Constraints on Gaussian Error Channels and Measurements for Quantum Communication

• URL: http://arxiv.org/abs/2206.11842v1
• Date: Thu, 23 Jun 2022 17:18:13 GMT
• Title: Constraints on Gaussian Error Channels and Measurements for Quantum Communication
• Authors: Alex Kwiatkowski, Ezad Shojaee, Sristy Agrawal, Akira Kyle, Curtis Rau, Scott Glancy, Emanuel Knill
• Abstract summary: We study joint Gaussian measurements on two modes $mathsfA$ and $mathsfB$ that take place after independent single-mode Gaussian error channels. We show that, for any Gaussian measurement, if $l_mathsfA + l_mathsfB + n_mathsfA + n_mathsfB geq 1$ then the effective total measurement is separable and unsuitable for teleportation or entanglement swapping of arbitrary input states.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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