2023/11/17 by Xin Wang, Mingrui Jing, Wang, Xin +3 · 2 citations
Computer Science · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Information Theory (cs.IT) #Mathematical Physics (math-ph) #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2311.10649
openalex publication_date 2023/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the generalized divergence of 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 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.