We propose a high-dimensional quantum key distribution (QKD) protocol that employs temporal correlations of entangled photons. The security of the protocol relies on measurements by Alice and Bob in one of two conjugate bases, implemented using dispersive optics. We show that this dispersion-based approach is secure against general coherent attacks. The protocol is additionally compatible with standard fiber telecommunications channels and wavelength division multiplexers. We offer multiple implementations to enhance the transmission rate and describe a heralded qudit source that is easy to implement and enables secret-key generation at up to 100 Mbps at over 2 bits per photon.Comment: 5 pages, 3 figures. v2 contains details of security analysis previously left to Supplemental Information (not included in v1

Quantum metrology utilizes nonclassical resources, such as entanglement or squeezed light, to realize sensors whose performance exceeds that afforded by classical-state systems. Environmental loss and noise, however, easily destroy nonclassical resources and, thus, nullify the performance advantages of most quantum-enhanced sensors. Quantum illumination (QI) is different. It is a robust entanglement-enhanced sensing scheme whose 6 dB performance advantage over a coherent-state sensor of the same average transmitted photon number survives the initial entanglement's eradication by loss and noise. Unfortunately, an implementation of the optimum quantum receiver that would reap QI's full performance advantage has remained elusive, owing to its having to deal with a huge number of very noisy optical modes. We show how sum-frequency generation (SFG) can be fruitfully applied to optimum multimode Gaussian-mixedstate discrimination. Applied to QI, our analysis and numerical evaluations demonstrate that our SFG receiver saturates QI's quantum Chernoff bound. Moreover, augmenting our SFG receiver with a feedforward (FF) mechanism pushes its performance to the Helstrom bound in the limit of low signal brightness. The FF-SFG receiver, thus, opens the door to optimum quantum-enhanced imaging, radar detection, state and channel tomography, and communication in practical Gaussian-state situations. DOI: 10.1103/PhysRevLett.118.040801 Introduction.-Entanglement is essential for deviceindependent quantum cryptography [1], quantum computing [2], and quantum-enhanced metrology [3]. It has also been employed in frequency and phase estimation to beat their standard quantum limits on measurement precision [4][5][6][7][8][9][10]. Furthermore, entanglement has applications across diverse research areas, including dynamic biological measurement [11], delicate material probing [12], gravitational wave detection [13], and quantum lithography [14]. Entanglement, however, is fragile; it is easily destroyed by quantum decoherence arising from environmental loss and noise. Consequently, the entanglement-enabled performance advantages of most quantum-enhanced sensing schemes quickly dissipate with increasing quantum decoherence, challenging their merits for practical situations.Quantum illumination (QI) is an entanglement-enhanced paradigm for target detection that thrives on entanglementbreaking loss and noise [15][16][17][18][19][20][21][22]. Its optimum quantum receiver enjoys a 6 dB advantage in error-probability exponent over optimum classical sensing using the same transmitted photon number. Remarkably, QI's advantage occurs despite the initial entanglement being completely destroyed.To date, the only in-principle realization of QI's optimum quantum receiver requires a Schur transform on a quantum computer [23], so that its physical implementation is unlikely to occur in the near future. At present, the best known suboptimum QI receivers [20,21]-one of which, the optical parametric amplifier (OPA) receiver, has been

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...

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.

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...