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arXiv:2605.19602 · International Journal of Quantum Information

Quantum communications in continuous variable systems

Michele N. Notarnicola

quant-phSubmitted May 19, 2026• Announced May 20, 2026• 3 citations
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Abstract

Nowadays, quantum communications provide a vast field of research in rapid expansion, with a huge potential impact on the future developments of quantum technologies. In particular, continuous variable systems, employing coherent-state encoding and quadrature measurements, represent a suitable platform, due to their compatibility with both the modulation and detection systems currently employed in standard fiber-optical communications. In this work, we address some relevant aspects of the field, and provide innovative results being also experimentally oriented. In particular, we focus on two relevant paradigms: quantum decision theory and continuous variable quantum key distribution (CVQKD). In the former case, we address the problem of coherent-state discrimination and design new hybrid receivers for binary phase-shift keying discrimination, obtaining a quantum advantage over conventional detection schemes, being also robust against typical experimental imperfections. In the latter scenario, we proceed in two different directions. On the one hand, we design new CVQKD protocols employing discrete modulation of coherent states, being a feasible solution compatible with the state of the art in optical communications technologies. On the other hand, we address the more fundamental problem of performing channel losses mitigation to enhance existing protocols, and investigate the role of optical amplifiers for the task. Finally, we make a first step towards a fully non-Gaussian CVQKD scheme by proposing, for the first time, the adoption of an optimized state-discrimination receiver, commonly adopted for quantum decision theory, within the context of CVQKD, obtaining a genuine quantum enhancement over conventional protocols.

Journal reference
Int. J. Quantum Inf. 23, 2550003 (2025)
DOI
10.1142/S0219749925500030
Comments
This is a Ph.D. thesis, and parts of it have been published in Refs. 16-22

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Nowadays, quantum communications provide a vast field of research in rapid expansion, with a huge potential impact on the future developments of quantum technologies. In particular, continuous variable systems, employing coherent-state encoding and quadrature measurements, represent a suitable platform, due to their compatibility with both the modulation and detection systems currently employed in standard fiber-optical communications. In this work, we address some relevant aspects of the field, and provide innovative results being also experimentally oriented. In particular, we focus on two relevant paradigms: quantum decision theory and continuous variable quantum key distribution (CVQKD). In the former case, we address the problem of coherent-state discrimination and design new hybrid receivers for binary phase-shift keying discrimination, obtaining a quantum advantage over conventional detection schemes, being also robust against typical experimental imperfections. In the latter scenario, we proceed in two different directions. On the one hand, we design new CVQKD protocols employing discrete modulation of coherent states, being a feasible solution compatible with the state of the art in optical communications technologies. On the other hand, we address the more fundamental problem of performing channel losses mitigation to enhance existing protocols, and investigate the role of optical amplifiers for the task. Finally, we make a first step towards a fully non-Gaussian CVQKD scheme by proposing, for the first time, the adoption of an optimized state-discrimination receiver, commonly adopted for quantum decision theory, within the context of CVQKD, obtaining a genuine quantum enhancement over conventional protocols.
We study the problem of decoding classical information encoded on quantum states at the output of a quantum channel, with particular focus on increasing the communication rates towards the maximum allowed by Quantum Mechanics. After a brief introduction to the main theoretical formalism employed in the rest of the thesis, i.e., continuous-variable Quantum Information Theory and Quantum Communication Theory, we consider several decoding schemes. First, we treat the problem from an abstract perspective, presenting a method to decompose any quantum measurement into a sequence of easier nested measurements through a binary-tree search. Furthermore we show that this decomposition can be used to build a capacity-achieving decoding protocol for classical communication on quantum channels and to solve the optimal discrimination of some sets of quantum states. These results clarify the structure of optimal quantum measurements, showing that it can be recast in a more operational and experimentally-oriented fashion. Second, we consider a more practical approach and describe three receiver structures for coherent states of the electromagnetic field with applications to single-mode state discrimination and multi-mode decoding at the output of a quantum channel. We treat the problem bearing in mind the technological limitations faced nowadays in the field of optical communications: we evaluate the performance of general decoding schemes based on such technology and report increased performance of two schemes, the first one employing a non-Gaussian transformation and the second one employing a code tailored to be read out easily by the most common detectors. Eventually we characterize a large class of multi-mode adaptive receivers based on common technological resources, obtaining a no-go theorem for their capacity.
Quantum key distribution (QKD) enables the establishment of secret keys between users connected via a channel vulnerable to eavesdropping, with information-theoretic security, that is, independently of the power of a malevolent party [1]. QKD systems based on the encoding of the key information on continuous variables (CV), such as the values of the quadrature components of coherent states [2], [3], present the major advantage that they only require standard telecommunication technology. However, the most general security proofs for CVQKD required until now the use of Gaussian modulation by the transmitter, complicating practical implementations [4]–[6]. Here, we experimentally implement a protocol that allows for arbitrary, Gaussian-like, discrete modulations, whose security is based on a theoretical proof that applies generally to such situations [7]. These modulation formats are compatible with the use of powerful tools of coherent optical telecommunication, allowing our system to reach an estimated performance of tens of megabit per second secret key rates over 25 km
Continuous-variable quantum key distribution (CV-QKD) has emerged as a promising approach for secure quantum communication, offering advantages such as high key generation rates, compatibility with standard telecommunication infrastructure, and potential for integration on photonic chips. This review provides an accessible introduction to the theory of CV-QKD, aimed at researchers entering this rapidly developing field. We focus on fundamental concepts, key protocols, and security analysis essential for understanding CV-QKD systems, with a special emphasis on prepare-and-measure protocols using coherent states under asymptotic security conditions. We explain their equivalence to entanglement-based protocols and detail the security proof framework against collective attacks, encompassing both Gaussian and discrete modulation schemes. We also briefly address more advanced topics, including measurement-device-independent CV-QKD and finite-size security analysis. This work is motivated by Brazil's growing investment in quantum communication technologies. By presenting a clear learning path from basic concepts to advanced topics, this work aims to equip newcomers with the essential tools to engage with current research in CV-QKD, thereby supporting the training of a new generation of researchers in this strategic field.
Quantum key distribution (QKD) offers a promising solution by providing information-theoretic security based on the principles of quantum mechanics. Beyond theoretical experiments, QKD network construction and verification are actively progressing in various locations worldwide. Continuousvariable QKD (CVQKD) has emerged as a strong candidate for integration into optical networks, particularly due to its compatibility with coherent detection schemes used in existing optical communication systems. Gaussian-modulated (GM) CVQKD enables simpler security analysis through covariance matrices, but its practical implementation typically requires highperformance optical components, leading to increased cost and complexity. In contrast, discrete-modulated (DM) CVQKD using modulation formats, such as quadrature amplitude modulation (QAM), can reduce implementation costs by utilizing the existing optical components. However, its security analysis requires more advanced techniques due to the non-Gaussian nature of the quantum states involved. This study evaluates the performance of GM- and DM-CVQKD under a common optical fiber channel model. Our results show that the secure key rates (SKRs) of DM-CVQKD with probabilistic constellation shaping (PCS) 64QAM and PCS-256QAM drop below zero at transmission distances of 277 km and 399 km, respectively. The results confirm the feasibility of DM-CVQKD for long-distance secure communication over optical fiber networks when appropriate modulation formats and PCS are employed.
Discrete-modulated coherent-state continuous-variable quantum key distribution (DMCS-CVQKD) is of great value for its simple implementation. However, the traditional DMCS-CVQKD scheme cannot tolerate the high channel excess noise and channel loss, compared to the Gaussian-modulated scheme, and its error correction is still difficult. In this paper, we propose a discrete-modulated coherent-state basis-encoding quantum key distribution (DMCS-BE-QKD) protocol, where the secret keys are encoded in the random choice of 2 measurement bases, i.e., the conjugate quadratures X and P of discrete-modulated coherent states, and it only needs simple binary sequence error correction. We analyze the secret key rate of DMCS-BE-QKD protocol under individual and collective attacks in the linear Gaussian channel. The results show that DMCS-BE-QKD can greatly enhance the ability to tolerate the channel loss and excess noise compared to the original DMCS-CVQKD protocol, which can tolerate approximately 40 dB more channel loss compared to the original DMCS-CVQKD for the realistic value of noise. Finally, a proof-of-principle experiment is conducted under a 50.5-km optical fiber to verify the feasibility of DMCS-BE-QKD. It is based on the consistent physical procedures of the traditional DMCS-CVQKD, which makes it perfectly compatible to deployed terminals and can serve as a multiplier for the practical secure quantum cryptography communication in harsh environments.
Abstract Continuous-variable quantum key distribution (CVQKD) is a highly promising method for building large-scale quantum networks due to its low cost and high capacity. However, current access networks involve hybrid channels and multiple users, where traditional CVQKD protocols may face limitations in performance. At the same time, as an emerging protocol, quantum key distribution with basis-encoding (BE-QKD) is compatible with traditional CVQKD protocols and has the potential to be applied in CVQKD access networks to provide performance advantages. But the performance of the BE-QKD protocol in current CVQKD access networks has not yet been fully exploited. In this work, we conduct an experimental demonstration of a heterogeneous continuous-variable quantum access network, which is based on the BE-QKD protocol with quadrature phase shift keying (QPSK) modulation and the traditional QPSK-CVQKD protocol. In addition, practical CVQKD access networks may involve different types of transmission links. Therefore, this access network is configured with four users, including two free-space channels and two fiber channels, to verify the feasibility of the proposed heterogeneous quantum access network scheme in a hybrid-channel environment. The experimental results demonstrate that the QPSK-BE-QKD protocol offers potential performance advantages across various channel scenarios in quantum access networks, such as the ability to withstand channel loss and secret key rates. And its compatibility with QPSK-CVQKD is confirmed. The proposed scheme is easy to deploy in existing CVQKD access networks and demonstrates significant performance potential, offering a new implementation paradigm for large-scale access scenarios of CVQKD networks with complex and hybrid channels.