Multi-Boson Correlation Sampling with Multi-mode Thermal Sources

TL;DR

This paper explores the use of multi-mode thermal sources in boson sampling, deriving matrix permanent formulations for multi-boson correlation functions, and discusses implications for quantum computing, metrology, and communication.

Contribution

It generalizes boson sampling to thermal sources using time-correlation measurements and links the properties of matrix permanents to multi-boson interference physics.

Findings

Derived equivalent formulations for multi-boson correlation functions as matrix permanents.

Highlighted the complexity-theoretic implications of multi-boson interference with thermal sources.

Suggested applications in quantum metrology and communication using bosonic thermal sources.

Abstract

The determination of the computational complexity of the boson sampling problem with single boson sources has opened a novel research direction in the quantum computing field. Some research effort has also been devoted towards the use of different input sources where the sampling from the output distribution of a linear interferometer is still a complex task not achievable by a classical device. In this letter, we discuss the use of multi-mode thermal sources, based on a generalization of the boson sampling problem which relies on time-correlation measurements. We derive, for any possible sample, two equivalent formulations for the respective multi-boson correlation functions in terms of matrix permanents. The properties of these permanents emerging from the physics of multi-boson interference raise essential questions in the field of complexity theory. Our results are a manifestation of the physics behind correlated measurements in either photonic or atomic interferometers with bosonic thermal sources. This fascinating physics paves the way towards important applications not only in quantum computing but also in quantum metrology and quantum communication, by taking advantage of different kinds of bosonic sources.