Continuous Variable Quantum Key Distribution with Single Quadrature Measurement at Arbitrary Reference Frame

TL;DR

This work addresses the practical challenge of measurement-frame drift in GMCS CV-QKD by proposing a homodyne-only scheme where Bob measures a single quadrature along an arbitrarily rotating frame, with Alice realigning post-measurement after Bob reveals the rotation. Using covariance-matrix formalism, it maps the scheme to GMCS and analyzes three drift scenarios: fixed-known to Eve, fixed-unknown to Eve, and drifting frames, showing that security remains intact against collective attacks and reduces to GG02 behavior when frames are fixed and revealed. The key contributions include a detailed security analysis under intercept-resend and entangled-cloner attacks, demonstration of equivalence to GG02 under certain conditions, and practical validation of LLO/TLO compatibility without a phase modulator. The results have significant practical impact, simplifying hardware for CV-QKD in free-space and fiber channels while preserving information-theoretic security and robustness to Bob's internal phase drift.

Abstract

We propose a simplified measurement scheme for a Gaussian modulated coherent state (GMCS) protocol for continuous variable quantum key distribution (CV-QKD), utilizing homodyne detection without quadrature switching. The reference frame of measurement is taken to be at an arbitrary angle, however, reconciliation converges the proposed scheme to GMCS with switching quadrature protocol. The arbitrary frame of measurement could also include the unknown random thermal drift within Bob's optical measurement setup. We found this scheme is advantageous for practical free-space and fibre-based GMCS protocol based CV-QKD systems as it does not require a phase modulator for random measurement selection quadrature at Bob.

Figures (6)

• Figure 1: CV-QKD with the homodyne detection setting. Alice prepares two mode squeezed vacuum states (TMSVS) and sends one of the modes to Bob. Bob's setup interferes the signal (S) with the Local Oscillator (LO) pulses using a beam splitter (BS) and performs homodyne measurements using photodiodes (D1 & D2). There could be a relative phase drift between signal and LO inside Bob's station (from the blue marker-'A' to the BS) represented by $\theta_{\text{Bob}}$ (see text below), that is independent from the phase drift in the channel and Alice's station. Contrary to standard homodyne measurement, we do not use a phase modulator (PM) in our scheme. $\hat{x}_{\text{B}}$ is the quadrature output of the homodyne along the measurement angle $\theta_{\text{Bob}}$. The eavesdropping by Eve is characterized by reduced transmittivity $T$, and excess noise from the channel $\xi$.
• Figure 2: (a) Rotated frame of measurement by the receiver Bob. He always measures along the quadrature $\hat{x}_{\text{B}} = \cos{\theta_{\text{Bob}}}(\hat{q}_{\text{B}}) + \sin{\theta_{\text{Bob}}}(\hat{p}_{\text{B}})$, where $\theta_{\text{Bob}}$ is the angle of the rotation w.r.t $\hat{q}_{\text{B}}$ (as well as $\hat{q}_{\text{A}}$). (b) After Bob's announcement of the angle $\theta_{\text{Bob}}$, Alice rotates her frame to coincide with $\hat{x}_{\text{B}}$.
• Figure 3: Secret key fraction as a function of distance. Here the angle of rotation is chosen to be $\theta_{\text{Bob}} = 90^\circ$. Blue (Orange) line corresponds to the noise $\xi=0.0001$ ($\xi=0.0107$, for a phase drift of $5^\circ$).
• Figure 4: Mutual information between Alice and Bob, as a function of the relative angle of the frame of references.
• Figure 5: Experimentally measured phase drift $\theta_{\text{Bob}}$ inside Bob's station, from the point 'A' to BS in Fig. \ref{['fig:cvqkd']}. The figure shows the randomness in the phase drift fluctuations along with the frequency of phase drift. We have taken the data with an asymmetric Mach-Zehnder interferometer, having 100 ns delay between the two paths - of signal and LO. This in principle emulates the phase drift due to thermal fluctuations inside Bob's station in a CV-QKD implementation.