Deep learning of quantum entanglement from incomplete measurements.

The quantification of the entanglement present in a physical system is of paramount importance for fundamental research and many cutting-edge applications. Now, achieving this goal requires either a priori knowledge on the system or very demanding experimental procedures such as full state tomography or collective measurements. Here, we demonstrate that, by using neural networks, we can quantify the degree of entanglement without the need to know the full description of the quantum state. Our method allows for direct quantification of the quantum correlations using an incomplete set of local measurements. Despite using undersampled measurements, we achieve a quantification error of up to an order of magnitude lower than the state-of-the-art quantum tomography. Furthermore, we achieve this result using networks trained using exclusively simulated data. Last, we derive a method based on a convolutional network input that can accept data from various measurement scenarios and perform, to some extent, independently of the measurement device.

Sub-0.1 degree phase locking of a single-photon interferometer.

We report a single-photon Mach-Zehnder interferometer stabilized to a phase precision of 0.05 degrees over 15 hours. To lock the phase, we employ an auxiliary reference light at a different wavelength than the quantum signal. The developed phase locking operates continuously, with negligible crosstalk, and for an arbitrary phase of the quantum signal. Moreover, its performance is independent of intensity fluctuations of the reference. Since the presented method can be used in a vast majority of quantum interferometric networks it can significantly improve phase-sensitive applications in quantum communication and quantum metrology.

Quantum non-Gaussianity certification of photon number-resolving detectors.

We report on direct experimental certification of the quantum non-Gaussian character of a photon number-resolving detector. The certification protocol is based on an adaptation of the existing quantum non-Gaussianity criteria for quantum states to quantum measurements. In our approach, it suffices to probe the detector with a vacuum state and two different thermal states to test its quantum non-Gaussianity. The certification is experimentally demonstrated for the detector formed by a spatially multiplexed array of ten single-photon avalanche photodiodes. We confirm the quantum non-Gaussianity of POVM elements Π^m associated with the m-fold coincidence counts, up to m = 7. The experimental ability to certify from the first principles the quantum non-Gaussian character of Π^m is for large m limited by low probability of the measurement outcomes, especially for vacuum input state. We find that the injection of independent Gaussian background noise into the detector can be helpful and may reduce the measurement time required for reliable confirmation of quantum non-Gaussianity. In addition, we modified and experimentally verified the quantum non-Gaussianity certification protocol employing a third thermal state instead of a vacuum to speed up the whole measurement. Our findings demonstrate the existence of efficient tools for the practical characterization of fundamental non-classical properties and benchmarking of complex optical quantum detectors.

High Extraction Efficiency Source of Photon Pairs Based on a Quantum Dot Embedded in a Broadband Micropillar Cavity.

The generation of photon pairs in quantum dots is in its nature deterministic. However, efficient extraction of photon pairs from the high index semiconductor material requires engineering of the photonic environment. We report on a micropillar device with 69.4(10)% efficiency that features broadband operation suitable for extraction of photon pairs. Opposing the approaches that rely solely on Purcell enhancement to realize the enhancement of the extraction efficiency, our solution exploits a suppression of the emission into the modes other than the cavity mode. Furthermore, the design of the device can be further optimized to allow for an extraction efficiency of 85%.

Non-blocking programmable delay line with minimal dead time and tens of picoseconds jitter.

We report a non-blocking high-resolution digital delay line based on an asynchronous circuit design. Field-programmable gate array logic primitives were used as a source of delay and optimally arranged using combinatorial optimization. This approach allows for an efficient trade-off of the resolution and a delay range together with a minimized dead time operation. We demonstrate the method by implementing the delay line adjustable from 23 ns up to 1635 ns with a resolution of 10 ps. We present a detailed experimental characterization of the device focusing on thermal instability, timing jitter, and pulse spreading, which represent three main issues of the asynchronous design. We found a linear dependence of the delay on the temperature with the slope of 0.2 ps K-1 per logic primitive. We measured the timing jitter of the delay to be in the range of 7-165 ps, linearly increasing over the dynamic range of the delay. We reduced the effect of pulse spreading by introducing pulse shrinking circuits and reached the overall dead time of 4-22.5 ns within the dynamic range of the delay. The presented non-blocking delay line finds usage in applications where the dead time minimization is crucial, and tens of picoseconds of excess jitter is acceptable, such as in many advanced photonic networks.

Accurate polarization preparation and measurement using twisted nematic liquid crystals.

Generation of particular polarization states of light, encoding information in polarization degree of freedom, and efficient measurement of unknown polarization are the key tasks in optical metrology, optical communications, polarization-sensitive imaging, and photonic information processing. Liquid crystal devices have proved to be indispensable for these tasks, though their limited precision and the requirement of a custom design impose a limit of practical applicability. Here we report fast preparation and detection of polarization states with unprecedented accuracy using liquid-crystal cells extracted from common twisted nematic liquid-crystal displays. To verify the performance of the device we use it to prepare dozens of polarization states with average fidelity 0.999(1) and average angle deviation 0.5(3) deg. Using four-projection minimum tomography as well as six-projection Pauli measurement, we measure polarization states employing the reported device with the average fidelity of 0.999(1). Polarization measurement data are processed by the maximum likelihood method to reach a valid estimate of the polarization state. In addition to the application in classical polarimetry, we also employ the reported liquid-crystal device for full tomographic characterization of a three-mode Greenberger-Horne-Zeilinger entangled state produced by a photonic quantum processor.

Direct Experimental Certification of Quantum Non-Gaussian Character and Wigner Function Negativity of Single-Photon Detectors.

Highly nonclassical character of optical quantum detectors, such as single-photon detectors, is essential for preparation of quantum states of light and a vast majority of applications in quantum metrology and quantum information processing. Therefore, it is both fundamentally interesting and practically relevant to investigate the nonclassical features of optical quantum measurements. Here we propose and experimentally demonstrate a procedure for direct certification of quantum non-Gaussianity and Wigner function negativity, two crucial nonclassicality levels, of photonic quantum detectors. Remarkably, we characterize the highly nonclassical properties of the detector by probing it with only two classical thermal states and a vacuum state. We experimentally demonstrate the quantum non-Gaussianity of a single-photon avalanche diode even under the presence of background noise, and we also certify the negativity of the Wigner function of this detector. Our results open the way for direct benchmarking of photonic quantum detectors with a few measurements on classical states.

Experimental entanglement-assisted weak measurement of phase shift.

Weak value amplification is a popular method in quantum metrology for enhancing the sensitivity at the expense of the signal intensity. Recently, it was suggested that the trade-off between signal intensity and sensitivity can be improved by using an entangled auxiliary system. Here, we experimentally investigate such entanglement-assisted weak measurement of small conditional phase shifts induced by an interaction between ancilla and meter qubits. We utilize entangled photon pairs and implement the required three-qubit quantum logic circuit with linear optics. The circuit comprises a two-qubit controlled phase gate and a three-qubit controlled-controlled phase gate with fully tunable conditional phase shifts. We fully characterize the output states of our circuit by quantum state tomography and perform a comprehensive analysis of the trade-off between the measurement sensitivity and the success probability of the protocol. The observed experimental results are in good qualitative agreement with theoretical predictions, but the overall performance of our setup is limited by various experimental imperfections. We provide a detailed theoretical analysis of the influence of dephasing of the entangled ancilla state, which is one of the main sources of imperfections in the experiment. We also discuss the ultimate scaling with the dimension of the entangled ancilla system.

Feedforward-enhanced Fock state conversion with linear optics.

Engineering quantum states of light represents a crucial task in the vast majority of photonic quantum technology applications. Direct manipulation of the number of photons in the light signal, such as single-photon subtraction and addition, proved to be an efficient strategy for the task. Here we propose an adaptive multi-photon subtraction scheme where a particular subtraction task is conditioned by all previous subtraction events in order to maximize the probability of successful subtraction. We theoretically illustrate this technique on the model example of conversion of Fock states via photon subtraction. We also experimentally demonstrate the core building block of the proposal by implementing a feedforward-assisted conversion of two-photon state to a single-photon state. Our experiment combines two elementary photon subtraction blocks where the splitting ratio of the second subtraction beam splitter is affected by the measurement result from the first subtraction block in real time using an ultra-fast feedforward loop. The reported optimized photon subtraction scheme applies to a broad range of photonic states, including highly nonclassical Fock states and squeezed light, advancing the photonic quantum toolbox.

Accurate Detection of Arbitrary Photon Statistics.

We report a measurement workflow free of systematic errors consisting of a reconfigurable photon-number-resolving detector, custom electronic circuitry, and faithful data-processing algorithm. We achieve an unprecedented accurate measurement of various photon-number distributions going beyond the number of detection channels with an average fidelity of 0.998, where the error is primarily caused by the sources themselves. Mean numbers of photons cover values up to 20 and faithful autocorrelation measurements range from g^{(2)}=6×10^{-3} to 2. We successfully detect chaotic, classical, nonclassical, non-Gaussian, and negative-Wigner-function light. Our results open new paths for optical technologies by providing full access to the photon-number information without the necessity of detector tomography.

Fully tunable and switchable coupler for photonic routing in quantum detection and modulation.

Photonic routing is a key building block of many optical applications challenging its development. We report a $2\times 2$2×2 photonic coupler with a splitting ratio switchable by a low-voltage electronic signal with 10 GHz bandwidth and tens of nanoseconds latency. The coupler can operate at any splitting ratio ranging from 0:100 to 100:0 with the extinction ratio of 26 dB in optical bandwidth of 1.3 THz. We show sub-nanosecond switching between arbitrary coupling regimes including a balanced 50:50 beam splitter, 0:100 switch, and a photonic tap. The core of the device is based on a Mach-Zehnder interferometer in a dual-wavelength configuration allowing real-time phase lock with long-term sub-degree stability at single-photon level. Using the reported coupler, we demonstrate for the first time, to the best of our knowledge, a perfectly balanced time-multiplexed device for photon-number-resolving detectors and also the active preparation of a photonic temporal qudit state up to four time bins. Verified long-term stable operation of the coupler at the single-photon level makes it suitable for a wide application range in quantum information processing and quantum optics in general.

Faithful Hierarchy of Genuine n-Photon Quantum Non-Gaussian Light.

Light is an essential tool for connections between quantum devices and for diagnostic processes in quantum technology. Both applications deal with advanced nonclassical states beyond Gaussian coherent and squeezed states. Current development requires a loss-tolerant diagnostic of such nonclassical aspects. We propose and experimentally verify a faithful hierarchy of genuine n-photon quantum non-Gaussian light. We conclusively witnessed three-photon quantum non-Gaussian light in the experiment. Measured data demonstrate a direct applicability of the hierarchy for a large class of real states.

Experimental realization of SWAP operation on hyper-encoded qubits.

Hyper-encoding enables storing several qubits in a single photon using its different degrees of freedom like polarization and spatial ones. This approach enables feasible implementation of multi-qubit operations. One of the basic manipulations of two or more qubits is to swap their quantum state. Here we report on feasible and stable experimental implementation of a deterministic single photon two-qubit SWAP gate that interchanges path and polarization qubits. We discuss the principle of its operation and give detailed information about experimental demonstration employing two Mach-Zehnder interferometers with one common arm. The gate characterization is done by full quantum process tomography using photons produced by heralded single-photon source. The achieved quantum process fidelity reached more than 0.94 with an effective phase uncertainty of the whole setup, evaluated by means of Allan deviation, below 2.5 deg for 2.5 h without any active stabilization. Our design provides a contribution to the hyper-encoded linear quantum optics toolbox.

Generator of arbitrary classical photon statistics.

We propose and experimentally demonstrate a device for generating light with arbitrary classical photon-number distribution. We use programmable acousto-optical modulation to control the intensity of light within the dynamic range of more than 30 dB and inter-level transitions faster than 500 ns. We propose a universal method that allows the high-fidelity generation of user-defined photon statistics. Extremely high precision <0.001 can be reached for lower photon numbers, and faithful tail behavior can be reached for very high photon numbers. We demonstrate arbitrary statistics generation for up to 500 photons. The proposed device can produce any classical light statistics with given parameters including Poissonian, super-Poissonian, thermal, and heavy-tailed distributions like log-normal. The presented method can be used to simulate communication channels, calibrate the response of photon-number-resolving detectors, or probe physical phenomena sensitive to photon statistics.

Arbitrary digital pulse sequence generator with delay-loop timing.

We propose an idea of an electronic multi-channel arbitrary digital sequence generator with temporal granularity equal to two clock cycles. We implement the generator with 32 channels using a low-cost ARM microcontroller and demonstrate its capability to produce temporal delays ranging from tens of nanoseconds to hundreds of seconds, with 24 ns timing granularity and linear scaling of delay with respect to the number of delay loop iterations. The generator is optionally synchronized with an external clock source to provide 100 ps jitter and overall sequence repeatability within the whole temporal range. The generator is fully programmable and able to produce digital sequences of high complexity. The concept of the generator can be implemented using different microcontrollers and applied for controlling of various optical, atomic, and nuclear physics measurement setups.

Optimal reordering of measurements for photonic quantum tomography.

Quantum tomography is an essential method of the photonic technology toolbox and is routinely used for evaluation of experimentally prepared states of light and characterization of devices transforming such states. The tomography procedure consists of many different sequentially performed measurements. We present considerable tomography speedup by optimally arranging the individual constituent measurements, which is equivalent to solving an instance of the traveling salesman problem. As an example, we obtain solutions for photonic systems of up to five qubits, and conclude that already for systems of three or more qubits, the total duration of the tomography procedure can be halved. The reported speedup has been verified experimentally for quantum state tomography and also for full quantum process characterization up to six qubits, without resorting to any complexity reduction or simplification of the system of interest. Our approach is versatile and reduces the time of an input-output characterization of optical devices and various scattering processes as well.

Experimental characterization of a non-local convertor for quantum photonic networks.

We experimentally characterize a quantum photonic gate that is capable of converting multiqubit entangled states while acting only on two qubits. It is an important tool in large quantum networks, where it can be used for re-wiring of multipartite entangled states or for generating various entangled states required for specific tasks. The gate can be also used to generate quantum information processing resources, such as entanglement and discord. In our experimental demonstration, we characterized the conversion of a linear four-qubit cluster state into different entangled states, including GHZ and Dicke states. The high quality of the experimental results show that the gate has the potential of being a flexible component in distributed quantum photonic networks.

Conditional cooling limit for a quantum channel going through an incoherent environment.

We propose and experimentally verify a cooling limit for a quantum channel going through an incoherent environment. The environment consists of a large number of independent non-interacting and non-interfering elementary quantum systems--qubits. The qubits travelling through the channel can only be randomly replaced by environmental qubits. We investigate a conditional cooling limit that exploits an additional probing output. The limit specifies when the single-qubit channel is quantum, i.e. it preserves entanglement. It is a fundamental condition for entanglement-based quantum technology.

Quantum non-Gaussian Depth of Single-Photon States.

We introduce and experimentally explore the concept of the non-Gaussian depth of single-photon states with a positive Wigner function. The depth measures the robustness of a single-photon state against optical losses. The directly witnessed quantum non-Gaussianity withstands significant attenuation, exhibiting a depth of 18 dB, while the nonclassicality remains unchanged. Quantum non-Gaussian depth is an experimentally approachable quantity that is much more robust than the negativity of the Wigner function. Furthermore, we use it to reveal significant differences between otherwise strongly nonclassical single-photon sources.

Highly stable polarization independent Mach-Zehnder interferometer.

We experimentally demonstrate optical Mach-Zehnder interferometer utilizing displaced Sagnac configuration to enhance its phase stability. The interferometer with footprint of 27×40 cm offers individually accessible paths and shows phase deviation less than 0.4° during a 250 s long measurement. The phase drift, evaluated by means of Allan deviation, stays below 3° or 7 nm for 1.5 h without any active stabilization. The polarization insensitive design is verified by measuring interference visibility as a function of input polarization. For both interferometer's output ports and all tested polarization states the visibility stays above 93%. The discrepancy in visibility for horizontal and vertical polarization about 3.5% is caused mainly by undesired polarization dependence of splitting ratio of the beam splitter used. The presented interferometer device is suitable for quantum-information and other sensitive applications where active stabilization is complicated and common-mode interferometer is not an option as both the interferometer arms have to be accessible individually.