MDI CV-QKD: Secure Quantum Key Distribution

• Measurement-device-independent CV-QKD is a protocol that uses Gaussian-modulated coherent states and untrusted relays to eliminate detector-side attacks.
• It incorporates advanced one-time calibration techniques to accurately model source imperfections and ensure secure shot-noise normalization.
• Enhanced protocol variants employing photon subtraction, quantum catalysis, and squeezed states extend secure transmission distances and boost key rates in realistic network conditions.

Measurement-device-independent continuous-variable quantum key distribution (CV-MDI QKD) is a quantum cryptographic protocol that fundamentally eliminates all detector-side channel attacks by pushing measurement to an untrusted relay. The protocol is based on the transmission and joint measurement of Gaussian-modulated coherent states over lossy and noisy quantum channels. CV-MDI QKD has witnessed rapid technical and theoretical advances, including protocols employing photon subtraction, quantum catalysis, squeezed states, one-time calibration countermeasures for imperfect sources, and high-rate digital implementations (Huang et al., 2023, Wang et al., 23 Feb 2025, Fletcher et al., 16 Jan 2025, Li et al., 2013, Ma et al., 2017, Ye et al., 2019, Hajomer et al., 2022). The following sections detail the protocol architecture, practical security challenges, countermeasures, protocol variants, finite-size security, and experimental realizations.

1. Protocol Architecture and Security Foundations

CV-MDI QKD operates in two equivalent frameworks: the prepare-and-measure (PM) scheme and the entanglement-based (EB) scheme. In PM, Alice and Bob independently prepare coherent states $\lvert \alpha \rangle = \lvert x_A + i p_A \rangle$ and $\lvert \beta \rangle = \lvert x_B + i p_B \rangle$, with $x, p$ drawn from zero-mean Gaussian distributions of variance $V = V_{\rm mod} + 1$, and send them through untrusted, lossy channels (transmissivities $\eta_A$, $\eta_B$) to a relay "Charlie" (Wang et al., 23 Feb 2025, Li et al., 2013, Fletcher et al., 16 Jan 2025). Charlie performs a continuous-variable Bell measurement—interferes the incoming modes on a 50:50 beam splitter, measures the $x$ and $p$ quadratures in separate homodynes, then publicly broadcasts the complex result $r=(x_c + i p_c)/\sqrt{2}$. Using $r$, Alice and Bob correlate their raw data and perform classical post-processing: parameter estimation, information reconciliation, and privacy amplification.

Security against collective attacks is guaranteed in theory by the protocol's reduction to an effective one-way CV-QKD scheme with appropriately modified channel parameters. All measurement devices are untrusted, so all detection-side vulnerabilities are relegated to Eve (Li et al., 2013, Wang et al., 23 Feb 2025, Fletcher et al., 16 Jan 2025).

2. Practical Source Imperfections and Security Loopholes

While measurement-device-independence closes all detector side-channels, CV-MDI QKD's practical security depends critically on the integrity of the sources (lasers and modulators). Realistic quantum sources exhibit:

• Modulation errors: Nonideal extinction ratios introduce preparation noise $E_s$.
• Relative intensity noise (RIN): Stochastic intensity fluctuations add excess variance $\xi_{\rm RIN}$.
• Calibration loophole: If RIN is neglected, shot-noise-unit calibration underestimates total excess noise, resulting in significant overestimation of the secret key rate and a residual vulnerability (Huang et al., 2023).

For example, simulation shows that ignoring a RIN variance of $\xi_{\rm RIN}=0.4$ leads to key rates overestimated by up to a factor of 26.6 at 18 km fiber in symmetric configuration (Huang et al., 2023).

3. One-time Calibration Countermeasure for Source Imperfections

To model and suppress the practical security risk arising from source imperfections, Huang et al. introduce a one-time calibration (OTC) countermeasure (Huang et al., 2023). The key idea is to perform a single shot-noise calibration that incorporates preparation noise, RIN, and detector electronic noise into the normalization (shot-noise-unit $u'$):

• Alice and/or Bob tap a fraction $T_M$ of each outgoing signal to a monitoring homodyne. With LO on but no quantum signal present, the variance is measured: $V_{\text{tot}} = u + V_{\text{el}} + \xi_{\rm RIN}$. The new SNU $u' \equiv V_{\text{tot}}$ is used for quadrature normalization.
• In security analysis, the monitoring is represented as additional beam splitters (with transmissivities $\eta_d$ for efficiency and $\eta_e$ for RIN + electronic noise).

Three practical configurations are considered:

• Case 1 (Alice-only): Only Alice monitors and calibrates her source noise.
• Case 2 (Bob-only): Only Bob monitors his source noise.
• Case 3 (Both users): Both Alice and Bob perform OTC monitoring.

OTC eliminates the hidden preparation-noise loophole, models all source noise as trusted, and precisely restores parameter estimation in security proofs. OTC reduces Eve's Holevo information $\chi_{AE|r}$ and prevents inflated secret key rates due to undetected excess noise (Huang et al., 2023).

4. Protocol Variants: Non-Gaussian Operations, Squeezing, Unidimensional Modulation

CV-MDI QKD supports several protocol-level enhancements to the Gaussian coherent-state baseline:

• Photon subtraction: Non-Gaussian operations such as photon subtraction or virtual photon subtraction increase the effective entanglement shared by Alice and Bob, boosting transmission distance and key rates. Single-photon subtraction, implemented via a low-reflectivity beam splitter and PNRD, nearly doubles secure range (e.g., 36 km symmetric, 63 km asymmetric for $V=15\text{--}100$, $\varepsilon=0.01$, $\beta=0.96$) (Ma et al., 2017).
• Quantum catalysis: Zero-photon catalysis achieves a noiseless attenuation map in phase space and further extends range and robustness against detector imperfections compared to SPS. For instance, ZPC-based CV-MDI-QKD increases key-rate by factors of 1.3–3 and extends secure distance by 20–30% over SPS, tolerating higher excess noise and lower detection efficiency (Ye et al., 2019, Singh et al., 2021).
• Squeezed-state CV-MDI-QKD: Gaussian-modulated squeezed states, with optimized addition of trusted Gaussian noise on the reconciliation side, attain higher secret key rates and longer transmission distances than coherent-state protocols (Zhang et al., 2014).
• Unidimensional modulation: Simplifies implementation by modulating only one quadrature per user; achieves performance comparable to full two-quadrature Gaussian modulation (Bai et al., 2019).

5. Finite-size Security, Parameter Estimation, and Composability

Finite-size effects crucially impact practical secret-key rates, especially in metropolitan scale deployments. Parameter estimation is typically carried out by maximum-likelihood estimation and central-limit theorem arguments over $m$ revealed pulses, yielding confidence intervals for transmission coefficients and excess noises (Zhang et al., 2017, Lupo et al., 2017, Hajomer et al., 2023). Security is defined composably: for block size $N$, the secret-key length $\ell$ at failure probability $\varepsilon_{\text{tot}}$ is

$$\ell \le \beta\,I(A: B) - \chi(B:E) - \sqrt{N}\,\Delta(N,\varepsilon_{\text{PE}}) - \log_2(1/\varepsilon_{\text{PA}}) - \ldots$$

where $\Delta$ quantifies parameter estimation uncertainty and privacy amplification overhead. Advanced proofs use min-entropy smoothing and Gaussian de Finetti reductions to extend security to general coherent attacks; positive rates are obtained for realistic $N \sim 10^7$–$10^9$ even under practical loss and noise (Lupo et al., 2017).

Optimal geometry places the relay close to one user (preferably Bob) to maximize effective transmittance and minimize end-to-end noise, with asymmetric configurations supporting link distances exceeding $40$ km for trusted source and OTC monitoring (Li et al., 2013, Huang et al., 2023, Zhang et al., 2017).

6. Experimental Realizations: Protocol Implementations and Performance

High-rate CV-MDI-QKD has been experimentally realized using a variety of digital, optical, and source-monitoring architectures:

• Digital relay structures: Polarization-based 90° optical hybrids, local oscillator distribution via heterodyne optical locking, and FPGA-based DSP pipelines have enabled throughput up to $20$ MBaud symbol rates and $2.6$ Mbit/s secure key rates over 10 km fiber links, validated against collective attacks in the finite-size regime (Hajomer et al., 2022, Hajomer et al., 2023, Wang et al., 23 Feb 2025).
• Practical countermeasures: One-time shot-noise calibration schemes, embedded monitoring homodynes, and finely tuned beam splitter transmissivities for OTC are incorporated to address source nonidealities (Huang et al., 2023).
• Metropolitan and access network topology: CV-MDI-QKD performance is further optimized with star-type topology for multi-user quantum access networks, exploiting relay proximity to minimize per-link loss.
• Physical-layer integration: Integration with DWDM classical telecommunication channels is possible provided noise from SpRS, FWM, and LCXT processes is managed through careful channel allocation and narrow optical filtering. Secure ranges of up to 6 km are sustainable with 10–40 DWDM classical channels, optimal in the C-band (Vorontsova et al., 2023).

Benchmark parameters from realized CV-MDI-QKD systems include quantum efficiencies $\eta_{\text{det}}\sim 0.90$–0.95, modulation variances $V\sim 6$–36 SNU, excess noises $\xi < 0.11$ SNU, reconciliation efficiency $\beta\sim 0.97$, and secure key rates of 0.12–0.19 bit/use over 10–17 km fiber (Hajomer et al., 2022, Hajomer et al., 2023, Wang et al., 23 Feb 2025).

7. Outlook and Practical Security

Measurement-device independence combined with continuous-variable encoding positions CV-MDI-QKD as a leading candidate for metro-scale quantum networks resistant to both detection- and source-side attacks. The OTC countermeasure fundamentally closes preparation-noise loopholes, robust protocol variants (photon subtraction, catalysis, squeezing) enhance rate and range, and advances in high-throughput digital architectures demonstrate scalability (Huang et al., 2023, Wang et al., 23 Feb 2025, Hajomer et al., 2022). Ongoing theoretical and experimental work focuses on further increasing detection efficiency, simplifying LO distribution, integrating photonic devices, extending multi-party and networked CV-MDI-QKD, and consolidating practical security by composable proof methodologies (Wang et al., 23 Feb 2025, Lupo et al., 2017).