Multiplexing scheme for simplified entanglement-based large-alphabet quantum key distribution

We propose a practical quantum cryptographic scheme which combines high information capacity, such as provided by high-dimensional quantum entanglement, with the simplicity of a two-dimensional Clauser-Horne-Shimony-Holt (CHSH) Bell test for security verification. By applying a state combining entanglement in a two-dimensional degree of freedom, such as photon polarization, with high-dimensional correlations in another degree of freedom, such as photon orbital angular momentum (OAM) or path, the scheme provides a considerably simplified route towards security verification in quantum key distribution (QKD) aimed at exploiting high-dimensional quantum systems for increased secure key rates. It also benefits from security against collective attacks and is feasible using currently available technologies.Comment: 7 pages, 3 figure

On Bell inequality violations with high-dimensional systems

Quantum correlations resulting in violations of Bell inequalities have generated a lot of interest in quantum information science and fundamental physics. In this paper, we address some questions that become relevant in Bell-type tests involving systems with local dimension greater than 2. For CHSH-Bell tests within 2-dimensional subspaces of such high-dimensional systems, it has been suggested that experimental violation of Tsirelson's bound indicates that more than 2-dimensional entanglement was present. We explain that the overstepping of Tsirelson's bound is due to violation of fair sampling, and can in general be reproduced by a separable state, if fair sampling is violated. For a class of Bell-type inequalities generalized to d-dimensional systems, we then consider what level of violation is required to guarantee d-dimensional entanglement of the tested state, when fair sampling is satisfied. We find that this can be used as an experimentally feasible test of d-dimensional entanglement for up to quite high values of d

Experimental high-dimensional two-photon entanglement and violations of generalised Bell inequalities

Quantum entanglement plays a vital role in many quantum information and communication tasks. Entangled states of higher dimensional systems are of great interest due to the extended possibilities they provide. For example, they allow the realisation of new types of quantum information schemes that can offer higher information-density coding and greater resilience to errors than can be achieved with entangled two-dimensional systems. Closing the detection loophole in Bell test experiments is also more experimentally feasible when higher dimensional entangled systems are used. We have measured previously untested correlations between two photons to experimentally demonstrate high-dimensional entangled states. We obtain violations of Bell-type inequalities generalised to d-dimensional systems with up to d = 12. Furthermore, the violations are strong enough to indicate genuine 11-dimensional entanglement. Our experiments use photons entangled in orbital angular momentum (OAM), generated through spontaneous parametric down-conversion (SPDC), and manipulated using computer controlled holograms

Quantum measurements of atoms using cavity QED

Generalized quantum measurements are an important extension of projective or von Neumann measurements, in that they can be used to describe any measurement that can be implemented on a quantum system. We describe how to realize two non-standard quantum measurements using cavity quantum electrodynamics (QED). The first measurement optimally and unabmiguously distinguishes between two non-orthogonal quantum states. The second example is a measurement that demonstrates superadditive quantum coding gain. The experimental tools used are single-atom unitary operations effected by Ramsey pulses and two-atom Tavis-Cummings interactions. We show how the superadditive quantum coding gain is affected by errors in the field-ionisation detection of atoms, and that even with rather high levels of experimental imperfections, a reasonable amount of superadditivity can still be seen. To date, these types of measurement have only been realized on photons. It would be of great interest to have realizations using other physical systems. This is for fundamental reasons, but also since quantum coding gain in general increases with code word length, and a realization using atoms could be more easily scaled than existing realizations using photons.Comment: 10 pages, 5 figure

Optimal simultaneous measurements of incompatible observables of a single photon

The ultimate limits of measurement precision are dictated by the laws of quantum mechanics. One of the most fascinating results is that joint or simultaneous measurements of noncommuting quantum observables are possible at the cost of increased unsharpness or measurement uncertainty. Many different criteria exist for determining what an “optimal” joint measurement is, with corresponding different trade-off relations for the measurements. It is generally a nontrivial task to devise or implement a strategy that minimizes the joint-measurement uncertainty. Here, we implement the simplest possible technique for an optimal four-outcome joint measurement and demonstrate a type of optimal measurement that has not been realized before in a photonic setting. We experimentally investigate a joint-measurement uncertainty relation that is more fundamental in the sense that it refers only to probabilities and is independent of values assigned to measurement outcomes. Using a heralded single-photon source, we demonstrate quantum-limited performance of the scheme on single quanta. Since quantum measurements underpin many concepts in quantum information science, this study is both of fundamental interest and relevant for emerging photonic quantum technologies

Polarization purity and dispersion characteristics of nested antiresonant nodeless hollow-core optical fiber at near- and short-wave-IR wavelengths for quantum communications

Advancements in quantum communication and sensing require improved optical transmission that ensures excellent state purity and reduced losses. While free-space optical communication is often preferred, its use becomes challenging over long distances due to beam divergence, atmospheric absorption, scattering, and turbulence, among other factors. In the case of polarization encoding, traditional silica-core optical fibers, though commonly used, struggle with maintaining state purity due to stress-induced birefringence. Hollow core fibers, and in particular nested antiresonant nodeless fibers (NANF), have recently been shown to possess unparalleled polarization purity with minimal birefringence in the telecom wavelength range using continuous-wave (CW) laser light. Here, we investigate a 1-km NANF designed for wavelengths up to the 2-μm waveband. Our results show a polarization extinction ratio between ~−30 dB and ~−70 dB across the 1520 to 1620 nm range in CW operation, peaking at ~−60 dB at the 2-μm design wavelength. Our study also includes the pulsed regime, providing insights beyond previous CW studies, e.g., on the propagation of broadband quantum states of light in NANF at 2 μm, and corresponding extinction-ratio-limited quantum bit error rates (QBER) for prepare-measure and entanglement-based quantum key distribution (QKD) protocols. Our findings highlight the potential of these fibers in emerging applications such as QKD, pointing towards a new standard in optical quantum technologies

Nanometric depth resolution from multi-focal images in microscopy

We describe a method for tracking the position of small features in three dimensions from images recorded on a standard microscope with an inexpensive attachment between the microscope and the camera. The depth-measurement accuracy of this method is tested experimentally on a wide-field, inverted microscope and is shown to give approximately 8 nm depth resolution, over a specimen depth of approximately 6 µm, when using a 12-bit charge-coupled device (CCD) camera and very bright but unresolved particles. To assess low-flux limitations a theoretical model is used to derive an analytical expression for the minimum variance bound. The approximations used in the analytical treatment are tested using numerical simulations. It is concluded that approximately 14 nm depth resolution is achievable with flux levels available when tracking fluorescent sources in three dimensions in live-cell biology and that the method is suitable for three-dimensional photo-activated localization microscopy resolution. Sub-nanometre resolution could be achieved with photon-counting techniques at high flux levels

Cumulative Effects in 100 kHz Repetition-Rate Laser-Induced Plasma Filaments in Air

[EN] Cumulative effects are crucial for applications of laser filaments, such as for the remote transfer of energy and the control of electric discharges. Up to now, studies of cumulative effects in the air of high-repetition-rate pulse trains have been performed at lower rates than 10 kHz. Herein, the nonlinear effects associated with short plasma filaments produced by pulses of moderate energy (0.4 mJ per pulse) and repetition rates up to 100 kHz are experimentally characterized. With increasing repetition rate, a decrease in absorption, fluorescence emission, and breakdown voltage and concurrently an increase in peak intensity and third-harmonic-generation efficiency are observed. Hydrodynamic simulations of the heated gas show that the observed decreases are directly related to a quasi-stationary state of reduced gas density in the filament. However, further investigations are required to fully understand the physics underpinning the observed sharp reduction of the breakdown voltage at 100 kHz repetition rates. The results may prove relevant for energy and information delivery applications by laser-induced air waveguide or electric discharge and lightning control.TJW acknowledges the support from NSAF (Grant no. U2130123), Strategic Priority Research Program of the Chinese Academy of Sciences (Grant no. XDB16), International Partnership Program of Chinese Academy of Sciences (Grant nos. 181231KYSB20200033 and 181231KYSB20200040), Shanghai Science and Technology Program (Grant no. 21511105000), and Oversea Training Program of Ministry of Science and Technology. MC acknowledges the support from UK Research and Innovation (UKRI) and the UK Engineering and Physical Sciences Research Council (EPSRC) (Fellowship "In-Tempo" EP/S001573/1), and the Royal Society (RGS\R1\201365). JCD acknowledges the support of NASA (SBIR grant 80NSSC22PB067). The authors wish to acknowledge Drs. Jean-Pierre Wolf, Jerome Kasparaian, Clara Saraceno, and Olga Kosareva for enlightening discussions.Wang, T.; Ebrahim, MH.; Afxenti, I.; Adamou, D.; Dada, AC.; Li, R.; Leng, Y.... (2023). Cumulative Effects in 100 kHz Repetition-Rate Laser-Induced Plasma Filaments in Air. Advanced Photonics Research. 4(3). https://doi.org/10.1002/adpr.2022003384

Electro-optical sampling of single-cycle Thz fields with single-photon detectors

Electro-optical sampling of Terahertz fields with ultrashort pulsed probes is a well-established approach for directly measuring the electric field of THz radiation. This technique usually relies on balanced detection to record the optical phase shift brought by THz-induced birefringence. The sensitivity of electro-optical sampling is, therefore, limited by the shot noise of the probe pulse, and improvements could be achieved using quantum metrology approaches using, e.g., NOON states for Heisenberg-limited phase estimation. We report on our experiments on THz electro-optical sampling using single-photon detectors and a weak squeezed vacuum field as the optical probe. Our approach achieves field sensitivity limited by the probe state statistical properties using phase-locked single-photon detectors and paves the way for further studies targeting quantum-enhanced THz sensing

Near-maximal two-photon entanglement for quantum communications at 2.1 μ\mum

Owing to a reduced solar background and low propagation losses in the atmosphere, the 2- to 2.5-$\mu$m waveband is a promising candidate for daylight quantum communication. This spectral region also offers low losses and low dispersion in hollow-core fibers and in silicon waveguides. We demonstrate for the first time near-maximally entangled photon pairs at 2.1 $\mu$m that could support device independent quantum key distribution (DIQKD) assuming sufficiently high channel efficiencies. The state corresponds to a positive secure-key rate (0.254 bits/pair, with a quantum bit error rate of 3.8%) based on measurements in a laboratory setting with minimal channel loss and transmission distance. This is promising for the future implementation of DIQKD at 2.1 $\mu$m