Vincenzo Tamma

Multiboson Correlation Interferometry with Arbitrary Single-Photon Pure States.

We provide a compact full description of multiboson correlation measurements of arbitrary order N in passive linear interferometers with arbitrary input single-photon pure states. This allows us to physically analyze the novel problem of multiboson correlation sampling at the output of random linear interferometers. Our results also describe general multiboson correlation landscapes for an arbitrary number of input single photons and arbitrary interferometers. In particular, we use two different schemes to demonstrate, respectively, arbitrary-order quantum beat interference and 100% visibility entanglement correlations even for input photons distinguishable in their frequencies.

From the Physics to the Computational Complexity of Multiboson Correlation Interference.

We demonstrate how the physics of multiboson correlation interference leads to the computational complexity of linear optical interferometers based on correlation measurements in the degrees of freedom of the input bosons. In particular, we address the task of multiboson correlation sampling (MBCS) from the probability distribution associated with polarization- and time-resolved detections at the output of random linear optical networks. We show that the MBCS problem is fundamentally hard to solve classically even for nonidentical input photons, regardless of the color of the photons, making it also very appealing from an experimental point of view. These results fully manifest the quantum computational supremacy inherent to the fundamental nature of quantum interference.

Multiboson correlation interferometry with multimode thermal sources

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.

Multi-boson correlation sampling

We give a full description of the problem of multi-boson correlation sampling (MBCS) at the output of a random interferometer for single input photons in arbitrary multi-mode pure states. The MBCS problem is the task of sampling at the interferometer output from the probability distribution associated with polarization- and time-resolved detections. We discuss the richness of the physics and the complexity of the MBCS problem for non-identical input photons. We also compare the MBCS problem with the standard boson sampling problem, where the input photons are assumed to be identical and the system is “classically” averaging over the detection times and polarizations.

Analogue algorithm for parallel factorization of an exponential number of large integers: I. Theoretical description

We describe a novel analogue algorithm that allows the simultaneous factorization of an exponential number of large integers with a polynomial number of experimental runs. It is the interference-induced periodicity of “factoring” interferograms measured at the output of an analogue computer that allows the selection of the factors of each integer. At the present stage, the algorithm manifests an exponential scaling which may be overcome by an extension of this method to correlated qubits emerging from n-order quantum correlations measurements. We describe the conditions for a generic physical system to compute such an analogue algorithm. A particular example given by an “optical computer” based on optical interference will be addressed in the second paper of this series (Tamma in Quantum Inf Process 11128:1189, 2015).

Analogue algorithm for parallel factorization of an exponential number of large integers: II--optical implementation

We report a detailed analysis of the optical realization of the analogue algorithm described in the first paper of this series (Tamma in Quantum Inf Process 11128:1190, 2015) for the simultaneous factorization of an exponential number of integers. Such an analogue procedure, which scales exponentially in the context of first-order interference, opens up the horizon to polynomial scaling by exploiting multi-particle quantum interference.

Multipath correlation interference and controlled-NOT gate simulation with a thermal source

We theoretically demonstrate a counter-intuitive phenomenon in optical interferometry with a thermal source: the emergence of second-order interference between two pairs of correlated optical paths even if the time delay imprinted by each path in one pair with respect to each path in the other pair is much larger than the source coherence time. This fundamental effect could be useful for experimental simulations of small-scale quantum circuits and of 100%-visibility correlations typical of entangled states of a large number of qubits, with possible applications in high-precision metrology and imaging. As an example, we demonstrate the polarization-encoded simulation of the operation of the quantum logic gate known as controlled-NOT gate.

Boson sampling with non-identical single photons

The boson-sampling problem has triggered a lot of interest in the scientific community because of its potential of demonstrating the computational power of quantum interference without the need of non-linear processes. However, the intractability of such a problem with any classical device relies on the realization of single photons approximately identical in their spectra. In this paper, we discuss the physics of boson sampling with non-identical single-photon sources, which is strongly relevant in view of scalable experimental realizations and triggers fascinating questions in the complexity theory.

The interface of gravity and quantum mechanics illuminated by Wigner phase space

We provide an introduction into the formulation of non-relativistic quantum mechanics using the Wigner phase-space distribution function and apply this concept to two physical situations at the interface of quantum theory and general relativity: (i) the motion of an ensemble of cold atoms relevant to tests of the weak equivalence principle, and (ii) the Kasevich-Chu interferometer. In order to lay the foundations for this analysis we first present a representation-free description of the Kasevich-Chu interferometer based on unitary operators.

Experimental controlled-NOT gate simulation with thermal light.

We report a recent experimental simulation of a controlled-NOT gate operation based on polarization correlation measurements of thermal fields in photon-number fluctuations. The interference between pairs of correlated paths at the very heart of these experiments has the potential for the simulation of correlations between a larger number of qubits.