Thresholds for reduction-related entanglement criteria in quantum information theory

Abstract

We consider random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state. We compute thresholds for the dimension of the system being traced out, so that the resulting bipartite quantum state satisfies the reduction criterion in different asymptotic regimes. We consider as well the basis-independent version of the reduction criterion (the absolute reduction criterion), computing thresholds for the corresponding eigenvalue sets. We do the same for other sets relevant in the study of absolute separability, using techniques from random matrix theory. Finally, we gather and compare the known values for the thresholds corresponding to different entanglement criteria, and conclude with a list of open questions.

References in corpus (5)

• Separability from Spectrum for Qubit-Qudit States
• Asymptotics of random density matrices
• Positive reduction from spectra
• On the reduction criterion for random quantum states
• $k$-extendibility of high-dimensional bipartite quantum states

Cited by in corpus (7)

• Random matrix techniques in quantum information theory
• Fundamental Limitation on the Detectability of Entanglement
• Characterizing the boundary of the set of absolutely separable states and their generation via noisy environments
• Timelessness strictly inside the Quantum Realm
• On the asymptotic distribution of block-modified random matrices
• $k$-extendibility of high-dimensional bipartite quantum states
• On the separability of unitarily invariant random quantum states - the unbalanced regime