Properties of random mixed states of dimension N distributed uniformly with respect to the Hilbert-Schmidt measure are investigated. We show that for large N, due to the concentration of measure phenomenon, the trace distance between two random states tends to a fixed number 1/4+1/π, which yields the Helstrom bound on their distinguishability. To arrive at this result we apply free random calculus and derive the symmetrized Marchenko-Pastur distribution. We consider also random quantum channels, especially the limiting behaviour of the diamond norm for two independent random quantum operations. In the case of flat measure on random channels, the limiting value of the diamond norm is equal to 1/2+2/π.
By Anthony Leverrier
By Zbigniew Puchała
By Benoit Collins
By Satya Majumdar
By Motohisa Fukuda
By Anand Natarajan
By Nilanjana Datta
By Daniel Stilck Franca
By Ke Li
By Radosław Adamczak
By Madalin Guta
By Antonio Acín
By Ashley Montanaro
By Ping Zhong
By James Mingo
By Camille Male
By Clément Delcamp
By Claudio Dappiaggi
By Alexander Strohmaier
By Misha Gromov
By Olivier Benoist
By Viviane Pons
By Viviane Pons
