Certifying the Topology of Quantum Networks: Theory and Experiment.

Distributed quantum information in networks is paramount for global secure quantum communication. Moreover, it finds applications as a resource for relevant tasks, such as clock synchronization, magnetic field sensing, and blind quantum computation. For quantum network analysis and benchmarking of implementations, however, it is crucial to characterize the topology of networks in a way that reveals the nodes between which entanglement can be reliably distributed. Here, we demonstrate an efficient scheme for this topology certification. Our scheme allows for distinguishing, in a scalable manner, different networks consisting of bipartite and multipartite entanglement sources. It can be applied to semi-device-independent scenarios also, where the measurement devices and network nodes are not well characterized and trusted. We experimentally demonstrate our approach by certifying the topology of different six-qubit networks generated with polarized photons, employing active feed-forward and time multiplexing. Our methods can be used for general simultaneous tests of multiple hypotheses with few measurements, being useful for other certification scenarios in quantum technologies.

Demonstration of Hong-Ou-Mandel interference in an LNOI directional coupler.

Interference between single photons is key for many quantum optics experiments and applications in quantum technologies, such as quantum communication or computation. It is advantageous to operate the systems at telecommunication wavelengths and to integrate the setups for these applications in order to improve stability, compactness and scalability. A new promising material platform for integrated quantum optics is lithium niobate on insulator (LNOI). Here, we realise Hong-Ou-Mandel (HOM) interference between telecom photons from an engineered parametric down-conversion source in an LNOI directional coupler. The coupler has been designed and fabricated in house and provides close to perfect balanced beam splitting. We obtain a raw HOM visibility of (93.5 ± 0.7) %, limited mainly by the source performance and in good agreement with off-chip measurements. This lays the foundation for more sophisticated quantum experiments in LNOI.

Direct Measurement of Higher-Order Nonlinear Polarization Squeezing.

We report on nonlinear squeezing effects of polarization states of light by harnessing the intrinsic correlations from a polarization-entangled light source and click-counting measurements. Nonlinear Stokes operators are obtained from harnessing the click-counting theory in combination with angular-momentum-type algebras. To quantify quantum effects, theoretical bounds are derived for second- and higher-order moments of nonlinear Stokes operators. The experimental validation of our concept is rendered possible by developing an efficient source, using a spectrally decorrelated type-II phase-matched waveguide inside a Sagnac interferometer. Correlated click statistics and moments are directly obtained from an eight-time-bin quasi-photon-number-resolving detection system. Macroscopic Bell states that are readily available with our source show the distinct nature of nonlinear polarization squeezing in up to eighth-order correlations, matching our theoretical predictions. Furthermore, our data certify nonclassical correlations with high statistical significance, without the need to correct for experimental imperfections and limitations. Also, our nonlinear squeezing can identify nonclassicality of noisy quantum states which is undetectable with the known linear polarization-squeezing criterion.

Scalable Generation of Multiphoton Entangled States by Active Feed-Forward and Multiplexing.

Multiphoton entangled quantum states are key to advancing quantum technologies such as multiparty quantum communications, quantum sensing, or quantum computation. Their scalable generation, however, remains an experimental challenge. Current methods for generating these states rely on stitching together photons from probabilistic sources, and state generation rates drop exponentially in the number of photons. Here, we implement a system based on active feed-forward and multiplexing that addresses this challenge. We demonstrate the scalable generation of four-photon and six-photon Greenberger-Horne-Zeilinger states, increasing generation rates by factors of 9 and 35, respectively. This is consistent with the exponential enhancement compared to the standard nonmultiplexed approach that is predicted by our theory. These results facilitate the realization of practical multiphoton protocols for photonic quantum technologies.

Spatially single mode photon pair source at 800 nm in periodically poled Rubidium exchanged KTP waveguides.

Photon pair sources in the visible to NIR wavelength region play a key role in quantum optics. The wavelength range around 800 nm provides an opportunity for using low cost detectors, which makes it highly interesting for practical, large scale quantum applications. Here, we report on the realization of single mode Rubidium (Rb) exchanged waveguides in periodically poled (PP) Potassium Titanyl Phosphate (Rb:KTiOPO4 or Rb:KTP) for frequency-non-degenerate type II parametric down-conversion pumped at 400 nm and generating pairs of photons at around 800 nm. The source exhibits a nonlinear conversion efficiency of 2.0%/(Wcm2), estimated from SHG measurements. Characterisation of the generated two-photon state confirms nonclassical photon-number correlations, characterized by g(1,1). The high nonlinear conversion efficiency and low temperature sensitivity make this source a promising candidate for operations in both classical and quantum integrated network applications.

Remotely projecting states of photonic temporal modes.

Two-photon time-frequency entanglement is a valuable resource in quantum information. Resolving the wavepacket of ultrashort pulsed single-photons, however, is a challenge. Here, we demonstrate remote spectral shaping of single photon states and probe the coherence properties of two-photon quantum correlations in the time-frequency domain, using engineered parametric down-conversion (PDC) and a quantum pulse gate (QPG) in nonlinear waveguides. Through tailoring the joint spectral amplitude function of our PDC source we control the temporal mode structure between the generated photon pairs and show remote state-projections over a range of time-frequency mode superpositions.

Tomography and Purification of the Temporal-Mode Structure of Quantum Light.

High-dimensional quantum information processing promises capabilities beyond the current state of the art, but addressing individual information-carrying modes presents a significant experimental challenge. Here we demonstrate effective high-dimensional operations in the time-frequency domain of nonclassical light. We generate heralded photons with tailored temporal-mode structures through the pulse shaping of a broadband parametric down-conversion pump. We then implement a quantum pulse gate, enabled by dispersion-engineered sum-frequency generation, to project onto programmable temporal modes, reconstructing the quantum state in seven dimensions. We also manipulate the time-frequency structure by selectively removing temporal modes, explicitly demonstrating the effectiveness of engineered nonlinear processes for the mode-selective manipulation of quantum states.

On-chip generation of photon-triplet states.

Efficient sources of many-partite non-classical states are key for the advancement of quantum technologies and for the fundamental testing of quantum mechanics. We demonstrate the generation of time-correlated photon triplets at telecom wavelengths via pulsed cascaded parametric down-conversion in a monolithically integrated source. By detecting the generated states with success probabilities of (6.25 ± 1.09) × 10(-11) per pump pulse at injected powers as low as 10 µW, we benchmark the efficiency of the complete system and deduce its high potential for scalability. Our source is unprecedentedly long-term stable, it overcomes interface losses intrinsically due to its monolithic architecture, and the photon-triplet states dominate uncorrelated noise significantly. These results mark crucial progress towards the proliferation of robust, scalable, synchronized and miniaturized quantum technology.

Ultrahigh and persistent optical depths of cesium in Kagomé-type hollow-core photonic crystal fibers.

Alkali-filled hollow-core fibers are a promising medium for investigating light-matter interactions, especially at the single-photon level, due to the tight confinement of light and high optical depths achievable by light-induced atomic desorption (LIAD). However, until now these large optical depths could only be generated for seconds, at most once per day, severely limiting the practicality of the technology. Here we report the generation of the highest observed transient (>10(5) for up to a minute) and highest observed persistent (>2000 for hours) optical depths of alkali vapors in a light-guiding geometry to date, using a cesium-filled Kagomé-type hollow-core photonic crystal fiber (HC-PCF). Our results pave the way to light-matter interaction experiments in confined geometries requiring long operation times and large atomic number densities, such as generation of single-photon-level nonlinearities and development of single photon quantum memories.

An optimized photon pair source for quantum circuits.

We implement an ultrafast pulsed type-II parametric down conversion source in a periodically poled KTP waveguide at telecommunication wavelengths with almost identical properties between signal and idler. As such, our source resembles closely a pure, genuine single mode photon pair source with indistinguishable modes. We measure the joint spectral intensity distribution and second order correlation functions of the marginal beams and find with both methods very low effective mode numbers corresponding to a Schmidt number below 1.16. We further demonstrate the indistinguishability as well as the purity of signal and idler photons by Hong-Ou-Mandel interferences between signal and idler and between signal/idler and a coherent field, respectively. Without using narrowband spectral filtering, we achieve a visibility for the interference between signal and idler of 94.8% and determine a purity of more than 80% for the heralded single photon states. Moreover, we measure raw heralding efficiencies of 20.5% and 15.5% for the signal and idler beams corresponding to detector-loss corrected values of 80% and 70%.

4-(4-Iodo-anilino)-2-methyl-ene-4-oxo-butanoic acid.

In the title compound, C11H10INO3, an addition product of itaconic acid anhydride and 4-iodo-aniline, the least-squares planes defined by the atoms of the aromatic moiety and the non-H atoms of the carb-oxy-lic acid group enclose an angle of 74.82 (11)°. In the crystal, classical O-H⋯O hydrogen bonds formed by carb-oxy-lic groups, as well as N-H⋯O hydrogen bonds formed by amide groups, are present along with C-H⋯O contacts. Together, these connect the mol-ecules into dimeric chains along the b-axis direction.

3-Chloro-4-fluoro-anilinium picrate.

In the title picrate salt of a dihalogenated aniline derivative, C(6)H(6)ClF(+)·C(6)H(2)N(3)O(7) (-), the intra-cyclic C-C-C angles in the picrate anion cover a broad range [111.95 (12)-125.38 (13)°], while those in the aromatic cation span a much narrower range [118.25 (14)-122.33 (13)°]. In the crystal, classical N-H⋯O hydrogen bonds, as well as C-H⋯O contacts, connect the ions into layers parallel to (001).

4-[Bis(4-fluoro-phen-yl)meth-yl]-1-[(2E)-3-phenyl-prop-2-en-1-yl]piperazin-1-ium 3-carb-oxy-propano-ate.

In the title salt, C(26)H(27)F(2)N(2) (+)·C(4)H(5)O(4) (-), the piperazine N atom bearing the vinylic substituent is protonated. The piperazine ring adopts a chair conformation. In ther crystal, the succinate monoanions are connected via short O-H⋯O hydrogen bonds between the carb-oxy-lic acid and carboxyl-ate groups into undulating chains extending along [001] and the flunarizinium monocations are attached to these chains via N(+)-H⋯O(-) hydrogen bonds. C-H⋯O inter-actions connect these chains into a three-dimensional network. The shortest centroid-centroid distance of 3.7256 (10) Šwas found between one of the fluorinated benzene rings and the non-fluorinated phenyl ring in the neighbouring mol-ecule related by a glide plane.

(2E)-3-[4-(Benz-yloxy)phen-yl]-1-(2,6-dichloro-3-fluoro-phen-yl)prop-2-en-1-one.

In the title compound, C22H15Cl2FO2, a chalcone derivative featuring a threefold-halogenated aromatic substituent, the conformation about the C=C bond is E. In the crystal C-H⋯F and C-H⋯Cl contacts connect the mol-ecules into undulating sheets parallel to (101). In addition, C-H⋯π inter-actions are also present.

1,5-Dibromo-2,4-dimeth-oxy-benzene.

In the title compound, C8H8Br2O2, all non-H atoms lie essentially in a common plane (r.m.s deviation of all fitted non-H atoms = 0.0330 Å). In the crystal, weak C-H⋯O hydrogen bonds connect the mol-ecules, forming chains which extend along the b-axis direction.

(2E)-1-(2,4-Dichloro-phen-yl)-3-[3-(4-nitro-phen-yl)-1-phenyl-1H-pyrazol-4-yl]prop-2-en-1-one.

In the title compound, C(24)H(15)Cl(2)N(3)O(3), the C=C double bond is E configured. The 1-phenyl-1H-pyrazole moiety is roughly planar (r.m.s. deviation of all fitted non-H atoms = 0.0780 Å), but the mean planes of the two components are inclined at an angle of 9.95 (7)°. The mean plane defined by the non-H atoms of the 1H-pyrazole ring encloses angles of 9.95 (7), 24.54 (6) and 43.02 (6)° with the mean planes of the different benzene rings. In the crystal, C-H⋯O contacts are present and result in the formation of a double-layer two-dimensional network lying parallel to (110). The shortest inter-centroid distance between two aromatic systems is 3.5455 (7) Šand is apparent between two pyrazole systems. Further π-π inter-actions are manifest between a pair of 4-nitro-phenyl rings [centroid-to-centroid distance = 3.6443 (7) Å] and a pair of 2,4-dichloro-phenyl rings [centroid-to-centroid distance = 3.7797 (7) Å].

A quantum pulse gate based on spectrally engineered sum frequency generation.

We introduce the concept of a quantum pulse gate (QPG), a method for accessing the intrinsic broadband spectral mode structure of ultrafast quantum states of light. This mode structure can now be harnessed for applications in quantum information processing. We propose an implementation in a PPLN waveguide, based on spectrally engineered sum frequency generation (SFG). It allows us to pick well-defined spectral broadband modes from an ultrafast multi-mode state for interconversion to a broadband mode at another frequency. By pulse-shaping the bright SFG pump beam, different orthogonal broadband modes can be addressed individually and extracted with high fidelity.

Highly efficient frequency conversion with bandwidth compression of quantum light.

Hybrid quantum networks rely on efficient interfacing of dissimilar quantum nodes, as elements based on parametric downconversion sources, quantum dots, colour centres or atoms are fundamentally different in their frequencies and bandwidths. Although pulse manipulation has been demonstrated in very different systems, to date no interface exists that provides both an efficient bandwidth compression and a substantial frequency translation at the same time. Here we demonstrate an engineered sum-frequency-conversion process in lithium niobate that achieves both goals. We convert pure photons at telecom wavelengths to the visible range while compressing the bandwidth by a factor of 7.47 under preservation of non-classical photon-number statistics. We achieve internal conversion efficiencies of 61.5%, significantly outperforming spectral filtering for bandwidth compression. Our system thus makes the connection between previously incompatible quantum systems as a step towards usable quantum networks.