BInd

The past few decades have seen a stunning development in the ability to control individual quantum systems. This not only allows us to test fundamental properties of quantum mechanics, such as quantum superposition or quantum entanglement, at an unprecedented scale but also we can use this control to develop new transformational technologies such as quantum cryptography, quantum metrology and quantum computers and simulators.

Many of these technologies are based on the ability to control a large number of bosonic particles such as photons or certain kinds of atoms which can be trapped in optical lattices. Indeed, recent experiments with large-scale photonic circuits have already claimed quantum computational advantage for a particular problem called boson sampling [Zh20]. The boson sampling problem has attracted a lot of recent interest because of its apparent simplicity and experimental feasibility: it is a purely linear interferometry experiment followed by photon counting measurements. The seminal work of computer scientists Aaronson and Arkhipov provided compelling arguments coming from complexity theory which show that no classical algorithm can efficiently simulate boson sampling [AA11]. The capability to do boson sampling is also seen as an important milestone on the road to develop a large-scale photonic quantum computer.

An important challenge for photonic quantum technologies is that photon sources are not perfect. Phhotons have its own internal degrees of freedom like polarization or frequency and imperfect photon sources as well as synchronization problems imply that photons that will have small differences in their internal degrees of freedom making them partially distinguishable [Ti15a, Sh15]. This is an important hindrance to potential technological applications. For example, it is known that partial distinguishability can be exploited by classical simulations of boson sampling, which may invalidate claims of quantum computational advantage [Re18]. Any such claim should thus be supported by tests that show that the output statistics is consistent bosons with a high degree of indistinguishability.

The study of linear interference with partially distinguishable bosons is thus motivated by practical reasons but also it is interesting in its own right – it provides a way to study the transition between the quantum behaviour of ideal indistinguishable bosons and the classical behaviour of fully distinguishable bosons, the latter being governed by classical statistics. Current photonic and atomic experiments are also able to tune bosonic distinguishability to explore this transition [Me17, Yo23].

The present research project will explore new theoretical avenues related to the interference of multiple partially distinguishable bosons and aims at contributing to fundamental theoretical aspects of quantum optics as well as the burgeoning field of quantum technologies. Our first tasks relates to the very foundations of quantum statistical physics. One of the most fundamental questions in this field is to explain how subsystems of large quantum systems evolving under unitary dynamics reach equilibrium. While this topic inspired a large amount of work, equilibration phenomena with non-interacting bosons has been mostly studied under the assumption of ideal indistinguishable bosons. In this project, we will generalize these results to partially distinguishable bosons and reach an understanding of what signatures of distinguishability can be observed after equilibration. These results will provide a practical way to test the degree of indistinguishability of particles in large scale boson sampling experiments, which cannot be simulated classically. Our second task is to significantly improve our understanding about how bosonic indistinguishability is an important resource for quantum computational advantage. This will be done by defining measures of indistinguishability which could be directly linked to the complexity of classical simulation of boson sampling. Our final task is to develop practical linear-optical protocols to improve photonic indistinguishability, taking into account realistic models of photon sources and, at the same time, contributing to establish a solid theory of indistiguishability distillation. We anticipate that such protocols should have wide applicability in linear optical-based quantum computing and quantum metrology.

The project will be a collaborative effort between the Quantum and Linear-Optical Computation (QLOC) group at INL and the Quantum Information and Communication (QuIC) at from Université Libre de Bruxelles. Both groups have a strong expertise in quantum optics, having made several seminal contributions to the theoretical foundations of multiboson interference and boson sampling.