Quantum Benchmark via an Uncertainty Product of Canonical Variables

We present an uncertainty-relation-type quantum benchmark for continuous-variable (CV) quantum channels that works with an input ensemble of Gaussian distributed coherent states and homodyne measurements. It determines an optimal trade-off relation between canonical quadrature noises unbeatable by entanglement breaking channels and refines the notion of two quantum duties introduced in the original papers of CV quantum teleportation. It can verify the quantum-domain performance for all one-mode Gaussian channels.We also address the case of stochastic channels and the effect of asymmetric gains.