Asymmetry effects in homodyne and heterodyne measurements: Positive operator-valued measures and asymptotic security of Gaussian-continuous-variable quantum key distribution
arXiv:2512.22591 · doi:10.1103/ctqn-dxg9
Abstract
We use the Gaussian approximation describing photocount statistics for both the homodyne and the double homodyne (heterodyne) measurements to study asymmetry effects arising from imbalance of the beam splitters and variations in quantum efficiencies of the photodetectors. After computing the symbols of the positive operator-valued measures (POVMs) of noisy measurements that take into account the asymmetry effects, the operator representations for the POVMs are obtained in the form that assumes applying the additive noise quantum channel to the POVMs of noiseless (ideal) measurements. For double homodyne detection, it was found that the noiseless measurements should generally be expressed in terms of the projectors onto squeezed-states and the corresponding squeezed-state operator representation of POVM along with the measurement noise channel depend on the squeezing parameter that lies in the interval dictated by the condition for the excess noise covariance matrix to be positive semi-definite. The analytical results are used to perform analysis of the asymptotic security of the Gaussian-modulated continuous variable quantum key distribution (CV-QKD) protocol in the untrusted-noise scenario where the measurement noise is assumed to be accessible to an adversary. The inherent non-uniqueness of the operator representation for the double-homodyne POVM manifests itself in the squeezing dependent Holevo information that needs to be additionally optimized. For both types of the measurements, the mutual information, the Holevo information and the asymptotic secret fraction are sensitive to asymmetry effects leading to degraded performance of the protocol.
arXiv comment23 pages, 17 figures, revised version
References in corpus (42)
- Quantum information with continuous variables
- The Security of Practical Quantum Key Distribution
- Gaussian Quantum Information
- Secure quantum key distribution with realistic devices
- Continuous variable quantum cryptography using coherent states
- Continuous-variable optical quantum state tomography
- Distillation of secret key and entanglement from quantum states
- Unconditional optimality of Gaussian attacks against continuous-variable QKD
- The characterization of Gaussian operations and Distillation of Gaussian States
- Quantum key distribution over 25 km with an all-fiber continuous-variable system
- Quantum Cryptography without Switching
- Optimality of Gaussian Attacks in Continuous Variable Quantum Cryptography
- Continuous-Variable Quantum Key Distribution with Gaussian Modulation -- The Theory of Practical Implementations
- Security of continuous-variable quantum key distribution via a Gaussian de Finetti reduction
- Analysis of Imperfections in Practical Continuous-Variable Quantum Key Distribution
- Continuous-variable quantum key distribution system: past, present, and future
- Quantum hacking: saturation attack on practical continuous-variable quantum key distribution
- Full characterization of Gaussian bipartite entangled states by a single homodyne detector
- A balanced homodyne detector for high-rate Gaussian-modulated coherent-state quantum key distribution
- Trusted Noise in Continuous-Variable Quantum Key Distribution: a Threat and a Defense
- Homodyne-detector-blinding attack in continuous-variable quantum key distribution
- Quantum Hacking on Quantum Key Distribution using Homodyne Detection
- Optimal Gaussian measurements for phase estimation in single-mode Gaussian metrology
- Operational Theory of Homodyne Detection
- Experimental quantum homodyne tomography via machine learning
- Quantum characterization of bipartite Gaussian states
- Tuning between photon-number and quadrature measurements with weak-field homodyne detection
- Homodyne detection for atmosphere channels
- Gaussian localizable entanglement
- Quantum key distribution with non-ideal heterodyne detection: composable security of discrete-modulation continuous-variable protocols
- Characterizing photon number statistics using conjugate optical homodyne detection
- General-dyne unravelling of a thermal master equation
- Homodyne tomography with homodyne-like detection
- When heterodyning beats homodyning: an assessment with quadrature moments
- Continuous-variable quantum key distribution with noisy squeezed states
- Analysis of the trusted-device scenario in continuous-variable quantum key distribution
- Inefficient eight-port homodyne detection and covariant phase space observables
- Photocounting measurements with dead time and afterpulses in the continuous-wave regime
- Full statistics of ideal homodyne detection using real (noisy) local oscillator
- Detector noise in continuous-variable quantum key distribution
- The eight-port homodyne detector: the effect of imperfections on quantum random number generation and on detection of quadratures
- Estimation of Wigner distribution of single mode Gaussian states: a comparative study