Converting separable conditions to entanglement-breaking conditions

We present a general method to derive entanglement breaking (EB) conditions for continuous-variable quantum gates. We start with an arbitrary entanglement witness and reach an EB condition. The resultant EB condition is applicable not only for quantum channels but also for general quantum operations; namely, the trace-non-increasing class of completely positive maps. We illustrate our method associated with a quantum benchmark based on the input ensemble of Gaussian distributed coherent states. We also exploit our idea for channels acting on finite-dimensional systems and present a Schmidt-number benchmark based on input states of two mutually unbiased bases and measurements of generalized Pauli operators.