Computable and Faithful Lower Bound on Entanglement Cost

• URL: http://arxiv.org/abs/2311.10649v3
• Date: Wed, 09 Apr 2025 17:15:46 GMT
• Title: Computable and Faithful Lower Bound on Entanglement Cost
• Authors: Xin Wang, Mingrui Jing, Chengkai Zhu,
• Abstract summary: We develop computable and faithful lower bounds on the entanglement cost under quantum operations.<n>Our bounds are efficiently computable via semidefinite programming.<n>We extend our methodology to derive lower bounds on the entanglement cost of both point-to-point and bipartite quantum channels.
• Score: 5.086696108576776
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantifying the minimum entanglement needed to prepare quantum states and implement quantum processes is a key challenge in quantum information theory. In this work, 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 logarithmic $k$-negativity, a generalization of logarithmic negativity. Our bounds are efficiently computable via semidefinite programming and provide non-trivial values for all states that are not PPT, establishing their faithfulness. 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 states and channels. These findings push the boundaries of understanding the structure of entanglement and the fundamental limits of entanglement manipulation.

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