Computable lower bounds on the entanglement cost of quantum channels

• URL: http://arxiv.org/abs/2201.09257v2
• Date: Wed, 15 Feb 2023 14:51:11 GMT
• Title: Computable lower bounds on the entanglement cost of quantum channels
• Authors: Ludovico Lami, Bartosz Regula
• Abstract summary: A class of lower bounds for the entanglement cost of any quantum state was recently introduced in [arXiv:2111.02438]. Here we extend their definitions to point-to-point quantum channels, establishing a lower bound for the quantum entanglement cost of any channel. This leads to a bound that is computable as a semidefinite program and that can outperform previously known lower bounds.
• Score: 8.37609145576126
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A class of lower bounds for the entanglement cost of any quantum state was recently introduced in [arXiv:2111.02438] in the form of entanglement monotones known as the tempered robustness and tempered negativity. Here we extend their definitions to point-to-point quantum channels, establishing a lower bound for the asymptotic entanglement cost of any channel, whether finite or infinite dimensional. This leads, in particular, to a bound that is computable as a semidefinite program and that can outperform previously known lower bounds, including ones based on quantum relative entropy. In the course of our proof we establish a useful link between the robustness of entanglement of quantum states and quantum channels, which requires several technical developments such as showing the lower semicontinuity of the robustness of entanglement of a channel in the weak*-operator topology on bounded linear maps between spaces of trace class operators.

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