Universal multiport interferometers, which can be programmed to implement any linear transformation between multiple channels, are emerging as a powerful tool for both classical and quantum photonics. These interferometers are typically composed of a regular mesh of beam splitters and phase shifters, allowing for straightforward fabrication using integrated photonic architectures and ready scalability. The current, standard design for universal multiport interferometers is based on work by Reck et al (Phys. Rev. Lett. 73, 58, 1994). We demonstrate a new design for universal multiport interferometers based on an alternative arrangement of beam splitters and phase shifters, which outperforms that by Reck et al. Our design occupies half the physical footprint of the Reck design and is significantly more robust to optical losses.

Although universal quantum computers ideally solve problems such as factoring integers exponentially more efficiently than classical machines, the formidable challenges in building such devices motivate the demonstration of simpler, problem-specific algorithms that still promise a quantum speedup. We constructed a quantum boson-sampling machine (QBSM) to sample the output distribution resulting from the nonclassical interference of photons in an integrated photonic circuit, a problem thought to be exponentially hard to solve classically. Unlike universal quantum computation, boson sampling merely requires indistinguishable photons, linear state evolution, and detectors. We benchmarked our QBSM with three and four photons and analyzed sources of sampling inaccuracy. Scaling up to larger devices could offer the first definitive quantum-enhanced computation.

Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here we investigate the joint estimation of a phase shift and the amplitude of phase diffusion at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshaped as a two-dimensional Hilbert space model, encompassing the description of an interferometer probed with relevant quantum statessplit single-photons, coherent states or N00N states. For these cases, we obtain a trade-off bound on the statistical variances for the joint estimation of phase and phase diffusion, as well as optimum measurement schemes. We use this bound to quantify the effectiveness of an actual experimental set-up for joint parameter estimation for polarimetry. We conclude by discussing the form of the trade-off relations for more general states and measurements.

Quantum interference of two independent particles in pure quantum states is fully described by the particles' distinguishability: the closer the particles are to being identical, the higher the degree of quantum interference. When more than two particles are involved, the situation becomes more complex and interference capability extends beyond pairwise distinguishability, taking on a surprisingly rich character. Here, we study many-particle interference using three photons. We show that the distinguishability between pairs of photons is not sufficient to fully describe the photons' behavior in a scattering process, but that a collective phase, the triad phase, plays a role. We are able to explore the full parameter space of threephoton interference by generating heralded single photons and interfering them in a fiber tritter. Using multiple degrees of freedom-temporal delays and polarization-we isolate three-photon interference from two-photon interference. Our experiment disproves the view that pairwise two-photon distinguishability uniquely determines the degree of nonclassical many-particle interference. DOI: 10.1103/PhysRevLett.118.153603 The famous Hong-Ou-Mandel (HOM) experiment in 1987 provided the first important example of nonclassical two-photon interference [1]. Two independent photons impinging on a beam splitter exhibit bunching behavior at the output ports that cannot be explained by a classical field model. The degree of bunching depends on how similar the two photons are in all degrees of freedom, for example, time, frequency, polarization, and spatial mode. Extending the study of interference to many particles is of interest from a fundamental as well as from a technological viewpoint [2][3][4][5][6][7]. The scattering of multiple photons in linear networks is related to solving problems in quantum information processing, metrology, and quantum state engineering [8][9][10][11][12][13][14][15][16]. Thus, understanding multiphoton interference is also of great relevance for practical applications.Here, we demonstrate how many-particle interference is fundamentally richer than two-particle interference [17]. Two situations with the same pairwise distinguishability can lead to a different output distribution. This is due to a phase, the triad phase, that occurs only when more than two photons interfere.We use independent photons and a tritter, a three-port symmetric beam splitter to investigate many-particle interference. We isolate the triad phase for the first time by interfering three photons in a tritter and exploiting multiple degrees of freedom, here time and polarization. We show that interfering three identical photons and varying time delays between them, as demonstrated in previous work [5,18,19], is not sufficient to study three-photon interference in full generality [20,21]. Our experiment allows us to isolate and tune the three-photon interference term as distinct from two-photon interference. In particular, manipulation of the triad phase goes beyond what is possible using temporal...

We demonstrate how boson sampling with photons of partial distinguishability can be expressed in terms of interference of fewer photons. We use this observation to propose a classical algorithm to simulate the output of a boson sampler fed with photons of partial distinguishability. We find conditions for which this algorithm is efficient, which gives a lower limit on the required indistinguishability to demonstrate a quantum advantage. Under these conditions, adding more photons only polynomially increases the computational cost to simulate a boson sampling experiment.