglement assistance, without resorting to feedback and repetition. Here, we require secrecy as well. An achievable secrecy rate region is derived for general quantum wiretap channels, and a multi-letter secrecy capacity formula for the special class of degraded channels.

DOI
10.1109/isit57864.2024.10619085

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Secure communication is considered with unreliable entanglement assistance, where the adversary may intercept the legitimate receiver's entanglement resource before communication takes place. The communication setting of unreliable assistance, without security aspects, was originally motivated by the extreme photon loss in practical communication systems. The operational principle is to adapt the transmission rate to the availability of entanglement assistance, without resorting to feedback and repetition. Here, we require secrecy as well. An achievable secrecy rate region is derived for general quantum wiretap channels, and a multi-letter secrecy capacity formula for the special class of degraded channels.
Entanglement resources can increase transmission rates substantially. Unfortunately, entanglement is a fragile resource that is quickly degraded by decoherence effects. In order to generate entanglement for optical communication, the transmitter and the receiver first prepare entangled spin-photon pairs locally, and then the photon at the transmitter is sent to the receiver through an optical fiber or free space. Without feedback, the transmitter does not know whether the entangled photon has reached the receiver. The present work introduces a new model of unreliable entanglement assistance, whereby the communication system operates whether entanglement assistance is present or not. While the sender is ignorant, the receiver knows whether the entanglement generation was successful. In the case of a failure, the receiver decodes less information. In this manner, the effective transmission rate is adapted according to the assistance status. Regularized formulas are derived for the classical and quantum capacity regions with unreliable entanglement assistance, characterizing the tradeoff between the unassisted rate and the excess rate that can be obtained from entanglement assistance. It is further established that time division between entanglement-assisted and unassisted coding strategies is optimal for the noiseless qubit channel, but can be strictly suboptimal for a noisy channel.
Entanglement resources can increase transmission rates substantially. Unfortunately, entanglement is a fragile resource that is quickly degraded by decoherence effects. In order to generate entanglement for optical communication, the transmitter and the receiver first prepare entangled spin-photon pairs locally, and then the photon at the transmitter is sent to the receiver through an optical fiber or free space. Without feedback, the transmitter does not know whether the entangled photon has reached the receiver. The present work introduces a new model of unreliable entanglement assistance, whereby the communication system operates whether entanglement assistance is present or not. While the sender is ignorant, the receiver knows whether the entanglement generation was successful. In the case of a failure, the receiver decodes less information. In this manner, the effective transmission rate is adapted according to the assistance status. Regularized formulas are derived for the classical and quantum capacity regions with unreliable entanglement assistance, characterizing the tradeoff between the unassisted rate and the excess rate that can be obtained from entanglement assistance. It is further established that time division between entanglement-assisted and unassisted coding strategies is optimal for the noiseless qubit channel, but can be strictly suboptimal for a noisy channel.
We study classical communication over quantum multiple-access channels and their wiretap counterparts with unreliable entanglement assistance. Using a robust superposition coding scheme, we characterize the trade-off between baseline rates that are guaranteed without entanglement and additional rates achievable when entanglement is available. We establish a regularized characterization of the classical capacity region for the quantum multiple-access channel and extend it to regularized secrecy capacity regions under two models: entanglement loss and interception. Specifically, for the class of entanglement-breaking channels, we demonstrate that these regularized regions reduce to computable single-letter formulas.
Entanglement resources can increase transmission rates substantially. Unfortunately, entanglement is a fragile resource that is quickly degraded by decoherence effects. The present work introduces a new model of unreliable entanglement assistance, whereby the communication system operates whether entanglement assistance is present or not. While the sender is ignorant, the receiver knows whether the entanglement generation was successful. In the case of a failure, the receiver decodes less information. In this manner, the effective transmission rate is adapted according to the assistance status. Regularized formulas are derived for the classical and quantum capacity regions with unreliable entanglement assistance, characterizing the tradeoff between the unassisted rate and the excess rate that can be obtained from entanglement assistance.
Semantic security is considered with unreliable entanglement assistance, due to one of two reasons: Interception or loss. We consider two corresponding models. In the first model, Eve may intercept the entanglement resource. In the second model, Eve is passive, and the resource may dissipate to the environment beyond her reach. We derive achievable rates for both models, subject to a maximal error criterion and semantic security. As an example, we consider the amplitude damping channel. Under interception, time division is not necessarily possible, and the boundary of our achievable region is disconnected. In the passive model, our rate region outperforms time division.
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.