On the separability of unitarily invariant random quantum states - the unbalanced regime
arXiv:1802.00067 · doi:10.1155/2018/7105074
Abstract
We study entanglement-related properties of random quantum states which are unitarily invariant, in the sense that their distribution is left unchanged by conjugation with arbitrary unitary operators. In the large matrix size limit, the distribution of these random quantum states is characterized by their limiting spectrum, a compactly supported probability distribution. We prove several results characterizing entanglement and the PPT property of random bipartite unitarily invariant quantum states in terms of the limiting spectral distribution, in the unbalanced asymptotical regime where one of the two subsystems is fixed, while the other one grows in size.
arXiv commentNew section on PPT matrices with large Schmidt number
References in corpus (26)
- Quantum entanglement
- Separability of Mixed States: Necessary and Sufficient Conditions
- Average Entropy of a Subsystem
- A complete family of separability criteria
- Induced measures in the space of mixed quantum states
- Symmetry implies independence
- Largest separable balls around the maximally mixed bipartite quantum state
- One-and-a-half quantum de Finetti theorems
- Random quantum correlations and density operator distributions
- Random matrix techniques in quantum information theory
- Typicality in random matrix product states
- Entanglement thresholds for random induced states
- Distinguishability of generic quantum states
- A Family of Norms With Applications In Quantum Information Theory
- High-Dimensional Entanglement in States with Positive Partial Transposition
- A new application of Random Matrices: Ext(C*_{red}(F_2)) is not a group
- Realigning random states
- Partial transpose of random quantum states: exact formulas and meanders
- On the asymptotic distribution of block-modified random matrices
- Random and free positive maps with applications to entanglement detection
- On the reduction criterion for random quantum states
- -extendibility of high-dimensional bipartite quantum states
- Thresholds for reduction-related entanglement criteria in quantum information theory
- Additivity rates and PPT property for random quantum channels
- Estimates for compression norms and additivity violation in quantum information
- A Family of Norms With Applications In Quantum Information Theory II