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International Conference on Quantum Communications, Networking, and Computing (QCNC)

Feasibility of entanglement-based QKD protocols with SPDC and QD sources

Mariia Gumberidze, Vladyslav C. Usenko

Published Mar 31, 2025• 0 citations
Publisher

Abstract

We theoretically analyze the feasibility of entanglement-based quantum key distribution (QKD) protocols [1], [2], considering both spontaneous parametric down-conversion (SPDC) and quantum dot (QD) sources. We account for multiphoton emission in SPDC sources and fine-structure splitting (FSS) in QD. In addition, we incorporate imperfect detection, including dark counts and limited efficiency. For SPDC sources, we confirm the presence of vacuum and multiphoton pairs renders them unsuitable for secure device-independent (DI) QKD implementations. Conversely, with QD sources, accounting for the effects of FSS results in reduced secret key rates compared to ideal conditions. Our findings are crucial for the practical implementation of entanglement-based QKD protocols using realistic sources and detectors.

DOI
10.1109/qcnc64685.2025.00107

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We theoretically analyze the feasibility of entanglement-based quantum key distribution (QKD) protocols [1], [2], considering both spontaneous parametric down-conversion (SPDC) and quantum dot (QD) sources. We account for multiphoton emission in SPDC sources and fine-structure splitting (FSS) in QD. In addition, we incorporate imperfect detection, including dark counts and limited efficiency. For SPDC sources, we confirm the presence of vacuum and multiphoton pairs renders them unsuitable for secure device-independent (DI) QKD implementations. Conversely, with QD sources, accounting for the effects of FSS results in reduced secret key rates compared to ideal conditions. Our findings are crucial for the practical implementation of entanglement-based QKD protocols using realistic sources and detectors.
We theoretically analyze the feasibility of entanglement-based quantum key distribution (QKD) protocols considering widely used spontaneous parametric down-conversion (SPDC) and novel quantum dot (QD) sources. We account for multiphoton emission in SPDC sources and fine-structure splitting (FSS) in QD. In addition, we incorporate imperfect detection, including dark counts and limited efficiency. For SPDC sources, we confirm that the presence of vacuum and multiphoton pairs renders them unsuitable for secure device-independent (DI) QKD implementations under standard detection strategies. Conversely, in the case of QD sources, accounting for the effects of FSS, results in reduced performance of protocols. Our findings are crucial for the practical implementation of entanglement-based QKD protocols using realistic sources and detectors.
We theoretically analyse the relation between non-Gaussianity and security of entanglement-based quantum key distribution (QKD) protocols, namely device-independent (DI) and entanglement-based BB848484. A similar analysis has already been made for prepare-and-measure (P\&M) protocols \cite{Lasota2017}. In addition, we consider imperfect detection with dark counts and limited efficiency. We assume a perfect source of entangled Bell states as produced by quantum-dot type sources, depolarisation in the channel and different noise statistics, namely thermal and Poissonian. We consider single-photon avalanche photodiodes (SPAD) and photon number resolving detectors (PNRD) and use their respective criteria for non-Gaussianity. The results show cross-regions for both security and non-Gaussianity, hence, the possibility to conclude about the suitability of a given channel for secret key distribution. Our results can be useful as a pre-check for the implementation of QKD protocols.
We theoretically analyze the feasibility of entanglement-based quantum key distribution (QKD) protocols-both device-independent QKD (DI-QKD) and entanglement-based BB84 (EPR-BB84)-using widely employed spontaneous parametric down-conversion (SPDC) and what we believe to be a novel semiconductor quantum-dot (QD) sources. Within a unified photodetection-theory framework, we jointly evaluate the Bell parameter, quantum bit error rate (QBER), and asymptotic Devetak-Winter secret key rate for both source types, accounting for multiphoton emission in SPDC, fine-structure splitting (FSS) in the QD, and imperfect detection including finite efficiency and dark counts. Our results demonstrate that, despite the detrimental effect of FSS, QD sources achieve sufficient Bell violation and positive secret key rates under realistic experimental conditions. In contrast, within the standard CHSH-based DI-QKD framework and the detection and binning strategies, bare SPDC sources do not yield a positive secret key rate, despite the feasibility of loophole-free Bell tests with such sources. Our findings are crucial for the practical implementation of entanglement-based QKD protocols using realistic sources and detectors.
Abstract The paper analyzes security aspects of practical entanglement-based quantum key distribution (QKD), namely, BBM92 or entanglement-based BB84 protocol. Similar to prepare-and-measure QKD protocols, practical implementations of the entanglement-based QKD have to rely upon non-ideal photon sources. A typical solution for entanglement generation is the spontaneous parametric down-conversion. However, this process creates not only single photon pairs, but also quantum states with more than two photons, which potentially may lead to security deterioration. We show that this effect does not impair the security of entanglement-based QKD systems. We also review the available security proofs and show that properties of the entanglement source have nothing to do with security degradation.
The concept of the Device-Independent Quantum Key Distribution (DI-QKD) constitutes the minimalist paradigm for quantum cryptography, in which the security of the distributed secret key is fully assured by the statistical properties of the data being shared between the parties that perform a quantum-based protocol. In particular, the secrecy of the distributed key is ultimately guaranteed not only thanks to the quantum nature of the underlying scheme, but also without making any assumptions about the operation of the devices being employed. Such a conservative approach is possible thanks to the non-local correlations exhibited within the shared data, i.e., the correlations of genuine quantum origin that, due to violation of a particular Bell inequality, cannot be explained by any form of common randomness pre-available to the parties. Such violation, however, must be revealed without performing any post-selection on the data, what would then open the so-called detection loophole and jeopardize the security of the protocol. In spite of the tremendous advances recently made to achieve higher detection efficiencies in Bell-violation experiments, DI-QKD remains a very experimentally difficult task due to the exponential increase of loss in the channel, e.g., implemented with optical fibres, with the distance separating the parties involved. Here, we describe a new and plausible solution to overcome the crucial problem of channel loss in the frame of DI-QKD optical implementations. In particular, we propose a novel protocol inspired by the entanglement swapping schemes, which by the usage of the state-of-the-art (e.g., quantum-dot-based or heralded) single-photon sources has potential, for the first time, to be implementable with current photonic and linear optics technologies. While allowing for any transmission losses that only decrease the rate of the key distribution without creating vulnerability, it tolerates overall detection efficiency at the 90% level even when requiring strict device-independence. We compare our scheme against protocols that involve sources based on spontaneous parametric down-conversion (SPDC), in order to explicitly show and explain why such SPDC-based proposals—even when enhanced by the entanglement swapping or qubit amplification techniques—are then largely outperformed when physical imperfections are rigorously taken into account.
A workflow for evaluation of entanglement source quality is proposed. Based on quantum state density matrices obtained from theoretical models and experimental data, we make an estimate of a potential performance of a quantum entanglement source in quantum key distribution protocols. This workflow is showcased for continuously pumped spontaneous parametric down-conversion (SPDC) source, where it highlights the trade-off between entangled pair generation rate and entanglement quality caused by multiphoton nature of the generated quantum states. We employ this characterization technique to show that secure key rate of down-converted photon pairs is limited to 0.029 bits per detection window due to intrinsic multiphoton contributions. We also report that there exists one optimum gain for continuous-wave down-conversion sources. We find a bound for secure key rate extracted from SPDC sources and make a comparison with perfectly single-pair quantum states, such as those produced by quantum dots.