Quantum de Moivre-Laplace theorem for noninteracting indistinguishable particles in random networks

Author(s)

Shchesnovich, V. S.

• Document type: Journal article
• Source: Journal of Physics A-Mathematical and Theoretical; v. 50, n. 50 DEC 15 2017.
• Web of Science Citations: 0

Abstract

The asymptotic form of the average probability to count N indistinguishable identical particles in a small number r << N of binned-together output ports of a M-port Haar-random unitary network, proposed recently in Shchesnovich (2017 Sci. Rep. 7 31) in a heuristic manner with some numerical confirmation, is presented with mathematical rigour and generalised to an arbitrary (mixed) input state of N indistinguishable particles. It is shown that, both in the classical (distinguishable particles) and quantum (indistinguishable particles) cases, the average counting probability into r output bins factorises into a product of r - 1 counting probabilities into two bins. This fact relates the asymptotic Gaussian law to the de Moivre-Laplace theorem in the classical case and similarly in the quantum case where an analogous theorem can be stated. The results have applications to the setups where randomness plays a key role, such as the multiphoton propagation in disordered media and the scattershot Boson sampling. (AU)

• FAPESP's process: 15/23296-8 - Behavior of identical particles in quantum networks and the Boson Sampling
• Grantee: Valery Shchesnovich
• Support Opportunities: Regular Research Grants