Multipartite entanglement distribution for random pure states

YANET ALVAREZ; MARIELA PORTESI; GUSTAVO MARTÍN BOSYK

Buenos Aires

Conferencia; XII Conference on Quantum Foundations: From Wave-Particle Duality To Quantum Technologies; 2023

Entanglement is a key concept in quantum mechanics and gives rise to various phenomena that cannot be addressed within classical physics. The general problem of how to quantify the degree of entanglement in an arbitrary multipartite system has not been completely solved yet. Although fullycharacterizing the multipartite nature of correlations is a challenging task, there are simple computable measures of entanglement that can be considered[1]. These different definitions often do not agree with each other, mainly because they tend to capture different aspects of the phenomenon; however, they can provide useful indicators. Here, we explore the distribution of multipartite entaglement for random pure states. Multipartite entanglement shares many characteristics with complex systems and can be analyzed appealing to a classical statistical mechanics approach. Several authors have used this approach to characterize both bipartite [2, 3] and multipartite [4–6] entanglement of random pure states, employing measures such as Renyi’s entropy and purity, respectively. In order to extend this analysis, we study the first moments of the distribution function of a multipartite entanglement measure for n qubits. Specifically, we use Tsallis entropy as an entanglement measure with an integer entropic index q > 2 (q = 2 it reduces to purity).1. A. J. Scott, Phys. Rev. A 69, 052330 (2004).2. C. Nadal, Phys. Rev. Lett. 104, 110501 (2010).3. P. Facchi, J. Phys. A: Math. Theor. 52, 414002 (2019).4. P. Facchi, J. Phys. A: Math. Theor. 43, 225303 (2010).5. P. Facchi, Rendiconti Lincei 20, 25–67 (2009).6. A. Borras, J. Phys. A: Math. Theor. 40, 13407 (2007).