Environmental noise and disorder play a critical role in quantum particle and wave transport in complex media, including solid-state and biological systems. Recent work has predicted that coupling between noisy environments and disordered systems, in which coherent transport has been arrested due to localization effects, could actually enhance transport. Photonic integrated circuits are promising platforms for studying such effects, with a central goal being the development of large systems providing low-loss, high-fidelity control over all parameters of the transport problem. Here, we fully map out the role of static and dynamic disorder in quantum transport using a low-loss, phase-stable, nanophotonic processor consisting of a mesh of 56 generalized beamsplitters programmable on microsecond timescales. Over 85,600 transport experiments, we observe several distinct transport regimes, including environment-enhanced transport in strong, statically disordered systems. Low loss and programmability make this nanophotonic processor a promising platform for many-boson quantum simulation experiments.Quantum walks (QWs), the coherent analogy to classical random walks, have emerged as a useful model for experimental simulations of quantum transport (QT) phenomena in physical systems. QWs have been implemented in platforms including trapped ions 1,2 , ultra-cold atoms 3 , bulk optics 4-8 and integrated photonics 4,9-16 . Integrated photonic implementations are particularly attractive for relatively large coherence lengths, high interferometric visibilities, integration with single-photon sources 17,18 and detectors 19 , and the promise of scaling to many active and reconfigurable components. The role of static and dynamic disorder in the transport of quantum walkers has been of particular interest in the field of quantum simulation 20,21 .Control over static (time-invariant) and dynamic (timevarying) disorder enables studies of fundamentally interesting and potentially useful QT phenomena in discrete-time (DT) QWs. In systems with strong dynamic disorder, illustrated in Fig. 1(a), a quantum walker evolving over T time steps travels a distance proportional to √ T ; the coherent nature of the quantum walker is effectively erased, resulting in classical, diffusive transport characteristics 22,23 . In contrast, a quantum walker (or coherent wave) traversing an ordered system travels a distance proportional to T as a result of coherent interference between superposition amplitudes -a regime known as ballistic transport (see Fig. 1(b)). Perhaps most notably, a quantum walker propagating through a system with strong, static disorder becomes exponentially localized in space and time, inhibiting transport, as illustrated in Fig. 1(c). This QT phenomena is known as Anderson localization 24 and it has been observed in several systems, including optical media [9][10][11]25,26 . For systems in which transport has been arrested due to Anderson localization, it has recently been predicted that adding environmental noise (dynamic disord...

We demonstrate a simple, robust, and ultrabright parametric down-conversion source of polarization-entangled photons based on a polarization Sagnac interferometer. Bidirectional pumping in type-II phase-matched periodically poled KTiOPO4 yields a measured flux of 5 000 polarization-entangled pairs/s per mW of pump power in a 1-nm bandwidth at 96.8% quantuminterference visibility. The common-path arrangement of the Sagnac interferometer eliminates the need for phase stabilization for the biphoton output state.PACS numbers: 42.65. Lm,03.65.Ud,03.67.Mn,42.50.Dv Polarization-entangled photons are essential quantum resources for many applications in quantum information processing, including quantum cryptography [1], teleportation [2], and linear optics quantum computing [3]. The standard technique for efficiently producing polarization entanglement is by means of spontaneous parametric down-conversion (SPDC) in a χ (2) nonlinear crystal such as beta barium borate (BBO) or periodically poled KTiOPO 4 (PPKTP). In SPDC a pump photon is converted into two subharmonic photons, and the SPDC outputs can be arranged in various configurations to yield polarization entanglement between the photon pair. For most practical applications, it is desirable to have a high flux of entangled photon pairs for a given spectral bandwidth, together with a high degree of entanglement. One can quantify the performance of a down-conversion source in terms of its spectral brightness, namely the detected pairs/s/mW of pump power per nm of optical bandwidth, and its quantum-interference visibility.A common approach uses a thin BBO crystal under type-II phase matching to generate non-collinearly propagating photon pairs that are polarization entangled [4]. This simple arrangement requires a small aperture to restrict the field of view in order to obtain a high degree of entanglement, and consequently the flux is generally low. A slightly different approach using a long PPKTP crystal with collinearly propagating outputs yields a higher spectral brightness of 300 pairs/s/mW/nm after postselection with a 50-50 beam splitter [5]. The increased flux is the result of a longer crystal and more efficient pair collection with the use of collinear propagation. Yet, because of spatial-mode distinguishability in both approaches, apertures must be used and most of the output photon pairs are not collected.We have recently demonstrated a bidirectionally pumped down-converter that eliminates the constraint of spatial-mode distinguishability and obtained a detected * Electronic address: thkim@mit.edu † Now at Hewlett-Packard Laboratories, 1501 Page Mill Road, Palo Alto, CA 90304, USA.flux of ∼12 000 pairs/s/mW in a 3-nm bandwidth with a quantum-interference visibility of 90% [6]. In this bidirectional pumping geometry, we used a single PPKTP crystal to implement a configuration of two coherentlydriven SPDC sources whose outputs were combined interferometrically with a Mach-Zehnder (MZ) interferometer. The output photon pairs are polarization entangled over th...

Imagers that use their own illumination can capture three-dimensional (3D) structure and reflectivity information. With photon-counting detectors, images can be acquired at extremely low photon fluxes. To suppress the Poisson noise inherent in low-flux operation, such imagers typically require hundreds of detected photons per pixel for accurate range and reflectivity determination. We introduce a low-flux imaging technique, called first-photon imaging, which is a computational imager that exploits spatial correlations found in real-world scenes and the physics of low-flux measurements. Our technique recovers 3D structure and reflectivity from the first detected photon at each pixel. We demonstrate simultaneous acquisition of sub-pulse duration range and 4-bit reflectivity information in the presence of high background noise. First-photon imaging may be of considerable value to both microscopy and remote sensing.

We demonstrate efficient single-photon detection at 1.55 microm by means of sum-frequency mixing with a strong pump at 1.064 microm in periodically poled lithium niobate followed by photon counting in the visible region. This scheme offers significant advantages over existing InGaAs photon counters: continuous-wave operation, higher detection efficiency, higher counting rates, and no afterpulsing. We achieved single-photon upconversion efficiency of 90% at 21.6 W of circulating power in a resonant pump cavity with a 400-mW Nd:YAG laser. We observed high background counts at strong circulating pump powers due to efficient upconversion of pump-induced fluorescence photons.

Conventional quantum key distribution (QKD) typically uses binary encoding based on photon polarization or time-bin degrees of freedom and achieves a key capacity of at most one bit per photon. Under photon-starved conditions the rate of detection events is much lower than the photon generation rate, because of losses in long distance propagation and the relatively long recovery times of available singlephoton detectors. Multi-bit encoding in the photon arrival times can be beneficial in such photonstarved situations. Recent security proofs indicate high-dimensional encoding in the photon arrival times is robust and can be implemented to yield high secure throughput. In this work we demonstrate entanglement-based QKD with high-dimensional encoding whose security against collective Gaussian attacks is provided by a high-visibility Franson interferometer. We achieve unprecedented key capacity and throughput for an entanglement-based QKD system because of four principal factors: Franson interferometry that does not degrade with loss; error correction coding that can tolerate high error rates; optimized time-energy entanglement generation; and highly efficient WSi superconducting nanowire single-photon detectors. The secure key capacity yields as much as 8.7 bits per coincidence. When optimized for throughput we observe a secure key rate of 2.7 Mbit s −1 after 20 km fiber transmission with a key capacity of 6.9 bits per photon coincidence. Our results demonstrate a viable approach to high-rate QKD using practical photonic entanglement and single-photon detection technologies.

Nonclassical states are essential for optics-based quantum information processing, but their fragility limits their utility for practical scenarios in which loss and noise inevitably degrade, if not destroy, nonclassicality. Exploiting nonclassical states in quantum metrology yields sensitivity advantages over all classical schemes delivering the same energy per measurement interval to the sample being probed. These enhancements, almost without exception, are severely diminished by quantum decoherence. Here, we experimentally demonstrate an entanglement-enhanced sensing system that is resilient to quantum decoherence. We employ entanglement to realize a 20% signal-to-noise ratio improvement over the optimum classical scheme in an entanglement-breaking environment plagued by 14 dB of loss and a noise background 75 dB stronger than the returned probe light. Our result suggests that advantageous quantumsensing technology could be developed for practical situations. DOI: 10.1103/PhysRevLett.114.110506 PACS numbers: 03.67.-a, 03.65.Ta, 42.50.Dv Quantum information processing (QIP) exploits fundamental quantum-mechanical properties to realize capabilities beyond the reach of classical physics. Nonclassical states are essential for optics-based QIP, providing the bases for quantum teleportation [1-3], device-independent quantum key distribution [4], quantum computing [5,6], and quantum metrology [7]. Nonclassical states can increase the signal-to-noise ratios (SNRs) of quantummetrology systems. Indeed, squeezed states have been employed to beat the classical-state limits in optical-phase tracking [8,9], biological sensing [10], and gravitational wave detection [11,12]. Squeezed states, however, are vulnerable to loss: a 10 dB SNR enhancement without loss degrades to 1 dB in a system with 6 dB of loss. Under ideal conditions, N00N states, which are superposition states of N photons in one mode and vacuum in another mode, and vice versa, yield SNR improvements comparable to those of squeezed states [13][14][15][16], but noise injection can easily render N00N states impotent in this regard [17,18]. Consequently, quantum decoherence, arising from environmental loss and noise, largely prevents any quantum-sensing performance advantage, casting doubt on the utility of QIP systems for practical situations.Quantum illumination (QI) is a radically different paradigm that utilizes nonclassical states to achieve an appreciable performance enhancement in the presence of quantum decoherence. QI can defeat eavesdropping on a communication link [19][20][21][22], and boost the SNR of a sensing system [23][24][25][26][27][28][29]. QI systems are comprised of (1) a source that emits entangled signal and idler beams; (2) an interaction in which the signal beam (used as a probe) is subjected to environmental loss, modulation, and noise en route from the source to the receiver; and (3) a receiver that makes a joint measurement on the returned signal beam and the idler beam, which has been stored in a quantum memory, to extract informat...

Entanglement is essential to many quantum information applications, but it is easily destroyed by quantum decoherence arising from interaction with the environment. We report the first experimental demonstration of an entanglement-based protocol that is resilient to loss and noise which destroy entanglement. Specifically, despite channel noise 8.3 dB beyond the threshold for entanglement breaking, eavesdropping-immune communication is achieved between Alice and Bob when an entangled source is used, but no such immunity is obtainable when their source is classical. The results prove that entanglement can be utilized beneficially in lossy and noisy situations, i.e., in practical scenarios.PACS numbers: 42.50.Dv, 03.67.Hk Entanglement is essential to many quantum information applications [1][2][3][4][5][6][7][8][9][10][11], but it is easily destroyed. Quantum illumination (QI) [12][13][14][15] is a radically different entanglement-based paradigm for bosonic channels: it thrives on entanglement-breaking loss and noise. For a given transmitter power, an initially entangled state's nonclassical correlation produces a classical state at the output of an entanglement-breaking channel whose correlation can greatly exceed what any classical input of the same power can yield through that channel. This suggests that bosonic entanglement can be utilized advantageously in practical situations where it does not survive.First proposed to increase the signal-to-noise ratio (SNR) for detecting a weakly-reflecting target in the presence of strong background noise [12][13][14], quantum illumination was later shown, theoretically, to enable high data-rate classical communication that is immune to passive eavesdropping [15]. In the latter application, Alice and Bob use an entangled-state input for their data transfer. Eve, however, has no access to Alice's retained portion of the entangled state, so her eavesdropping performance is that of a classical-state input. The resulting disparity between Alice and Eve's performance-in bit-error rate (BER) and information received per transmitted bit-guarantees Alice and Bob's communication security. In this Letter we report the first experimental demonstration of QI's passive-eavesdropping immunity. Aside from its relevance to secure communication, our experiment represents the first time that bosonic entanglement has yielded a strong performance benefit over an entanglement-breaking channel. Thus it implies that the use of entanglement should not be dismissed for environments in which it will be destroyed. Moreover, unlike the recent experiment [16] reporting the target-detection advantage of photon-pair correlations, our eavesdroppingimmune QI protocol requires an initial state that is entangled. Also, our communication protocol uses only one pulse to decode a bit, whereas target detection in [16] depends on the accumulation of enough data to accurately estimate a covariance.Our QI communication experiment is shown schematically in Fig. 1. Alice prepares maximally-entangled signal and i...

Increasing the dimensionality of quantum entanglement is a key enabler for high-capacity quantum communications and key distribution [1, 2], quantum computation [3] and information processing [4, 5], imaging [6], and enhanced quantum phase measurement [7,8]. A large Hilbert space can be achieved through entanglement in more than one degree of freedom (known as hyperentanglement [2,7,9]), where each degree of freedom can also be expanded to more than two dimensions (known as high-dimensional entanglement). The high-dimensional entanglement can be prepared in several physical attributes, for example, in orbital angular momentum [1,[10][11][12] and other spatial modes [13][14][15]. The drawback of these high-dimensional spatial states is complicated beam-shaping for entanglement generation and detection, which reduces the brightness of the sources as the dimension scales up, and complicates their use in optical-fiber-based communications systems. In contrast, the continuous-variable energy-time entanglement [16][17][18][19][20][21][22] is intrinsically suitable for high-dimensional coding and, if successful, can potentially be generated and be communicated in the telecommunication network. However, most studies focus on time-bin entanglement, which is discrete-variable entanglement with typical dimensionality of two [23][24][25]. Difficulties in pump-pulse shaping and phase control limit the dimensionality of the time-bin entanglement [26], and high-dimensional time-bin entanglement has not been fully characterized because of the overwhelmingly complicated analyzing interferometers. On the other hand, a biphoton state with a comb-like spectrum could potentially serve for high-dimensional entanglement generation and take full advantage of the continuous-variable energy-time subspace. Based on this state, promising applications have been proposed for quantum computing, secure wavelength-division multiplexing, and dense quantum key distribution [3,27,28]. A phase-coherent biphoton frequency comb (BFC) is also known for 3 its mode-locked behavior in its second-order correlation. Unlike classical frequency combs, where mode-locking directly relies on phase coherence over individual comb lines, the mode-locked behavior of a BFC is the representation of the phase coherence of a biphoton wavepacket over comb-line pairs, and results in periodic recurrent correlation at different time-bins [29, 30]. This time correlation feature can be characterized through quantum interference when passing the BFC through an unbalanced Hong-Ou-Mandel (HOM)-type interferometer [31]. A surprising revival of the correlation dips can be observed at time-bins with half the period of the BFC revival time.However, because of the limited type-I collinear spontaneous parametric downconversion (SPDC) configuration in the prior studies [29], post-selection was necessary for the BFC generation where the signal and idler photons are indistinguishable, limiting the maximum two-photon interference to 50 %.Here we achieve high-dimensional hyperentangle...