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IEEE International Symposium on Information Theory (ISIT)

The Quantum Identification Capacity with Entanglement Assistance

Johannes Rosenberger, Holger Boche, Christian Deppe, Uzi Pereg

Published Jun 22, 2025• 0 citations
Publisher

Abstract

The understanding of achievable rates for quantum identification is far behind that of quantum transmission, as well as classical identification and transmission. Notably, in the classical case, common randomness shared between Alice and Bob before communication begins can greatly enhance the identification capacity. In the quantum regime, pre-shared entanglement may have an even more profound impact on the quantum identification (ID) capacity. This paper presents a regularized expression for the quantum ID capacity with entanglement assistance and demonstrates how it grows with the entanglement rate. Additionally, we provide deeper insights into the nature of quantum ID capacity. Interestingly, while the classical ID capacity becomes unbounded with unlimited common randomness, we find that the quantum ID capacity remains bounded even with unlimited entanglement assistance. Additionally, we find that entanglement plays the same role as an additional noiseless channel that is amortized, i.e., only used to make the rate positive.

DOI
10.1109/isit63088.2025.11195684

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The understanding of achievable rates for quantum identification is far behind that of quantum transmission, as well as classical identification and transmission. Notably, in the classical case, common randomness shared between Alice and Bob before communication begins can greatly enhance the identification capacity. In the quantum regime, pre-shared entanglement may have an even more profound impact on the quantum identification (ID) capacity. This paper presents a regularized expression for the quantum ID capacity with entanglement assistance and demonstrates how it grows with the entanglement rate. Additionally, we provide deeper insights into the nature of quantum ID capacity. Interestingly, while the classical ID capacity becomes unbounded with unlimited common randomness, we find that the quantum ID capacity remains bounded even with unlimited entanglement assistance. Additionally, we find that entanglement plays the same role as an additional noiseless channel that is amortized, i.e., only used to make the rate positive.
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​.
Entanglement assisted communication is advocated by numerous authors as an alternative to classical communication offering significant improvement in channel capacity, in particular in noisy regime. In all those papers it is always assumed that entanglement can be distributed without any imperfections, except for attenuation. We demonstrate that under imperfect pre-shared entanglement distribution, assuming that entanglement distribution channel is modeled as a noisy and lossy Bosonic channel, the entanglement assisted communication can be inferior compared to the classical communication, depending on the parameters of the distribution channel. We identify the conditions under which entanglement assistance can still provide an advantage over the classical case. In particular, when both communication and entanglement distribution channels are not used for entanglement assisted communication but rather for classical transmission instead then the classical capacity is always higher than the entanglement assisted capacity. We also study the entanglement assisted communication under the strong atmospheric turbulence effects.
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.
The entanglement-assisted capacity of a quantum channel admits an additive single-letter characterization, implying that joint encodings across channel uses cannot increase the ultimate communication rate. Here, we show that this additive picture does not extend to communication reliability. Specifically, we prove that the Petz-Rényi channel information can be strictly superadditive for every α∈[1/2,1)α\in[1/2,1)α∈[1/2,1), yielding a genuine multi-copy enhancement of the entanglement-assisted random-coding error exponent, even though the entanglement-assisted capacity remains additive. We establish this phenomenon analytically already for measurement channels, which are entanglement-breaking and have additive unassisted capacity. Remarkably, this strict superadditivity is witnessed by a separable, classically correlated two-copy channel-input marginal, demonstrating that no entanglement between the transmitted systems is required. Our results show that, although correlations across channel uses cannot increase the ultimate rate of entanglement-assisted communication, they can enhance its reliability.
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.