Today’s Image of the Week comes from a study of *The difference between two random mixed quantum states: exact and asymptotic spectral analysis* from the Universidad de los Andes and ETH Zürich. In this recent JPhysA paper, José Mejía, Camilo Zapata and Alonso Botero investigate the spectral statistics of the difference of two density matrices, each of which is independently obtained by partially tracing a random bipartite pure quantum state. Their results make it possible to quantify the typical asymptotic distance between the two random mixed states using various distance measures.

Joint probability density function of eigenvalues as a function of two independent eigenvalues taken from José Mejía et al 2017 J. Phys. A: Math. Theor. 50 025301 . © IOP Publishing, All Rights Reserved.

The multi-lobe shape of the probability density function (PDF) is a signature of the eigenvalue repulsion phenomenon, causing the PDF to vanish whenever two of the eigenvalues are the same.

**Read More: **The difference between two random mixed quantum states: exact and asymptotic spectral analysis

This work is licensed under a Creative Commons Attribution 3.0 Unported License

Front and article image taken from José Mejía *et al* 2017 *J. Phys. A: Math. Theor.* **50** 025301, © IOP Publishing, All Rights Reserved.

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Categories: Journal of Physics A: Mathematical and Theoretical

Tags: Image of the week, quantum physics, Theoretical Physics