Erratum: Linear Optical Quantum Computation with Frequency-Comb Qubits and Passive Devices [Phys. Rev. Lett. 130, 200602 (2023)].

This corrects the article DOI: 10.1103/PhysRevLett.130.200602.

Quantum frequency conversion using 4-port fiber-pigtailed PPLN module.

Quantum frequency conversion (QFC), which involves the exchange of frequency modes of photons, is a prerequisite for quantum interconnects among various quantum systems, primarily those based on telecom photonic network infrastructures. Compact and fiber-closed QFC modules are in high demand for such applications. In this paper, we report such a QFC module based on a fiber-coupled 4-port frequency converter with a periodically poled lithium niobate (PPLN) waveguide. The demonstrated QFC shifted the wavelength of a single photon from 780 to 1541 nm. The single photon was prepared via spontaneous parametric down-conversion (SPDC) with heralding photon detection, for which the cross-correlation function was 40.45 ± 0.09. The observed cross-correlation function of the photon pairs had a nonclassical value of 13.7 ± 0.4 after QFC at the maximum device efficiency of 0.73, which preserved the quantum statistical property. Such an efficient QFC module is useful for interfacing atomic systems and fiber-optic communication.

Linear Optical Quantum Computation with Frequency-Comb Qubits and Passive Devices.

We propose a linear optical quantum computation scheme using time-frequency degrees of freedom. In this scheme, a qubit is encoded in single-photon frequency combs, and manipulation of the qubits is performed using time-resolving detectors, beam splitters, and optical interleavers. This scheme does not require active devices such as high-speed switches and electro-optic modulators and is robust against temporal and spectral errors, which are mainly caused by the detectors' finite resolution. We show that current technologies almost meet the requirements for fault-tolerant quantum computation.

Wave-particle duality of light appearing in an intensity interferometric scenario.

A single photon exhibits wave-particle duality in the Young's double-slit interferometer. The duality characterized by an interference visibility and a which-path information has trade-off relation known as complementarity. These quantities are related to the first-order coherence, and the interference is based on the phase correlation between lights coming from two arms. However according to quantum optics theory, such a simple wave-particle picture is not enough to understand the nature because the theory showed an importance of higher-order coherence in the sense of both interference and statistical distribution of photons. Second-order intensity correlation is especially crucial to reveal distinctive quantum features of photons with no classical analogue. Here, in an intensity interferometric scenario as represented by the Hong-Ou-Mandel interferometer, we discuss a wave-particle duality of light based on a which-path information and a quantity characterizing a magnitude of the intensity interferometric effect. We show, for classical light, the two quantities obey the complementary principle similar to the case of the double-slit experiment, but do not for nonclassical light. The nonclassical light such as photons at two arms is allowed to show larger which-path information and intensity interference simultaneously beyond the complementary relation. Moreover, the violation reveals a new nonclassical nature of light although both of the above two quantities seem to be understandable classically, which is never found from a consideration of only one side of wave-particle duality.

Entanglement distribution using a biphoton frequency comb compatible with DWDM technology.

We demonstrate a distribution of frequency-multiplexed polarization-entangled photon pairs over 16 frequency channels using demultiplexers for the signal and idler photons with a frequency spacing of 25 GHz, which is compatible with dense wavelength division multiplexing (DWDM) technology. Unlike conventional frequency-multiplexed photon-pair distribution by a broadband spontaneous parametric down-conversion (SPDC) process, we use photon pairs produced as a biphoton frequency comb by SPDC inside a cavity where one of the paired photons is confined. Owing to the free spectral range of 12.5 GHz and the finesse of over 10 of the cavity, the generated photons having a narrow linewidth in one channel are separated well from those in the other channels, which minimizes channel cross-talk in advance. The observed fidelities of the photon pairs range from 81 % to 96 % in the 16 channels. The results show the usefulness of the polarization-entangled biphoton frequency comb for frequency-multiplexed entanglement distribution via a DWDM system.

Massive-mode polarization entangled biphoton frequency comb.

A frequency-multiplexed entangled photon pair and a high-dimensional hyperentangled photon pair are useful to realize a high-capacity quantum communication. A biphoton frequency comb (BFC) with entanglement can be used to prepare both states. We demonstrate polarization entangled BFCs with over 1400 frequency modes, which is approximately two orders of magnitude larger than those of earlier entangled BFCs, by placing a singly resonant periodically poled LiNbO3 waveguide resonator within a Sagnac loop. The BFCs are demonstrated by measuring the joint spectral intensity, cross-correlation, and autocorrelation. Moreover, the polarization entanglement at representative groups of frequency modes is verified by quantum state tomography, where each fidelity is over 0.7. The efficient generation of a massive-mode entangled BFC is expected to accelerate the increase of capacity in quantum communication.

Frequency-Multiplexed Photon Pairs Over 1000 Modes from a Quadratic Nonlinear Optical Waveguide Resonator with a Singly Resonant Configuration.

We demonstrate a frequency multiplexed photon pair generation based on a quadratic nonlinear optical waveguide inside a cavity which confines only signal photons without confining idler photons and the pump light. We monolithically constructed the photon pair generator by a periodically poled lithium niobate (PPLN) waveguide with a high reflective coating for the signal photons around 1600 nm and with antireflective coatings for the idler photons around 1520 nm and the pump light at 780 nm at the end faces of the PPLN waveguide. We observed a comblike photon pair generation with a mode spacing of the free spectral range of the cavity. Unlike the conventional multiple resonant photon pair generation experiments, the photon pair generation was incessant within a range of 80 nm without missing teeth due to a mismatch of the energy conservation and the cavity resonance condition of the photons, resulting in over 1000-mode frequency multiplexed photon pairs in this range.

Experimental time-reversed adaptive Bell measurement towards all-photonic quantum repeaters.

An all-optical network is identified as a promising infrastructure for fast and energy-efficient communication. Recently, it has been shown that its quantum version based on 'all-photonic quantum repeaters'-inheriting, at least, the same advantages-expands its possibility to the quantum realm, that is, a global quantum internet with applications far beyond the conventional Internet. Here we report a proof-of-principle experiment for a key component for the all-photonic repeaters-called all-photonic time-reversed adaptive (TRA) Bell measurement, with a proposal for the implementation. In particular, our TRA measurement-based only on optical devices without any quantum memories and any quantum error correction-passively but selectively performs the Bell measurement only on single photons that have successfully survived their lossy travel over optical channels. In fact, our experiment shows that only the survived single-photon state is faithfully teleported without the disturbance from the other lost photons, as the theory predicts.

Frequency comb generation in a quadratic nonlinear waveguide resonator.

Enhancement of a nonlinear optical interaction through waveguides or resonators disclose unconventional interplay among multiple lights. Microresonator-based optical frequency comb (OFC) generation via third order nonlinearity is a typical example of such enhancements. Recently, quadratic-nonlinearity-based OFC with an external cavity configuration has been found and its on-chip implementation is highly demanded. Here we for the first time demonstrate such an on-chip OFC with a quadratic nonlinear waveguide resonator. Furthermore, we controlled the comb spectra separation by adjusting frequency difference of two pump light. This on-chip quadratic device will be useful for not only metrologies but also integrated quantum information technologies.

Long-Distance Single Photon Transmission from a Trapped Ion via Quantum Frequency Conversion.

Trapped atomic ions are ideal single photon emitters with long-lived internal states which can be entangled with emitted photons. Coupling the ion to an optical cavity enables the efficient emission of single photons into a single spatial mode and grants control over their temporal shape. These features are key for quantum information processing and quantum communication. However, the photons emitted by these systems are unsuitable for long-distance transmission due to their wavelengths. Here we report the transmission of single photons from a single ^{40}Ca^{+} ion coupled to an optical cavity over a 10 km optical fiber via frequency conversion from 866 nm to the telecom C band at 1530 nm. We observe nonclassical photon statistics of the direct cavity emission, the converted photons, and the 10 km transmitted photons, as well as the preservation of the photons' temporal shape throughout. This telecommunication-ready system can be a key component for long-distance quantum communication as well as future cloud quantum computation.

Polarization insensitive frequency conversion for an atom-photon entanglement distribution via a telecom network.

Long-lifetime quantum storages accessible to the telecom photonic infrastructure are essential to long-distance quantum communication. Atomic quantum storages have achieved subsecond storage time corresponding to 1000 km transmission time for a telecom photon through a quantum repeater algorithm. However, the telecom photon cannot be directly interfaced to typical atomic storages. Solid-state quantum frequency conversions fill this wavelength gap. Here we report on the experimental demonstration of a polarization-insensitive solid-state quantum frequency conversion to a telecom photon from a short-wavelength photon entangled with an atomic ensemble. Atom-photon entanglement has been generated with a Rb atomic ensemble and the photon has been translated to telecom range while retaining the entanglement by our nonlinear-crystal-based frequency converter in a Sagnac interferometer.

High-fidelity entanglement swapping and generation of three-qubit GHZ state using asynchronous telecom photon pair sources.

We experimentally demonstrate a high-fidelity entanglement swapping and a generation of the Greenberger-Horne-Zeilinger (GHZ) state using polarization-entangled photon pairs at telecommunication wavelength produced by spontaneous parametric down conversion with continuous-wave pump light. While spatially separated sources asynchronously emit photon pairs, the time-resolved photon detection guarantees the temporal indistinguishability of photons without active timing synchronizations of pump lasers and/or adjustment of optical paths. In the experiment, photons are sufficiently narrowed by fiber-based Bragg gratings with the central wavelengths of 1541 nm & 1580 nm, and detected by superconducting nanowire single-photon detectors with low timing jitters. The observed fidelities of the final states for entanglement swapping and the generated three-qubit state were 0.84 ± 0.04 and 0.70 ± 0.05, respectively.

High visibility Hong-Ou-Mandel interference via a time-resolved coincidence measurement.

A high visibility Hong-Ou-Mandel (HOM) interference between two independently prepared photons plays an important role in various photonic quantum information processing. In a standard HOM experiment using photons generated by pulse-pumped spontaneous parametric down conversion (SPDC), larger detection time windows than the coherence time of photons have been employed for measuring the HOM visibility and/or drawing the HOM dip. If large amounts of stray photons continuously exist within the detection time windows, employing small detection time windows is favorable for reducing the effect of background noises. Especially, such a setup is helpful for the HOM experiment using continuous wave (cw)-pumped SPDC and the time-resolved coincidence measurement. Here we argue that the method for determining the HOM visibility used in the previous cw experiments tends to suffer from distortion arising from biased contribution of the background noises. We then present a new method with unbiased treatment of the cw backgrounds. By using this method, we experimentally demonstrate a high visibility HOM interference of two heralded telecom photons independently generated by SPDC with employing cw pump light. An observed HOM visibility is 0.87 ± 0.04, which is as high as those observed by using pulse-pumped SPDC photons.

Mach-Zehnder interferometer using frequency-domain beamsplitter.

We demonstrate a first-order interference between coherent light at 1580 nm and 795 nm by using a frequency-domain Mach-Zehnder interferometer (MZI). The MZI is implemented by two frequency-domain BSs based on a second-order nonlinear optical effect in a periodically-poled lithium niobate waveguide with a strong pump light. The observed visibility is over 0.99 at 50% conversion efficiencies of the BSs. Toward photonic quantum information processing, sufficiently small background photon rate is necessary. From measurement results with a superconducting single photon detector (SSPD), we discuss the feasibility of the frequency-domain MZI in a quantum regime. Our estimation shows that the single photon interference with the visibility above 0.9 is feasible with practical settings.

Experimental demonstration of robust entanglement distribution over reciprocal noisy channels assisted by a counter-propagating classical reference light.

Embedding a quantum state in a decoherence-free subspace (DFS) formed by multiple photons is one of the promising methods for robust entanglement distribution of photonic states over collective noisy channels. In practice, however, such a scheme suffers from a low efficiency proportional to transmittance of the channel to the power of the number of photons forming the DFS. The use of a counter-propagating coherent pulse can improve the efficiency to scale linearly in the channel transmission, but it achieves only protection against phase noises. Recently, it was theoretically proposed [Phys. Rev. A 87, 052325(2013)] that the protection against bit-flip noises can also be achieved if the channel has a reciprocal property. Here we experimentally demonstrate the proposed scheme to distribute polarization-entangled photon pairs against a general collective noise including the bit flip noise and the phase noise. We observed an efficient sharing rate scaling while keeping a high quality of the distributed entangled state. Furthermore, we show that the method is applicable not only to the entanglement distribution but also to the transmission of arbitrary polarization states of a single photon.

Stimulated Brillouin scattering and Brillouin-coupled four-wave-mixing in a silica microbottle resonator.

We report the first observation of stimulated Brillouin scattering (SBS) with Brillouin lasing, and Brillouin-coupled four-wave-mixing (FWM) in an ultra-high-Q silica microbottle resonator. The Brillouin lasing was observed at the frequency of ΩB = 2π × 10.4 GHz with a threshold power of 0.45 mW. Coupling between Brillouin and FWM was observed in both backward and forward scattering directions with separations of 2ΩB. At a pump power of 10 mW, FWM spacing reached to 7th and 9th order anti-Stokes and Stokes, respectively.

Distillation of photon entanglement using a plasmonic metamaterial.

Plasmonics is a rapidly emerging platform for quantum state engineering with the potential for building ultra-compact and hybrid optoelectronic devices. Recent experiments have shown that despite the presence of decoherence and loss, photon statistics and entanglement can be preserved in single plasmonic systems. This preserving ability should carry over to plasmonic metamaterials, whose properties are the result of many individual plasmonic systems acting collectively, and can be used to engineer optical states of light. Here, we report an experimental demonstration of quantum state filtering, also known as entanglement distillation, using a metamaterial. We show that the metamaterial can be used to distill highly entangled states from less entangled states. As the metamaterial can be integrated with other optical components this work opens up the intriguing possibility of incorporating plasmonic metamaterials in on-chip quantum state engineering tasks.

Extracting an entangled photon pair from collectively decohered pairs at a telecommunication wavelength.

We experimentally demonstrated entanglement extraction scheme by using photons at the telecommunication band for optical-fiber-based quantum communications. We generated two pairs of non-degenerate polarization entangled photons at 780 nm and 1551 nm by spontaneous parametric down-conversion and distributed the two photons at 1551 nm through a collective phase damping channel which gives the same amount of random phase shift on the two photons. Through local operation and classical communication, we extracted an entangled photon pair from two phase-disturbed photon pairs. An observed fidelity of the extracted photon pair to a maximally entangled photon pair was 0.73 ± 0.07 which clearly shows the recovery of entanglement.

Frequency down-conversion of 637 nm light to the telecommunication band for non-classical light emitted from NV centers in diamond.

We demonstrate a low-noise frequency down-conversion of photons at 637 nm to the telecommunication band at 1587 nm by the difference frequency generation in a periodically-poled lithium niobate. An internal conversion efficiency of the converter is estimated to be 0.44 at the maximum which is achieved by a pump power of 0.43 W, whereas a rate of internal background photons caused by the strong cw pump laser is estimated to be 9 kHz/mW within a bandwidth of about 1 nm. By using the experimental values related to the intrinsic property of the converter, and using the intensity correlation and the average photon number of a 637 nm input light pulse, we derive the intensity correlation of a converted telecom light pulse. Then we discuss feasibility of a single-photon frequency conversion to the telecommunication band for a long-distance quantum communication based on NV centers in diamond.

Measurement-device-independent quantum key distribution for Scarani-Acin-Ribordy-Gisin 04 protocol.

The measurement-device-independent quantum key distribution (MDI QKD) was proposed to make BB84 completely free from any side-channel in detectors. Like in prepare & measure QKD, the use of other protocols in MDI setting would be advantageous in some practical situations. In this paper, we consider SARG04 protocol in MDI setting. The prepare & measure SARG04 is proven to be able to generate a key up to two-photon emission events. In MDI setting we show that the key generation is possible from the event with single or two-photon emission by a party and single-photon emission by the other party, but the two-photon emission event by both parties cannot contribute to the key generation. On the contrary to prepare & measure SARG04 protocol where the experimental setup is exactly the same as BB84, the measurement setup for SARG04 in MDI setting cannot be the same as that for BB84 since the measurement setup for BB84 in MDI setting induces too many bit errors. To overcome this problem, we propose two alternative experimental setups, and we simulate the resulting key rate. Our study highlights the requirements that MDI QKD poses on us regarding with the implementation of a variety of QKD protocols.