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arXiv:2404.12880 · IEEE Information Theory Workshop (ITW)

Semantic Security with Unreliable Entanglement Assistance: Interception and Loss

Meir Lederman, Uzi Pereg

Published Nov 24, 2024• 3 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1109/itw61385.2024.10806955

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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.
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.
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. 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. 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.
The state-dependent (SD) wiretap channel (WTC) with non-causal channel state information (CSI) available at the encoder is considered. An inner bound on the trade-off region between admissible secret key (SK) and secret message (SM) rates is provided. The result is derived under the stringent semantic-security metric. Our inner bound recovers the best-known achievability results for either SK generation, SM transmission, or simultaneous execution of both. Since some of these past benchmarks were derived under weaker security metrics, our results imply that an upgrade to semantic-security is possible without inflicting any rate loss. It is shown that for certain instances of the considered SD-WTC, the derived region is strictly larger than the previously best-known SK-SM trade-off region reported by Prabhakaran et al., and that a recently reported SK rate for this setup cannot be achieved.