# On the separability of unitarily invariant random quantum states - the unbalanced regime

@article{Nechita2018OnTS,
title={On the separability of unitarily invariant random quantum states - the unbalanced regime},
author={Ion Nechita},
journal={arXiv: Mathematical Physics},
year={2018}
}
• I. Nechita
• Published 31 January 2018
• Physics, Mathematics
• arXiv: Mathematical Physics
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… Expand
1 Citations

#### Figures from this paper

Diagonal unitary and orthogonal symmetries in quantum theory
• Mathematics, Physics
• Quantum
• 2021
We analyze bipartite matrices and linear maps between matrix algebras, which are respectively, invariant and covariant, under the diagonal unitary and orthogonal groups' actions. By presenting anExpand

#### References

SHOWING 1-10 OF 51 REFERENCES
Thresholds for reduction-related entanglement criteria in quantum information theory
• Computer Science, Mathematics
• Quantum Inf. Comput.
• 2015
This work considers random bipartite quantum states obtained by tracing out one subsystem from a random, uniformly distributed, tripartite pure quantum state, and computing thresholds for the corresponding eigenvalue sets. Expand
On the reduction criterion for random quantum states
• Mathematics, Physics
• 2014
In this paper, we study the reduction criterion for detecting entanglement of large dimensional bipartite quantum systems. We first obtain an explicit formula for the moments of a random quantumExpand
Induced measures in the space of mixed quantum states
• Physics, Mathematics
• 2000
We analyse several product measures in the space of mixed quantum states. In particular, we study measures induced by the operation of partial tracing. The natural, rotationally invariant measure onExpand
Partial transpose of random quantum states: exact formulas and meanders
• Mathematics, Physics
• 2012
We investigate the asymptotic behavior of the empirical eigenvalues distribution of the partial transpose of a random quantum state. The limiting distribution was previously investigated via WishartExpand
Random matrix techniques in quantum information theory
• Physics, Mathematics
• 2015
The purpose of this review article is to present some of the latest developments using random techniques, and in particular, random matrix techniques in quantum information theory. Our review is aExpand
A matrix realignment method for recognizing entanglement
• Mathematics, Computer Science
• Quantum Inf. Comput.
• 2003
This paper develops a very simple method to assess the inseparability of bipartite quantum systems, which is based on a realigned matrix constructed from the density matrix, and gives an estimate for the degree of entanglement of the quantum state. Expand
High-Dimensional Entanglement in States with Positive Partial Transposition.
• Physics, Mathematics
• Physical review letters
• 2018
This work provides the first explicit construction of a family of PPT states that achieves linear scaling in the local dimension and proves that random PPTStates typically share this feature, and links the Schmidt number to entangled sub-block matrices of a quantum state. Expand
Largest separable balls around the maximally mixed bipartite quantum state
• Physics
• 2002
For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral ${l}_{p}$ norms for $1l~pl~\ensuremath{\infty},$ of separable (unentangled) matrices aroundExpand
Realigning random states
• Mathematics, Physics
• 2012
We study how the realignment criterion (also called computable cross-norm criterion) succeeds asymptotically in detecting whether random states are separable or entangled. We consider random statesExpand
$k$-extendibility of high-dimensional bipartite quantum states
The idea of detecting the entanglement of a given bipartite state by searching for symmetric extensions of this state was first proposed by Doherty, Parrilo and Spedialeri. The complete family ofExpand