Constraints on Gaussian Error Channels and Measurements for Quantum Communication

TL;DR

This paper investigates how Gaussian error channels affect the entanglement capability of joint Gaussian measurements in quantum communication, establishing conditions under which measurements become separable and unsuitable for teleportation.

Contribution

It provides a criterion involving error parameters that determines when Gaussian measurements lose their entanglement potential due to errors.

Findings

If the sum of loss and noise parameters exceeds or equals 1, measurements become separable.

For sums less than 1, some Gaussian measurements can still be inseparable.

The paper characterizes pairs of error channels that make all Gaussian measurements separable.

Abstract

Joint Gaussian measurements of two quantum systems can be used for quantum communication between remote parties, as in teleportation or entanglement swapping protocols. Many types of physical error sources throughout a protocol can be modeled by independent Gaussian error channels acting prior to measurement. In this work we study joint Gaussian measurements on two modes $\mathsf{A}$ and $\mathsf{B}$ that take place after independent single-mode Gaussian error channels, for example loss with parameters $l_\mathsf{A}$ and $l_\mathsf{B}$ followed by added noise with parameters $n_\mathsf{A}$ and $n_\mathsf{B}$. We show that, for any Gaussian measurement, if $l_\mathsf{A} + l_\mathsf{B} + n_\mathsf{A} + n_\mathsf{B} \geq 1$ then the effective total measurement is separable and unsuitable for teleportation or entanglement swapping of arbitrary input states. If this inequality is not satisfied then there exists a Gaussian measurement that remains inseparable. We extend the results and determine the set of pairs of single-mode Gaussian error channels that render all Gaussian measurements separable.