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An optimal single-photon source should deterministically deliver one and only one photon at a time, with no trade-off between the source's efficiency and the photon indistinguishability. However, all reported solid-state sources of indistinguishable single photons had to rely on polarization filtering which reduced the efficiency by 50%, which fundamentally limited the scaling of photonic quantum technologies. Here, we overcome this final long-standing challenge by coherently driving quantum dots deterministically coupled to polarization-selective Purcell microcavities-two examples are narrowband, elliptical micropillars and broadband, elliptical Bragg gratings. A polarization-orthogonal excitation-collection scheme is designed to minimize the polarization-filtering loss under resonant excitation. We demonstrate a polarized single-photon efficiency of 0.60(2), a single-photon purity of 0.991(3), and an indistinguishability of 0.973(5). Our work provides promising solutions for truly optimal single-photon sources combining near-unity indistinguishability and near-unity system efficiency simultaneously.Single photons are appealing candidates for quantum communications 1,2 , quantumenhanced metrology 3,4 and quantum computing 5,6 . In view of the quantum information applications, the single photons are required to be controllably prepared with a high efficiency into a given quantum state. Specifically, the single photons should possess the same polarization, spatial mode, and transform-limited spectro-temporal profile for a high-visibility Hong-Ou-Mandel-type quantum interference 1,7 .Self-assembled quantum dots show so far the highest quantum efficiency among solid-state quantum emitters and thus can potentially serve as an ideal single-photon source 8-15 . There has been encouraging progress in recent years in developing highperformance single-photon sources 11 . Pulsed resonant excitation on single quantum dots has been developed to eliminate dephasing and time jitter, which created single photons with near-unity indistinguishability 15 . Further, by combining the resonant excitation with Purcell-enhanced micropillar 16,17 or photonic crystals 18,19 , the generated transform-limited 20,21 single photons have been efficiently extracted out of the bulk and funneled into a single mode at far field. Despite the recent progress 16-22 , the experimentally achieved polarized-single-photon efficiency (defined as the number of single-polarized photons extracted from the bulk semiconductor and collected by the first lens per pumping pulse) is ~33% in ref. 16 and ~15% in ref. 17, still fell short of the minimally required efficiency of 50% for boson sampling to show computational advantage to classical algorithms 23 , and was below the efficiency threshold of 67% for photon-loss-tolerant encoding in cluster-state models of optical quantum computing 24 . It should be noted that a <50% single-photon efficiency would render nearly all linear optical quantum computing schemes 1,5 not scalable.The indistinguishable single-photon...

By pulsed s-shell resonant excitation of a single quantum dot-micropillar system, we generate long streams of 1000 near-transform-limited single photons with high mutual indistinguishability. The HongOu-Mandel interference of two photons is measured as a function of their emission time separation varying from 13 ns to 14.7 μs, where the visibility slightly drops from 95.9(2)% to a plateau of 92.1(5)% through a slow dephasing process occurring at a time scale of 0.7 μs. A temporal and spectral analysis reveals the pulsed resonance fluorescence single photons are close to the transform limit, which are readily useful for multiphoton entanglement and interferometry experiments. DOI: 10.1103/PhysRevLett.116.213601 Self-assembled InGaAs quantum dots (QDs) are promising single-photon emitters with a high quantum efficiency and a fast decay rate [1]. In the past decades, extensive efforts have been devoted to producing single photons with high purity (that is, a vanishing two-photon emission probability), near-unity indistinguishability, and high extraction efficiency [2][3][4][5][6][7][8][9][10]. These key properties have been compatibly combined simultaneously on the same QD micropillar very recently [11][12][13].An important next challenge is to extend the singlephoton sources to multiple photonic quantum bits [14], as required by various quantum information protocols such as boson sampling [15], quantum teleportation [16], quantum computation [17], and quantum metrology [18]. To this aim, one approach is to use many independent QDs [19] that are tuned into an identical emission wavelength [20] and efficiently emit single photons stringently at the transform limit, that is, T 2 ¼ 2T 1 , where T 2 and T 1 are the photon's coherence time and lifetime, respectively. Another-probably less demanding-solution is based on only one perfect QD emitting single-photon pulse trains with high efficiency [11,12], which are then either demultiplexed into N spatial modes or dynamically controlled using time-bin encoding in a loop-based architecture [21]. Implementing N-photon quantum circuits in this configuration demands streams of N mutually indistinguishable single photons far apart in emission time.However, previous Hong-Ou-Mandel (HOM) type interference experiments [7][8][9][10][11][12][13] were performed with a time separation of only a few nanoseconds between two photons emitted consecutively from a QD. Spectral diffusions [22] with a time scale much slower than nanoseconds were speculated-yet without a conclusive study-to account for the mismatch between the observed near-unity transient indistinguishability and the nonunity time-averaged T 2 =2T 1 ratio [7][8][9][10]13]. Thus, it is highly desirable to study the two-photon interference as a function of their emission time separation and test how far apart the high indistinguishability persists. The ultimate goal is to generate efficient and truly transform-limited single photons, with which perfect interference can be achieved regardless of their time separation, and ...

We report an experiment to test quantum interference, entanglement and nonlocality using two dissimilar photon sources, the Sun and a semiconductor quantum dot on the Earth, which are separated by ~150 million kilometers. By making the otherwise vastly distinct photons indistinguishable in all degrees of freedom, we observe time-resolved two-photon quantum interference with a raw visibility of 0.796(17), well above the 0.5 classical limit, providing the first evidence of quantum nature of thermal light. Further, using the photons with no common history, we demonstrate post-selected two-photon entanglement with a state fidelity of 0.826(24), and a violation of Bell's inequality by 2.20(6). The experiment can be further extended to a larger scale using photons from distant stars, and open a new route to quantum optics experiments at an astronomical scale.Can any two photons in the Universe, no matter how distantly and independently they originate from, show quantum interference and entanglement? According to quantum theory, when two quantum-mechanically indistinguishable single photons impinge upon a 50/50 beam splitter, they bunch together out of the same output port due to bosonic statistics. The classical picture of electromagnetic fields failed in understanding the interference of two photons from independent sources with a visibility better than 50% 1-4 , which can be explained by quantum interference of the probability amplitudes of the twophoton events 5 . This effect, also known as Hong-Ou-Mandel (HOM) two-photon interference 6 , poses a strong conceptual challenge to the celebrated statement by Dirac that "Each photon then interferes only with itself. Interference between different photons never occurs" 7 .

Efficient excitation of a single two-level system usually requires that the driving field is at the same frequency as the atomic transition. However, the scattered laser light in solid-state implementations can dominate over the single photons, imposing an outstanding challenge to perfect single-photon sources. Here, we propose a background-free method using a phase-locked dichromatic electromagnetic field with no spectral overlap with the optical transition for a coherent control of a twolevel system, and we demonstrate this method experimentally with a single quantum dot embedded in a micropillar. Single photons generated by π excitation show a purity of 0.988(1) and indistinguishability of 0.962(6). Further, the phasecoherent nature of the two-color excitation is captured by the resonancefluorescence intensity dependence on the relative phase between the two pulses.

Photonic graph states are underlying resources for one-way optical quantum computation, quantum error correction, fundamental test of quantum mechanics, and quantum communication network. Most of existing works, however, are based on spontaneous parametric down-conversion source that intrinsically suffers from probabilistic generation and double pair components. Here, we create two important classes of graph states, a polarization-encoded four-photon Greenberger-Horne-Zeilinger (GHZ) state and a linear cluster state, by actively demultiplexing a deterministic single photon source from a semiconductor quantum dot embedded in a micropillar. A state fidelity of 0.763±0.004 (0.790±0.009) and a count rate of ∼13 Hz are observed for the four-photon cluster (GHZ) state. The results constitute a new route towards the multiphoton entanglement with deterministic single-photon sources.

We report a proof-of-principle demonstration of Shor's algorithm with photons generated by an on-demand semiconductor quantum dot single-photon source for the first time. A fully compiled version of Shor's algorithm for factoring 15 has been accomplished with a significantly reduced resource requirement that employs the four-photon cluster state. Genuine multiparticle entanglement properties are confirmed to reveal the quantum character of the algorithm and circuit. The implementation realizes the Shor's algorithm with deterministic photonic qubits, which opens new applications for cluster state beyond one-way quantum computing.

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