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arXiv · 2201.09257

Computable lower bounds on the entanglement cost of quantum channels

Ludovico Lami·Bartosz Regula
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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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Ludovico Lami, Bartosz Regula. 2022-01-23. Computable lower bounds on the entanglement cost of quantum channels. https://doi.org/10.1088/1751-8121%2Faca731

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