⚛️ quantum physics

Co-transmission of classical data and continuous-variable entanglement over a single quantum channel

This paper proposes a displacement-based protocol that enables the simultaneous transmission of classical data and continuous-variable Gaussian entanglement over a single quantum channel, overcoming previous limitations to support repeater-based networks and demonstrating improved secret key generation rates compared to standard simultaneous quantum-classical communication schemes.

Original authors: Nicholas Zaunders, Timothy C. Ralph

Published 2026-07-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Nicholas Zaunders, Timothy C. Ralph

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine the internet as a vast, bustling highway where data packets are like cars zooming from one city to another. For decades, we've been driving these cars on a single-lane road, sending only one type of cargo at a time: either regular information (like emails and videos) or something far more exotic and fragile called "quantum information." This quantum cargo is special because it relies on a spooky connection known as entanglement. Think of entanglement like a pair of magical dice; no matter how far apart they are, if you roll a six on one, the other instantly shows a six too. This isn't just a party trick; it's the fuel for future super-secure communication and ultra-fast computing.

However, there's a catch. In the quantum world, looking at something changes it. If you try to read a quantum message directly, you often break the magical connection, destroying the entanglement. For a long time, scientists thought you had to choose: send a normal message or send the quantum magic, but not both at the same time on the same wire. This paper tackles that dilemma, asking a bold question: Can we drive a "hybrid car" that carries both regular data and the fragile quantum magic down the same road without crashing either one?

The authors, Nicholas Zaunders and Timothy C. Ralph from the University of Queensland, propose a clever new way to do exactly that. They describe a protocol called Classically-Modulated Quantum Communication (CMQC). Instead of trying to read the quantum signal directly (which would break it), they use a trick called quantum teleportation. Imagine Alice wants to send a secret message to Bob. She encodes her message by nudging a quantum particle slightly, like shifting a marble on a table. She sends this nudged marble to Bob through a noisy, lossy channel (like a bumpy road).

Here is where the magic happens. Bob doesn't look at the marble directly. Instead, he uses a second, pre-shared "entangled" marble that he already has. He mixes the incoming marble with his own on a special splitter and measures the result. This measurement tells him two things at once: it reveals the direction of the "nudge" (which is the classical message) and it teleports the quantum connection to a new marble in his lab. It's like Bob looking at the ripples in a pond to guess where a stone was thrown, while simultaneously making a perfect copy of the stone appear in his hand without ever touching the original.

The paper finds that this scheme works, but it comes with a delicate trade-off. The team ran simulations to see how well the quantum connection survives when they also try to send a strong classical message. They discovered that the system is very sensitive to errors. If the classical message is too noisy or the road is too bumpy (high signal loss), the "nudge" becomes hard to guess correctly. When Bob guesses the wrong direction for the nudge, he accidentally adds a little bit of "static" or noise to the quantum marble.

In their simulations, the researchers found that for the quantum connection to remain useful, the classical message needs to be incredibly precise. For example, if they want to send a message with a bit-error rate (the chance of getting a 0 instead of a 1) of one in a million ( $10^{-6}$ ), the system can only handle a certain amount of signal loss. If the loss gets too high (around 27 decibels in their model), the quantum connection breaks down completely. However, if they are willing to accept a much stricter requirement—where the classical message is almost perfect, with errors as rare as one in ten trillion ( $10^{-14}$ )—the system can handle much more loss and still keep the quantum magic alive.

The paper explicitly argues against the idea that this new method is a "one-size-fits-all" replacement for existing quantum key distribution (QKD) systems that just send classical data. They show that their hybrid approach is actually more fragile to classical errors than those older, simpler methods. The reason is physical: in the older methods, the "correction" of the message happens in a computer after the measurement, which is a virtual fix. In this new method, the correction must happen physically to the quantum state, and if you guess wrong, you physically mess up the quantum marble.

Ultimately, the authors suggest that this protocol is a promising tool for the future, particularly for building "quantum repeaters"—devices that act like rest stops on the quantum highway to boost signals over long distances. By integrating classical and quantum data, existing fiber-optic networks could be upgraded to distribute entanglement without needing entirely new cables. But the paper makes it clear: this isn't a magic wand that solves everything instantly. It's a sophisticated, high-wire act that requires extremely clean signals to keep the quantum connection from snapping. The results are based on mathematical models and simulations, showing that while the physics allows for this dual transmission, the engineering challenge of keeping the classical signal perfectly clean is significant.

Technical Summary: Co-transmission of Classical Data and Continuous-Variable Entanglement over a Single Quantum Channel

Problem Statement
Current displacement-based simultaneous quantum-classical communication (SQCC) protocols face a fundamental incompatibility with most useful quantum communication schemes, such as entanglement distribution and repeater-based quantum key distribution (QKD). In standard SQCC, the classical signal is encoded via displacement on a quantum state. However, extracting this classical information typically requires a direct measurement of the quadratures (homodyne or heterodyne detection). This direct measurement collapses the quantum state, thereby destroying the entanglement required for other protocols. Consequently, existing SQCC schemes are strictly limited to point-to-point Gaussian QKD, where the quantum state is measured immediately to distill a key. There is a lack of a method to distribute continuous-variable (CV) entanglement simultaneously with classical data over a single channel without destroying the quantum resource.

Methodology
The authors propose applying the Classically-Modulated Quantum Communication (CMQC) protocol, originally introduced in [1], to the specific case of distributing CV Gaussian entanglement alongside classical information. The protocol operates as follows:

State Preparation: Alice and Bob each generate a two-mode squeezed vacuum state (TMSV). Alice retains one mode and prepares the other for transmission.
Classical Modulation: Alice encodes classical information by performing a phase-space displacement operation on her outgoing mode. The displacement vector is drawn from a discrete alphabet (specifically Quadrature Phase-Shift Keying, QPSK, in the analysis), associating specific displacements with classical symbols.
Transmission: The displaced mode is transmitted to Bob over a lossy bosonic channel characterized by transmissivity $\eta$ and thermal noise $\epsilon$ .
Teleportation and Demodulation: Upon reception, Bob does not directly measure the incoming mode, as this would destroy the entanglement. Instead, he utilizes his retained half of the TMSV to perform continuous-variable teleportation. He mixes the incoming mode with his auxiliary mode on a balanced beamsplitter and performs dual homodyne detection on the outputs.
- The measurement outcomes serve a dual purpose: they provide an estimator for Alice's classical displacement (allowing Bob to decode the classical symbol) and they facilitate the teleportation of the quantum correlations to Bob's output mode.
Feedforward and Reconstruction: Based on the measurement outcomes, Bob applies a feedforward displacement to his output mode.
- A gain parameter is chosen to convert the teleporter into an effective pure-loss channel.
- Crucially, Bob attempts to remove the classical displacement to return the state to zero-mean. However, because the classical decoding is probabilistic (subject to bit errors), this removal is imperfect. If Bob guesses the wrong classical symbol, he applies an incorrect inverse displacement, introducing non-Gaussian noise into the quantum state.

Key Contributions

Protocol Adaptation: The paper demonstrates the application of the CMQC protocol to the simultaneous distribution of CV entanglement and classical data, circumventing the measurement-destruction limitation of previous SQCC schemes.
Theoretical Characterization: The authors provide a rigorous mathematical analysis of the joint output state. They derive the mean vector and covariance matrix of the ensemble state, accounting for the non-Gaussian noise introduced by classical bit errors.
Performance Metrics: The study characterizes the protocol using three key metrics:
1. Reverse Coherent Information (RCI) as a lower bound on distillable entanglement.
2. Entanglement of Formation ( $E_F$ ).
3. Asymptotic secret-key generation rate ( $K_\infty$ ).
Error Analysis: The paper explicitly quantifies the trade-off between classical signal strength, bit-error rate ( $e_C$ ), and the degradation of quantum entanglement. It identifies that classical bit errors introduce an effective excess noise term ( $\Delta$ ) that scales with the square of the signal amplitude and the error rate.

Results

Entanglement Distribution: The protocol successfully distributes entanglement, but the quality is sensitive to classical bit errors. In the unconstrained regime (infinite squeezing), the protocol approaches the repeaterless bound in the absence of classical signals. However, the presence of classical data introduces decoherence.
Sensitivity to Errors: The Gaussian CMQC scheme is found to be significantly more sensitive to classical bit errors than SQCC-QKD protocols. For the CMQC scheme to saturate the upper bound of the secret-key rate, the classical bit-error rate must be extremely low ( $e_C \leq 10^{-14}$ ), whereas SQCC-QKD can tolerate rates up to $e_C = 10^{-6}$ . This is attributed to the physical nature of the re-displacement operation in CMQC, which cannot "virtually" reduce noise as post-processing in SQCC-QKD can.
Loss and Noise: The protocol fails to deliver distillable entanglement when the effective excess noise caused by classical errors exceeds the maximally tolerable excess noise (MTEN). For a fixed channel loss of 30 dB, the protocol can only distill entanglement if the classical bit-error rate is below $\sim 5 \times 10^{-7}$ (unconstrained regime).
Constrained vs. Unconstrained: The authors show that limiting the squeezing to realistic values (10 dB) does not significantly degrade the maximum tolerable noise compared to the unconstrained (infinite squeezing) case, though it reduces the magnitude of the distillable entanglement at very low error rates.

Significance and Claims
The paper claims that this scheme offers a pathway for integrating classical and quantum information into a single hybrid signal, which is advantageous for future quantum-integrated networks. Specifically:

It allows existing classical communication networks to be retrofitted to distribute entanglement synchronously without major quality loss.
It enables nodes in a classical network to passively generate and store high-quality entanglement with other nodes while maintaining classical uptime, potentially utilizing high-lifetime optical quantum memories.
It provides a physically valid proof of security for CV-QKD with simultaneous classical communication, avoiding the "non-physical" re-displacement assumptions required in previous SQCC-QKD security arguments.

The authors conclude that while the protocol is less robust to classical errors than dedicated SQCC-QKD schemes, it is the first to demonstrate the simultaneous distribution of entanglement and classical data, making it a viable candidate for repeater-based networks where entanglement swapping is required.

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