Computable and Faithful Lower Bound on Entanglement Cost.

Authors

Xin Wang, Mingrui Jing, Chengkai Zhu

Published in

Physical review letters. Volume 134. Issue 19. Pages 190202. May 16, 2025.

Abstract

Quantifying the minimum entanglement needed to prepare quantum states and implement quantum processes is a key challenge in quantum information theory. In this Letter, we develop computable and faithful lower bounds on the entanglement cost under quantum operations that completely preserve the positivity of partial transpose (PPT operations), by introducing the generalized divergence of k-negativity, a generalization of logarithmic negativity. Our bounds are efficiently computable via semidefinite programming and provide nontrivial values for all states that are non-PPT (NPT), establishing their faithfulness for the resource theory of NPT entanglement. Notably, we find and affirm the irreversibility of asymptotic entanglement manipulation under PPT operations for full-rank entangled states. Furthermore, we extend our methodology to derive lower bounds on the entanglement cost of both point-to-point and bipartite quantum channels. Our bound demonstrates improvements over previously known computable bounds for a wide range of quantum states and channels. These findings push the boundaries of understanding the structure of entanglement and the fundamental limits of entanglement manipulation.

PMID:
40446230
Bibliographic data and abstract were imported from PubMed on 31 May 2025.

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