Quantum walk represents one of the most promising resources for the simulation of physical quantum systems, and has also emerged as an alternative to the standard circuit model for quantum computing. Here we investigate how the particle statistics, either bosonic or fermionic, influences a two-particle discrete quantum walk. Such an experiment has been realized by exploiting polarization entanglement to simulate the bunching-antibunching feature of noninteracting bosons and fermions. To this scope a novel three-dimensional geometry for the waveguide circuit is introduced, which allows accurate polarization independent behavior, maintaining remarkable control on both phase and balancement.

Waves fail to propagate in random media. First predicted for quantum particles in the presence of a disordered potential, Anderson localization has been observed also in classical acoustics, electromagnetism and optics. Here, for the first time, we report the observation of Anderson localization of pairs of entangled photons in a two-particle discrete quantum walk affected by position dependent disorder. A quantum walk on a disordered lattice is realized by an integrated array of interferometers fabricated in glass by femtosecond laser writing. A novel technique is used to introduce a controlled phase shift into each unit mesh of the network. Polarization entanglement is exploited to simulate the different symmetries of the two-walker system. We are thus able to experimentally investigate the genuine effect of (bosonic and fermionic) statistics in the absence of interaction between the particles. We will show how different types of randomness and the symmetry of the wave-function affect the localization of the entangled walkers.In 1958 P.W. Anderson [1] predicted that the wavefunction of a quantum particle can be localized in the presence of a static disordered potential. As a consequence of this mechanism it is expected that particle and energy transport through a disordered medium should be strongly suppressed and that an initially localized wave packet should not spread out with time. After more than fifty years from its discovery Anderson localization is still widely studied and it has pervaded many different areas of physics ranging from condensed matter and cold atomic physics to wave dynamics and quantum chaos [2]. This phenomenon emerges quite generically in the behavior of waves in complex media, and it has been experimentally observed in a variety of different systems: BoseEinsten condensates [3,4] Anderson localization is a single-particle process which arises from the destructive interference among different scattering paths. Nevertheless, even in the absence of a direct interaction between particles, pure quantum correlations [13] are expected to influence in a non-trivial way the underlying localization dynamics [14][15][16][17]. By taking advantage of the perfect phase stability provided by miniaturized integrated waveguide circuits [18], we experimentally simulate a quantum walk of a two-photon polarization-entangled state in a disordered medium. We are thus able, through a mapping derived in Ref. [14], to test the localization of a pair of non interacting particles obeying bosonic/fermionic statistics [19].A quantum walk (QW) [20] is an extension of the classical random walk, where the walker goes back and forth along a line and the direction at each step depends on the result of a fair coin flip. At the quantum level, interference and superposition phenomena lead to a non-classical behavior of the walker giving rise to new interesting effects, which can be harnessed to exponentially speed up search algorithms [21] and to realize universal quantum computation [22]. Besides, QWs have also been pr...

Boson Sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require a universal control over the quantum system, which favours current photonic experimental platforms. Here, we introduce Gaussian Boson Sampling, a classically hardto-solve problem that uses squeezed states as a non-classical resource. We relate the probability to measure specific photon patterns from a general Gaussian state in the Fock basis to a matrix function called the hafnian, which answers the last remaining question of sampling from Gaussian states. Based on this result, we design Gaussian Boson Sampling, a #P hard problem, using squeezed states. This approach leads to a more efficient photonic boson sampler with significant advantages in generation probability and measurement time over currently existing protocols.

The ability to manipulate quantum states of light by integrated devices may open new perspectives both for fundamental tests of quantum mechanics and for novel technological applications. However, the technology for handling polarization-encoded qubits, the most commonly adopted approach, is still missing in quantum optical circuits. Here we demonstrate the first integrated photonic controlled-NOT (CNOT) gate for polarization-encoded qubits. This result has been enabled by the integration, based on femtosecond laser waveguide writing, of partially polarizing beam splitters on a glass chip. We characterize the logical truth table of the quantum gate demonstrating its high fidelity to the expected one. In addition, we show the ability of this gate to transform separable states into entangled ones and vice versa. Finally, the full accessibility of our device is exploited to carry out a complete characterization of the CNOT gate through a quantum process tomography.

The orbital angular momentum (OAM) of light, associated with a helical structure of the wavefunction, has great potential in quantum photonics, as it allows a higher dimensional quantum space to be attached to each photon. Hitherto, however, the use of OAM has been hindered by difficulties in its manipulation. Here, by making use of the recently demonstrated spin-OAM information transfer tools, we report the first observation of the Hong–Ou–Mandel coalescence of two incoming photons having non-zero OAM into the same outgoing mode of a beamsplitter. The coalescence can be switched on and off by varying the input OAM state of the photons. Such an effect has then been used to carry out the 1 -> 2 universal optimal quantum cloning of OAM-encoded qubits, using the symmetrization technique already developed for polarization. These results are shown to be scalable to quantum spaces of arbitrary dimensions, even combining different degrees of freedom of the photons

The emerging strategy to overcome the limitations of bulk quantum optics consists of taking advantage of the robustness and compactness achievable by integrated waveguide technology. Here we report the realization of a directional coupler, fabricated by femtosecond laser waveguide writing, acting as an integrated beam splitter able to support polarization-encoded qubits. This maskless and single step technique allows us to realize circular transverse waveguide profiles which are able to support the propagation of gaussian modes with any polarization state. Using this device, we demonstrate quantum interference with polarization-entangled states and singlet state projection.

Since the development of Boson sampling, there has been a quest to construct more efficient and experimentally feasible protocols to test the computational complexity of sampling from photonic states. In this paper we interpret and extend the results presented in [Phys. Rev. Lett. 119, 170501 (2017)]. We derive an expression that relates the probability to measure a specific photon output pattern from a Gaussian state to the hafnian matrix function and us it to design a Gaussian Boson sampling protocol. Then, we discuss the advantages that this protocol has relative to other photonic protocols and the experimental requirements for Gaussian Boson Sampling. Finally, we relate it to the previously most general protocol, Scattershot Boson Sampling [Phys. Rev. Lett. 113, 100502 (2014)].

Boson Sampling has emerged as a tool to explore the advantages of quantum over classical computers as it does not require a universal control over the quantum system, which favours current photonic experimental platforms. Here, we introduce Gaussian Boson Sampling, a classically hardto-solve problem that uses squeezed states as a non-classical resource. We relate the probability to measure specific photon patterns from a general Gaussian state in the Fock basis to a matrix function called the hafnian, which answers the last remaining question of sampling from Gaussian states. Based on this result, we design Gaussian Boson Sampling, a #P hard problem, using squeezed states. This approach leads to a more efficient photonic boson sampler with significant advantages in generation probability and measurement time over currently existing protocols.