Distribution of Bipartite Entanglement of a Random Pure State

Dezi Liu, Dongsheng Zhou

Satya N. Majumdar, O. Bohigas, Arul Lakshminarayan

Olivier Giraud

We calculate analytic expressions for the distribution of bipartite entanglement for pure random quantum states. All moments of the purity distribution are derived and an asymptotic expansion for the distribution itself is deduced. An approximate expression for moments and distribution of Meyer–Wallach entanglement for random pure states is then obtained.

Céline Nadal, Satya N. Majumdar, Massimo Vergassola

Awais Khan, Ahmad Farooq, Youngmin Jeong +1 more

George Biswas, Shaohua Hu, Jun-Yi Wu +2 more

Abstract We investigate the fidelity of Haar random bipartite pure states from a fixed reference quantum state and their bipartite entanglement. By plotting the fidelity and entanglement on perpendicular axes, we observe that the resulting plots exhibit non-uniform distributions. The distribution depends on the entanglement of the fixed reference quantum state used to quantify the fidelity of the random pure bipartite states. We find that the average fidelity of typical random pure bipartite qubits within a narrow entanglement range with respect to a randomly chosen fixed bipartite qubit is 1 4 . Extending our study to higher dimensional bipartite qudits, we find that the average fidelity of typical random pure bipartite qudits with respect to a randomly chosen fixed bipartite qudit remains constant within a narrow entanglement range. The values of these constants are 1 d 2 , with d being the dimension of the local Hilbert space of the bipartite qudit system, suggesting a consistent relationship between entanglement and fidelity across different dimensions. The probability distribution functions of fidelity with respect to a product state are analytically studied and used as a reference for the benchmarking of distributed quantum computing devices.