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arXiv:2609.23818

A four-state quantum communication protocol with mesoscopic twin beams

Stefano Carsi

quant-phphysics.ins-detSubmitted Sep 20, 2026• Announced Sep 22, 2026• 0 citations

Abstract

Twin-beam (TWB) states generated by parametric down-conversion exhibit strong photon-number correlations that can be exploited for quantum communication. In the mesoscopic regime, these correlations can be directly investigated using photon-number-resolving detectors, such as silicon photomultipliers (SiPMs). Their nonclassical nature is quantified by the noise reduction factor (NRF), which provides a witness of quantum correlations and a means of monitoring channel security. In this work, a quantum communication protocol based on TWB states, originally proposed for binary encoding, is extended to a four-state scheme capable of transmitting two bits per use. Information is encoded by combining two mean photon-number values and two mode numbers of thermal noise superimposed on one arm of the twin beam, defining four distinguishable states in the (m,R) plane. While the mean detected photon number enables the retrieval of one bit, the NRF provides discrimination of the second bit and a security check against intercept-and-resend attacks, which introduce additional noise and degrade the quantum correlations. The protocol is investigated through two experimental measurement campaigns. First, the twin-beam source is characterized in terms of photon-number statistics, NRF, and detection efficiency to establish the operating conditions of the communication channel. Subsequently, the four-state protocol is implemented and evaluated through the analysis of state distributions and their 95% confidence regions, error probability as a function of sample size, and a comparative assessment of machine learning classifiers for state discrimination. Finally, the response of the NRF to an intercept-and-resend attack is investigated to assess the protocol's ability to detect eavesdropping.

Comments: 37 pages 17 figures. It is a laboratory report for a Master course which, according to the teacher, will lead to an article

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Mesoscopic optical states are a promising resource for quantum communication, combining robustness against losses with the preservation of genuine quantum features. Here, we propose a quantum communication protocol in which information is encoded in the first and second moments of the photon-number distributions of classical optical states, and then decoded by photon-number-resolving detectors. Security relies on the nonclassical photon-number correlations of a twin-beam state transmitted alongside the signal in the quantum channel, providing an experimentally accessible security witness against both intercept-resend and beam-splitter attacks investigated in this work. Numerical simulations performed in experimentally accessible parameter regimes support the feasibility and security of the proposed communication protocol, yielding nonzero key generation rates under the considered eavesdropping attacks, and motivating its future experimental implementation.

Quantum resources can improve the quality and security of data transmission. A novel communication protocol based on the use of mesoscopic twin-beam (TWB) states of light is proposed and discussed. The message sent by Alice to Bob is encoded in binary single-mode thermal states having two possible mean values, both smaller than the mean value of the TWB. Such thermal states are alternately superimposed to the portion of TWB sent to Bob. We demonstrate that in the presence of an eavesdropping attack that intercepts and substitutes part of the signal with a thermal noise, Bob can still successfully decrypt the message by evaluating the noise reduction factor for detected photons. The protocol opens new perspectives in the exploitation of quantum states of light for applications to Quantum Communication.

Abstract State discrimination is a key challenge in the implementation of quantum communication protocols. Most optical communication protocols rely on either coherent states of light or fragile single-photon states, making it often difficult to achieve robustness and security simultaneously. In this work, we propose a hybrid strategy that operates in the mesoscopic intensity regime, leveraging robust quantum states of light. Our approach combines classical and quantum features: reliable state discrimination based on a classical property of light, and security stemming from nonclassical correlations. Specifically, the receiver uses photon-number-resolving detectors to access the mean photon number of the binary thermal signals encoding the information. The communication channel exploits twin-beam states, inherently sensitive to eavesdropping attacks, to provide a layer of security. This strategy is scalable, allowing for straightforward extension to more complex signal alphabets, and offers a promising route for robust and secure quantum communication in the mesoscopic intensity domain.

Quantum resources can improve the security of information transmission between two parties. So far, Quantum Communication protocols have been implemented at the single-photon level by means of entangled states [1]. In contrast to this domain, where the presence of losses can reduce the transmission rate of information [2], in the mesoscopic one the optical pulses contain sizeable numbers of photons, thus resulting more robust against any kind of external degradation [3]. In a recent work of ours, we have demonstrated that the transmission of one arm of a twin-beam (TWB) state through a lossy and noisy channel does not prevent the observation of nonclassical correlations between the two parties [4]. Based on these successful results, here we consider a more realistic scenario, in which a portion of TWB produced in a

\beta

-Barium Borate (BBO) crystal is sent through water-filled tubes, while the other one undergoes free-space propagation [5]. We investigate the role played by the length of the tubes, the number of optical elements (OE), and the divergence of the beams through the different media. We demonstrate that, by properly acting on the light beams, we can still observe nonclassical correlations at moderate distances by using the noise reduction factor,

R

, as a criterion for nonclassicality. The experimental implementations involve commercial photon-number-resolving (PNR) detectors. In particular, hybrid photodetectors and Silicon Photomultipliers have been used and compared.

Nowadays, optical Quantum Communication has reached a mature level, especially in free space and through optical fibers. Experimental implementations usually involve single-photon states or weak coherent states detected by single-photon detectors. In contrast to these standard configurations, in our work we consider mesoscopic twin-beam (TWB) states revealed by photon-number-resolving detectors. By properly acting on the natural divergence of the generated beams, we show that they remain nonclassical even at a moderate distance from the nonlinear crystal in which they are produced. We also consider the case where one of the two parties of TWB is partially transmitted through water, and show that the nonclassicality of the states is preserved. This result suggests that mesoscopic TWB states can be considered for the new and growing scenario of underwater Quantum Communication.

We address binary and quaternary communication channels based on correlated multiphoton two-mode states of radiation in the presence of losses. The protocol are based on photon number correlations and realized upon choosing a shared set of thresholds to convert the outcome of a joint photon number measurement into a symbol from a discrete alphabet. In particular, we focus on channels built using feasible photon-number entangled states (PNES) as two-mode coherently-correlated (TMC) or twin-beam (TWB) states and compare their performances with that of channels built using feasible classically correlated (separable) states. We found that PNES provide larger channel capacity in the presence of loss, and that TWB-based channels may transmit a larger amount of information than TMC-based ones at fixed energy and overall loss. Optimized bit discrimination thresholds, as well as the corresponding maximized mutual information, are explicitly evaluated as a function of the beam intensity and the loss parameter. The propagation of TMC and TWB in lossy channels is analyzed and the joint photon number distribution is evaluated, showing that the beam statistics, either sub-Poissonian for TMC or super-Poissonian for TWB, is not altered by losses. Although entanglement is not strictly needed to establish the channels, which are based on photon-number correlations owned also by separable mixed states, purity of the support state is relevant to increase security. The joint requirement of correlation and purity individuates PNES as a suitable choice to build effective channels. The effects of losses on channel security are briefly discussed.