Physics – Quantum Physics
Scientific paper
2012-02-14
Physics
Quantum Physics
39 pages, 10 figures
Scientific paper
The entanglement between two arbitrary subsystems of random pure states is studied via properties of the density matrix's partial transpose, $\rho_{12}^{T_2}$. The density of states of $\rho_{12}^{T_2}$ is close to the semicircle law when both subsystems have dimensions which are not too small and are of the same order. A simple random matrix model for the partial transpose is found to capture the entanglement properties well, including a transition across a critical dimension. Log-negativity is used to quantify entanglement between subsystems and approximate analytic formulas for this are derived. The skewness of the eigenvalue density of $\rho_{12}^{T_2}$ is derived analytically, using the average of the third moment that is also shown to be related to a generalization of the Kempe invariant. Extreme value statistics, especially the Tracy-Widom distribution, is found to be useful in calculating the fraction of entangled states at critical dimensions. These results are tested in a quantum dynamical system of three coupled standard maps, where one finds that if the parameters represent a strongly chaotic system, the results are close to those of random states, although there are some systematic deviations at critical dimensions.
Bhosale Udaysinh T.
Lakshminarayan Arul
Tomsovic Steven
No associations
LandOfFree
Entanglement between two subsystems, the Wigner semicircle and extreme value statistics does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Entanglement between two subsystems, the Wigner semicircle and extreme value statistics, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Entanglement between two subsystems, the Wigner semicircle and extreme value statistics will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-88956