On the generation of random ensembles of qubits and qutrits Computing separability probabilities for fixed rank states

TL;DR

This paper discusses methods for generating random mixed quantum states and computes the probabilities of these states being separable, focusing on qubit and qutrit pairs of fixed rank using Hilbert-Schmidt and Bures ensembles.

Contribution

It introduces procedures for generating random mixed states and calculates separability probabilities for fixed rank states in qubit and qutrit systems.

Findings

Computed separability probabilities for fixed rank states.

Analyzed Hilbert-Schmidt and Bures ensembles.

Provided insights into quantum state separability.

Abstract

The question of the generation of random mixed states is discussed, aiming for the computation of probabilistic characteristics of composite finite dimensional quantum systems. Particularly, we consider the generation of the random Hilbert-Schmidt and Bures ensembles of qubit and qutrit pairs and compute the corresponding probabilities to find a separable state among the states of a fixed rank.