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Verifying the violation of Bell's inequality is one of the most representative methods to demonstrate that entangled photon pairs prepared in a quantum optics-based system exhibit quantum properties. While experiments on Bell inequality violations have been theoretically well-established and extensively conducted to implement various quantum information technologies in laboratory settings, mathematical modeling for accurately predicting the distribution of high-intensity entangled photon pairs in high-loss environments remains an issue that requires further research. As the brightness of the entangled photon pairs increases, the influence of multi-photon effects becomes more significant, leading to a decrease in the CHSH value $S$ and also a reduction in the standard deviation of the CHSH value $\Delta S$. Therefore, a new analysis of the $(S-2)/\Delta S$ value is required to more precisely confirm the degree of CHSH inequality violation including the reliability of $S$. In this paper, we propose a mathematical model to predict the $(S-2)/\Delta S$ value as a function of the brightness of the entangled photon pair source, and we also suggest the need to optimize the brightness of this source. Additionally, we provide experimental evidence supporting this model. The experiment confirms that when the mean photon number is $\mu=0.026$ in an entanglement distribution setup with a total loss of $-19.03$ dB, the CHSH value drops to 2.69, while the $(S-2)/\Delta S$ value increases to 60.95., Comment: 11 pages, 1 table, and 4 figures

A high-brightness entangled photon pair (HBEPP) source is essential for conducting entanglement-based quantum key distribution (QKD) between a satellite and a ground station. While an ultrabright source can overcome significant losses in satellite-based QKD (SQKD) and increase the sifted key rate, it also induces the multi-photon effect, raising the system's error rate. To accurately estimate system performance, we first present an analytical model for calculating the measurement probabilities of HBEPP distribution through an asymmetric loss channel. Based on this model, we propose the use of a passive-intensity HBEPP source for SQKD systems, assuming a polarization-independent channel and threshold detectors for measurement. We confirm that fixing the mean photon number at $\bar{\mu}=0.1$ achieves a performance of $99.7\%$ compared to the ideal one-way communication entanglement-based SQKD protocol, which is effectively optimizing the HBEPP source brightness in accordance with system losses., Comment: 9 pages, 5 figures, 3 tables

A Greenberger Horne Zeilinger (GHZ) entangled state with a phase is crucial for realizing desired multipartite quantum states for practical applications. Here, we report violations of the general Bell inequality (GBI) introduced in [1] using the four photon polarization entangled phase GHZ state realized via intrinsic polarization correlation and collective two-photon coherence in the 5S1/2 5P3/2 5D5/2 transition of 87Rb atoms. The phase GHZ state can be achieved by the unitary transformation of only one local phase of the four photons. Theoretically, the GHZ state with the {\pi}/4 phase affords maximal violation of the GBI of 2sqrt(2) at the local measurement settings of the Pauli operators {\sigma}_x and {\sigma}_y. We experimentally demonstrate strong violations of the GBI of the phase-GHZ state by 47 standard deviations. In addition to the entanglement witness for the phase GHZ state, the results represent a genuine four photon entanglement of the phase GHZ state, thereby providing a novel resource for realizing photonic quantum computation, magic state distillation from entangled states, and quantum networks based on atom photon interactions.

Multiphoton interference is an important phenomenon in modern quantum mechanics and experimental quantum optics, and it is fundamental for the development of quantum information science and technologies. Over the last three decades, several theoretical and experimental studies have been performed to understand the essential principles underlying such interference and to explore potential applications. Recently, the two-photon interference (TPI) of phase-randomized weak coherent states has played a key role in the realization of long-distance quantum communication based on the use of classical light sources. In this context, we investigated TPI experiments with weak coherent pulses at the single-photon level and quantitatively analyzed the results in terms of the single- and coincidence-counting rates and one- and two-photon interference-fringe shapes. We experimentally examined the Hong-Ou-Mandel-type TPI of phase-randomized weak coherent pulses to compare the TPI effect with that of correlated photons. Further experiments were also performed with two temporally- and spatially separated weak coherent pulses. Although the observed interference results, including the results of visibility and fringe shape, can be suitably explained by classical intensity correlation, the physics underlying the TPI effect needs to be interpreted as the interference between the two-photon states at the single-photon level within the utilized interferometer. The results of this study can provide a more comprehensive understanding of the TPI of coherent light at the single-photon level., Comment: 18 pages, 10 figures

The observation of the Hong-Ou-Mandel (HOM)-type two-photon interference (TPI) has played an important role in the development of photonic quantum technologies. The time-resolved coincidence-detection technique has been effectively used to identify and characterize the TPI phenomena of long-coherence optical fields. Here, we report on the experimental demonstration of the TPI of two phase-randomized weak coherent pulses with time-resolved coincidence detection. The mutual coherence time between the two weak coherent lights is determined by applying a frequency noise to one of the two interfering lights. We analyze the HOM-type TPI-fringe visibility according to the ratio of the coherence time to the pulse duration., Comment: 6 pages, 4 figures, Accepted for publication in Appl. Phys. Lett

Bright, entangled multiphoton sources based on atom photon interactions are an essential requirement in the realization of several quantum information and quantum computation schemes based on photonic quantum systems. Here, we experimentally demonstrate a four photon polarization entangled GHZ state obtained from Doppler broadened atomic ensembles of 87Rb atoms. Owing to collective two photon coherence in the Doppler broadened cascade-type atomic system, our setup enables the generation of robust four photon GHZ states with a fidelity of 0.82 and a measured four photon average coincidence rate of 0.58 Hz. We believe that the generation of such bright and stable multiphoton GHZ states from atomic media is an important step toward realizing photonic quantum computation and practical quantum networks based on atom photon interactions.

The distinguishing of the multiphoton quantum interference effect from the classical one forms one of the most important issues in modern quantum mechanics and experimental quantum optics. For a long time, the two-photon interference (TPI) of correlated photons has been recognized as a pure quantum effect that cannot be simulated with classical lights. In the meantime, experiments have been carried out to investigate the classical analogues of the TPI. In this study, we conduct TPI experiments with uncorrelated photons with different center frequencies from a luminescent light source, and we compare our results with the previous ones of correlated photons. The observed TPI fringe can be expressed in the form of three phase terms related to the individual single-photon and two-photon states, and the fringe pattern is strongly affected by the two single-photon-interference fringes and also by their visibilities. With the exception of essential differences such as valid and accidental coincidence events within a given resolving time and the two-photon spectral bandwidth, the interference phenomenon itself exhibits the same features for both correlated and uncorrelated photons in the single-photon counting regime., Comment: 19 pages, 5 figures, to be published in Sci. Rep

We report a source of polarization-entangled photon pairs in the 1550-nm telecommunication band, which is based on non-collinear spontaneous parametric down-conversion in a periodically poled lithium niobate crystal pumped by picosecond pulses. This source is realized utilizing a polarization-based Sagnac interferometer employing a type-0 non-collinear quasi-phase-matching configuration. Polarization entanglement is verified through measurement of the polarization-correlation interference fringes with visibility >96% and by testing the experimental violation of the Clauser-Horne-Shimony-Holt (CHSH) form of Bell inequality. The CHSH-Bell parameter S is found to be 2.72 \pm 0.04, with 18 standard deviations from the statistical uncertainty., Comment: 14 pages, 4 figures

We propose disturbance-free measurement using a "weak-value" scheme, in which a weakly measured quantum system is post-selected (to the initial state) to confirm that there is no disturbance. The probability of obtaining the non-disturbed state is asymptotically close to unity. We theoretically show that outcomes of the disturbance-free measurement for a two-qubit state satisfy the Clauser--Horne--Shimony--Holt inequality. We experimentally demonstrate the test for a typical (maximally entangled) two-qubit state based on a linear optical system. In experiments, polarization-entangled photon-pairs generated by the spontaneous parametric down-conversion process are measured by instruments such as strength-variable polarization-measurement apparatuses and a fiber-based Bell state analyzer.

We present two-photon interference experiments with polarization-entangled photon pairs in a polarization-based Franson-type interferometer. Although the two photons do not meet at a common beamsplitter, a phase-insensitive Hong-Ou-Mandel type two-photon interference peak and dip fringes are observed, resulting from the two-photon interference effect between two indistinguishable two-photon probability amplitudes leading to a coincidence detection. A spatial quantum beating fringe is also measured for nondegenerate photon pairs in the same interferometer, although the two-photon states have no frequency entanglement. When unentangled polarization-correlated photons are used as an input state, the polarization entanglement is successfully recovered through the interferometer via delayed compensation., Comment: 13 pages, 4 figures, accepted for publication in Scientific Reports

Multiphoton interference effects can be measured with a single detector when two input photons are temporally well separated when compared with the dead time of the single-photon avalanche detector. Here we experimentally demonstrate that the Hong-Ou-Mandel interference effect can be observed with a single non-photon-number resolving detector via a time-delayed coincidence measurement of successive electrical signals from the detector. The two-photon interference experiment is performed by utilizing temporally well-separated pairwise weak coherent pulses and the interference fringes are successfully measured with a high visibility in the range of the limited upper bound for the weak coherent photon source., Comment: 4 pages, 3 figures, to be published in Optics Letters

To realize a quantum network based on quantum entanglement swapping, bright and completely autonomous sources are essentially required. Here, we experimentally demonstrate Hong-Ou-Mandel (HOM) quantum interference between two independent bright photon pairs generated via the spontaneous four-wave mixing in Doppler-broadened ladder-type 87Rb atoms. Bright autonomous heralded single photons are operated in a continuous-wave (CW) mode with no synchronization or supplemental filters. The four-fold photon coincidence counts per hour correspond to 5000 events for a temporal range of 10 ns, one order higher than those of previously reported for autonomous single photons. We observe an HOM dip with 83% visibility with the two autonomous heralded single photons for an effective measurement time of 900 s. The achievement of the HOM interference between the two bright autonomous photon-pair sources has made an important step towards a practical scalable quantum network.

We report a bright photon-pair source with a coincidence counting rate per input power (cps/mW) of tens of thousands, obtained via spontaneous four-wave mixing from a Doppler-broadened atomic ensemble of the 5S1/2-5P3/2-5D5/2 transition of 87Rb. The photon-pair generation rate is enhanced by the two-photon coherence contributions from almost all the atomic velocity groups in the Doppler-broadened ladder-type atomic system. We obtained the violation of the Cauchy-Schwarz inequality by a factor of 2370(150). We believe that our scheme for highly bright paired photons is important as a useful quantum light source for quantum entanglement swapping between completely autonomous sources.

We present experimental demonstrations of two-photon interference involving temporally separated photons within two types of interferometers: a Mach-Zehnder interferometer and a polarization-based Michelson interferometer. The two-photon states are probabilistically prepared in a symmetrically superposed state within the two interferometer arms by introducing a large time delay between two input photons; this state is composed of two temporally separated photons, which are in two different or the same spatial modes. We then observe two-photon interference fringes involving both the Hong-Ou-Mandel interference effect and the interference of path-entangled two-photon states simultaneously in a single interferometric setup. The observed two-photon interference fringes provide simultaneous observation of the interferometric properties of the single-photon and two-photon wavepackets. The observations can also facilitate a more comprehensive understanding of the origins of the interference phenomena arising from spatially bunched/anti-bunched two-photon states comprised of two temporally separated photons within the interferometer arms., Comment: 25 pages, 6 figures. arXiv admin note: text overlap with arXiv:1601.00469

With a recent rising interest of single photon superradiance due to its potential usefulness for efficient collection of single photon from an atomic ensemble, bright and narrow photon pair source is a key component in realization of quantum communication and quantum computer based on coherent interaction between light and atomic ensemble. We report the superradiant emission of ultra-bright photon pairs with a coincidence counting rate per input power of 64,600 cps/mW via spontaneous four-wave mixing in a thermal vapour cell. The photon-pair generation rate is enhanced by the contribution of two-photon coherence of almost atomic velocity groups in the Doppler-broadened ladder-type atomic system. The quadratic proportionality of the probability of detecting a heralded single photon as a function of the optical depth clarifies that the ultra-brightness results from the superradiance. In addition, a single photon superradiant beating at a high optical depth of the atomic ensemble is observed for the first time.

We propose and experimentally demonstrate two-photon interference effects in a Mach-Zehnder interferometer in which two different kinds of two-photon states are prepared by introducing a time delay between the two input photons. The two-photon states are simultaneously prepared in a symmetrically superposed state with two temporally separated photons in two different spatial modes or in the same spatial mode within the interferometer. We observe two-photon interference fringes involving both the Hong-Ou-Mandel interference effect and the interference of path-entangled two-photon states simultaneously in a single interferometric setup. The observed two-photon interference effect can provide a simultaneous observation of the interferometric properties of the single-photon and two-photon wavepackets, Comment: superseded by arXiv:1607.03678

We demonstrate a polarization-entangled photon-pair source obtained via a type-II non-collinear quasi-phase-matched spontaneous parametric down-conversion process with a 10-mm periodically poled KTiOPO$_4$ crystal, which is as stable and wavelength-tunable as the well-known Sagnac configuration scheme. A brightness of 4.2 kHz/mW is detected and a concurrence of 0.975 is estimated using quantum state tomography. Without loss of entanglement and brightness, the photon-pair wavelengths are tunable through control of the crystal temperature. This improvement is achieved using the non-collinear configuration and a stable interferometric distinguishability compensator.

We present a highly efficient source for discrete frequency-entangled photon pairs based on spontaneous parametric down-conversion using 3rd order type-0 quasi-phase matching in a periodically poled MgO-doped stoichiometric LiTaO3 crystal pumped by a 355.66 nm laser. Correlated two-photon states were generated with automatic conservation of energy and momentum in two given spatial modes. These states have a wide spectral range, even under small variations in crystal temperature, which consequently results in higher discreteness. Frequency entanglement was confirmed by measuring two-photon quantum interference fringes without any spectral filtering., Comment: 4 pages, 4 figures, to be published in Optics Letters

Superposition and indistinguishablility between probability amplitudes have played an essential role in observing quantum interference effects of correlated photons. The Hong-Ou-Mandel interference and interferences of the path-entangled photon number state are of special interest in the field of quantum information technologies. However, a fully generalized two-photon quantum interferometric scheme accounting for the Hong-Ou-Mandel scheme and path-entangled photon number states has not yet been proposed. Here we report the experimental demonstrations of the generalized two-photon interferometry with both the interferometric properties of the Hong-Ou-Mandel effect and the fully unfolded version of the path-entangled photon number state using photon-pair sources, which are independently generated by spontaneous parametric down-conversion. Our experimental scheme explains two-photon interference fringes revealing single- and two-photon coherence properties in a single interferometer setup. Using the proposed interferometric measurement, it is possible to directly estimate the joint spectral intensity of a photon pair source.

We describe and characterize an equal-fidelity surface in Bloch space targeted for a qubit state by means of equal-distance concept. The distance is generalized and defined as the Euclidean distance between extended Bloch vectors for arbitrary dimensional states. The distance is a genuine distance according to the definition and is related to other distances between quantum states and super-fidelity.

We propose and experimentally demonstrate an approximate universal-NOT (U-NOT) operation that is robust against operational errors. In our proposal, the U-NOT operation is composed of stochastic unitary operations represented by the vertices of regular polyhedrons. The operation is designed to be robust against random operational errors by increasing the number of unitary operations (i.e., reference axes). Remarkably, no increase in the total number of measurements nor additional resources are required to perform the U-NOT operation. Our method can be applied in general to reduce operational errors to an arbitrary degree of precision when approximating any anti-unitary operation in a stochastic manner.

We propose and demonstrate the scaling up of photonic graph state through path qubit fusion. Two path qubits from separate two-photon four-qubit states are fused to generate a two-dimensional seven-qubit graph state composed of polarization and path qubits. Genuine seven-qubit entanglement is verified by evaluating the witness operator. Six qubits from the graph state are used to execute the general two-qubit Deutsch-Jozsa algorithm with a success probability greater than 90%., Comment: 4 pages. Supplementary Material is included in the zip file

Spatial interference of quantum mechanical particles exhibits a fundamental feature of quantum mechanics. A two-mode entangled state of N particles known as N00N state can give rise to non-classical interference. We report the first experimental observation of a three-photon N00N state exhibiting Young's double-slit type spatial quantum interference. Compared to a single-photon state, the three-photon entangled state generates interference fringes that are three times denser. Moreover, its interference visibility of $0.49 \pm 0.09$ is well above the limit of 0.1 for spatial super-resolution of classical origin. The demonstration of spatial quantum interference by a N00N state composed of more than two photons represents an important step towards applying quantum entanglement to technologies such as lithography and imaging.

We describe an experimental demonstration of a novel three-photon NOON state generator using a single source of photons based on spontaneous parametric down-conversion (SPDC). The three-photon number-entangled state is deterministically generated by the detection of a heralding photon. Interference fringes measured with an emulated three-photon absorber reveal the three-photon de Broglie wavelength and exhibit visibility > 70% without background subtraction., Comment: 3 figures