Practical quantum cryptography based on two-photon interferometry

Interferometry-Integrated Noise-Immune Quantum Memory

A quantum memory with the performances of low noise, high efficiency, and high bandwidth is of crucial importance for developing practical quantum information technologies. However, the excess noises generated during the highly efficient processing of quantum information inevitably destroy quantum state. Here, we present a quantum memory with built-in excess-noise eraser by integrating a photon-correlated quantum interferometry in quantum memory, where the memory efficiency can be enhanced and the excess noises can be suppressed to the vacuum level via destructive interference. This quantum memory is demonstrated in a rubidium vapor cell with a 10-ns-long photonics signal. We observe ∼80% noise suppression, the write-in efficiency enhancement from 87% to 96.2% without and with interferometry, and the corresponding memory efficiency excluding the noises from 70% to 77%. The fidelity is 93.7% at the single-photon level, significantly exceeding the no-cloning limit. Such interferometry-integrated quantum memory, the first expansion of quantum interference techniques to quantum information processing, simultaneously enables low noise, high bandwidth, high efficiency, and easy operation.

High spectro-temporal purity single-photons from silicon micro-racetrack resonators using a dual-pulse configuration

Single-photons with high spectro-temporal purity are an essential resource for quantum photonic technologies. The highest reported purity up until now from a conventional silicon photonic device is 92% without any spectral filtering. We have experimentally generated and observed single-photons with 98.0±0.3% spectro-temporal purity, an upper bound of the stimulated emission tomography, using a conventional micro-racetrack resonator and an engineered dual pump pulse.

Describing and Simulating Concurrent Quantum Systems

We present a programming language for describing and analysing concurrent quantum systems. We have an interpreter for programs in the language, using a symbolic rather than a numeric calculator, and we give its performance on examples from quantum communication and cryptography.

Efficient multiuser quantum cryptography network based on entanglement

We present an efficient quantum key distribution protocol with a certain entangled state to solve a special cryptographic task. Also, we provide a proof of security of this protocol by generalizing the proof of modified of Lo-Chau scheme. Based on this two-user scheme, a quantum cryptography network protocol is proposed without any quantum memory.

Electrically driven single photon source at high temperature

We present a theoretical model for an electrically driven single photon source operating at high temperatures. We show that decoherence, which is usually the main obstacle for operating single photon sources at high temperatures, ensures an efficient operation of the presented electrically driven single photon source at high temperatures. The single-photon source is driven by a single electron source attached to a heterostructure semiconductor nanoring. The electron's dynamics in the nanoring and the subsequent recombination with the hole is described by the generalized master equation with a Hamiltonian based on tight-binding model, taking into account the electron-LO phonon interaction. As a result of decoherence, an almost 100% single photon emission with a strong antibunching behavior i.e. g(2)(0) << 1 at high temperature up to 300 K is achieved.

General immunity and superadditivity of two-way Gaussian quantum cryptography

We consider two-way continuous-variable quantum key distribution, studying its security against general eavesdropping strategies. Assuming the asymptotic limit of many signals exchanged, we prove that two-way Gaussian protocols are immune to coherent attacks. More precisely we show the general superadditivity of the two-way security thresholds, which are proven to be higher than the corresponding one-way counterparts in all cases. We perform the security analysis first reducing the general eavesdropping to a two-mode coherent Gaussian attack, and then showing that the superadditivity is achieved by exploiting the random on/off switching of the two-way quantum communication. This allows the parties to choose the appropriate communication instances to prepare the key, accordingly to the tomography of the quantum channel. The random opening and closing of the circuit represents, in fact, an additional degree of freedom allowing the parties to convert, a posteriori, the two-mode correlations of the eavesdropping into noise. The eavesdropper is assumed to have no access to the on/off switching and, indeed, cannot adapt her attack. We explicitly prove that this mechanism enhances the security performance, no matter if the eavesdropper performs collective or coherent attacks.

Equivalence of wave-particle duality to entropic uncertainty

Interferometers capture a basic mystery of quantum mechanics: a single particle can exhibit wave behaviour, yet that wave behaviour disappears when one tries to determine the particle's path inside the interferometer. This idea has been formulated quantitatively as an inequality, for example, by Englert and Jaeger, Shimony and Vaidman, which upper bounds the sum of the interference visibility and the path distinguishability. Such wave-particle duality relations (WPDRs) are often thought to be conceptually inequivalent to Heisenberg's uncertainty principle, although this has been debated. Here we show that WPDRs correspond precisely to a modern formulation of the uncertainty principle in terms of entropies, namely, the min- and max-entropies. This observation unifies two fundamental concepts in quantum mechanics. Furthermore, it leads to a robust framework for deriving novel WPDRs by applying entropic uncertainty relations to interferometric models. As an illustration, we derive a novel relation that captures the coherence in a quantum beam splitter.

Polarization-Entangled Photon Pairs From Periodically-Poled Crystalline Waveguides Over a Range of Frequencies

We propose a method to extend the frequency range of polarization entanglement in periodically poled rubidium-doped potassium titanyl phosphate (Rb:KTP) waveguides. Our calculations predict that output wavelengths from 1130 nm to 1257 nm may be achieved using Rb:KTP by the appropriate selection of a direction of propagation for the waveguide. The fidelity using a poling period of 1 mm is approximately 0.98.

Stabilized fiber-optic Mach-Zehnder interferometer for carrier-frequency rejection

We have demonstrated stabilization of a fiber-optic Mach-Zehnder interferometer, with a centimeter-scale path difference, to the transmission minimum for the carrier wave of a frequency-modulated laser beam. A time-averaged extinction of 32 dB, limited by the bandwidth of the feedback, was maintained over several hours. The interferometer was used to remove the carrier wave from a 780 nm laser beam that had been phase modulated at 2.7 GHz.

State engineering of photon pairs produced through dual-pump spontaneous four-wave mixing

We study theoretically the joint spectral properties of photon-pairs produced through spontaneous four-wave mixing (SFWM) with two spectrally distinct pump pulses in optical fibers. We show that, due to the group velocity difference between the pulses, the signature of the interaction can be significantly different from spontaneous parametric down-conversion or SFWM with a single pump pulse. Specifically, we study the case where temporal walk-off between the pumps enables a gradual turn-on and turn-off of the interaction. By utilizing this property, we develop a new approach towards tailoring the spectral correlations within the generated photon pairs, demonstrating the ability to produce factorable photon-pair states, and hence heralded single photons in a pure wave-packet. We show that the use of two pumps is advantageous over single-pump SFWM approaches towards this goal: the usage of the dual-pump configuration enables, in principle, the creation of completely factorable states without any spectral filtering, even in media for which single-pump SFWM tailoring techniques are unsatisfactory, such as standard polarization-maintaining fiber.

Biphoton generation in quadratic waveguide arrays: a classical optical simulation

Quantum entanglement became essential in understanding the non-locality of quantum mechanics. In optics, this non-locality can be demonstrated on impressively large length scales, as photons travel with the speed of light and interact only weakly with their environment. Spontaneous parametric down-conversion (SPDC) in nonlinear crystals provides an efficient source for entangled photon pairs, so-called biphotons. However, SPDC can also be implemented in nonlinear arrays of evanescently coupled waveguides which allows the generation and the investigation of correlated quantum walks of such biphotons in an integrated device. Here, we analytically and experimentally demonstrate that the biphoton degrees of freedom are entailed in an additional dimension, therefore the SPDC and the subsequent quantum random walk in one-dimensional arrays can be simulated through classical optical beam propagation in a two-dimensional photonic lattice. Thereby, the output intensity images directly represent the biphoton correlations and exhibit a clear violation of a Bell-like inequality.

Spontaneous parametric down-conversion and quantum walks in arrays of quadratic nonlinear waveguides

We analyze the process of photon-pair generation with simultaneous quantum walks in a quadratic nonlinear waveguide array. We demonstrate that the spontaneous parametric down-conversion in the array allows for creating quantum states with strongly pronounced spatial correlations, which are qualitatively different from those possible in bulk crystals or through quantum walks in linear waveguide arrays. Most importantly, the photon correlations can be controlled entirely classically by varying the spatial profile of the pump beam or the phase-matching conditions.

Witnessing effective entanglement over a 2 km fiber channel

We present a fiber-based continuous-variable quantum key distribution system. In the scheme, a quantum signal of two non-orthogonal weak optical coherent states is sent through a fiber-based quantum channel. The receiver simultaneously measures conjugate quadratures of the light using two homodyne detectors. From the measured Q-function of the transmitted signal, we estimate the attenuation and the excess noise caused by the channel. The estimated excess noise originating from the channel and the channel attenuation including the quantum efficiency of the detection setup is investigated with respect to the detection of effective entanglement. The local oscillator is considered in the verification. We witness effective entanglement with a channel length of up to 2 km.

Narrowband high-fidelity all-fibre source of heralded single photons at 1570 nm

An all-fibre heralded single photon source operating at 1570 nm has been demonstrated. The device generates correlated photon pairs, widely spaced in frequency, through four-wave mixing in a photonic crystal fibre. Separation of the pair photons and narrowband filtering is all achieved in fibre. The output heralded single photon rate was 9.2 x 10(4) per second, with a counts-to-accidentals ratio of 10.4 and a heralding fidelity of 52 %. Furthermore, narrowband filtering ensured that the output single photon state was near time-bandwidth limited with a coherence length of 4 ps. Such a source is well suited to quantum information processing applications.

Tailored photon-pair generation in optical fibers

We experimentally control the spectral structure of photon pairs created via spontaneous four-wave mixing in microstructured fibers. By fabricating fibers with designed dispersion, one can manipulate the photons' wavelengths, joint spectrum, and, thus, entanglement. As an example, we produce photon pairs with no spectral correlations, allowing direct heralding of single photons in pure-state wave packets without filtering. We achieve an experimental purity of (85.9+/-1.6)%, while theoretical analysis and preliminary tests suggest that 94.5% purity is possible with a much longer fiber.

Generation of correlated photon pairs in a microstructure fiber

We propose and experimentally demonstrate a new method of generating correlated photons in a microstructure fiber by means of a reversed degenerate four-wave-mixing process. Here one photon is annihilated from each of the bichromatic pump pulses to generate a pair of photons at the mean frequency. For a microstructure fiber as short as 1.5 m the measured coincidence counting rate is approximately eight times that of the accidental coincidences with a peak pump power of 0.25 W.

Temporal shaping of entangled photons

We experimentally demonstrate shaping of the two-photon wave function of entangled-photon pairs, utilizing coherent pulse-shaping techniques. By performing spectral-phase manipulations we tailor the second-order correlation function of the photons exactly like a coherent ultrashort pulse. To observe the shaping we perform sum-frequency generation with an ultrahigh flux of entangled photons. At the appropriate conditions, sum-frequency generation performs as a coincidence detector with an ultrashort response time (approximately 100 fs), enabling a direct observation of the two-photon wave function. This property also enables us to demonstrate background-free, high-visibility two-photon interference oscillations.

Quantum networks

As classical information technology approaches limits of size and functionality, practitioners are searching for new paradigms for the distribution and processing of information. Our goal in this Introduction is to provide a broad view of the beginning of a new era in information technology, an era of quantum information, where previously underutilized quantum effects, such as quantum superposition and entanglement, are employed as resources for information encoding and processing. The ability to distribute these new resources and connect distant quantum systems will be critical. We present an overview of network implications for quantum communication applications, and for quantum computing. This overview is a selection of several illustrative examples, to serve as motivation for the network research community to bring its expertise to the development of quantum information technologies.

Quantum communications and beyond

We introduce the concept of encoding and manipulation of information on single photons. This is exploited in the technique of quantum cryptography to distribute random bit strings in a secure way. More general quantum information processing requires a conditional interaction between separate photons. This can be achieved by exploiting the interference between two photons at a beam-splitter and the non-linearity inherent in detection. As yet the efficiency of such gates is low.

Efficient two-photon light amplification by a coherent biexciton wave

A reversible coupling between photon pair states and a long-lived, highly coherent biexciton wave in CuCl allows efficient phase-sensitive two-photon amplification or attenuation of ultrashort light pulses. We demonstrate a gain of 350 cm(-1) for a pump intensity of 1 MW/cm(2), nearly 2 orders of magnitude higher than that achievable with conventional parametric crystal amplifiers. We develop a theoretical model that describes this new type of parametric converter where the light pump is replaced by a coherent biexciton wave and show that it is well suited for the generation of entangled photons and the squeezing of an optical beam with ultrafast time gating.

High efficiency photon counting using stored light

We propose a method that can, in principle, achieve nearly ideal photon counting, by combining the techniques of photonic quantum memory and ion-trap quantum-state measurements. After mapping the quantum state of a propagating light pulse onto metastable collective excitations of a trapped cold atomic gas, it is possible to monitor the resonance fluorescence induced by an additional laser field that couples only to the metastable excited state. Even with a photon collection/detection efficiency as low as 10%, it is possible to achieve photon counting with efficiency exceeding 99%.

Conditional-phase switch at the single-photon level

We present an experimental realization of a two-photon conditional phase switch, related to the " c-phis;" gate of quantum computation. This gate relies on quantum interference between photon pairs and generates entanglement between two optical modes through the process of spontaneous parametric down-conversion (SPDC). The interference effect serves to enhance the effective nonlinearity by many orders of magnitude, so it is significant at the quantum (single-photon) level. By adjusting the relative optical phase between the classical pump for SPDC and the pair of input modes, one can impress a large phase shift on one beam which depends on the presence or absence of a single photon in a control mode.

Counterpropagating twin photons by parametric fluorescence

An original geometry for parametric fluorescence is proposed and analyzed theoretically, in which counterpropagating twin photons are emitted in a thin waveguide. In this original down-conversion process, a dramatic decrease of the spectral signal bandwidth at degeneracy is expected, as compared to usual parametric fluorescence processes. The possibility of using the counterpropagating twin photons for quantum cryptography is emphasized. It is shown that the realization of a fibered semiconductor source of Einstein-Podolsky-Rosen photons is possible by this method.

Experimental violation of a spin-1 bell inequality using maximally entangled four-photon states

We demonstrate the experimental violation of a spin-1 Bell inequality. The spin-1 inequality is based on the Clauser, Horne, Shimony, and Holt formalism. For entangled spin-1 particles, the maximum quantum-mechanical prediction is 2.55 as opposed to a maximum of 2, predicted using local hidden variables. We obtained an experimental value of 2.27+/-0.02 using the four-photon state generated by pulsed, type-II, stimulated parametric down-conversion. This is a violation of the spin-1 Bell inequality by more than 13 standard deviations.

Stimulated emission of polarization-entangled photons

Entangled photon pairs-discrete light quanta that exhibit non-classical correlations-play a crucial role in quantum information science (for example, in demonstrations of quantum non-locality, quantum teleportation and quantum cryptography). At the macroscopic optical-field level non-classical correlations can also be important, as in the case of squeezed light, entangled light beams and teleportation of continuous quantum variables. Here we use stimulated parametric down-conversion to study entangled states of light that bridge the gap between discrete and macroscopic optical quantum correlations. We demonstrate experimentally the onset of laser-like action for entangled photons, through the creation and amplification of the spin-1/2 and spin-1 singlet states consisting of two and four photons, respectively. This entanglement structure holds great promise in quantum information science where there is a strong demand for entangled states of increasing complexity.

Mesoscopic superpositions of vibronic collective states of N trapped ions

We propose a scalable procedure to generate superpositions of motional coherent states and also entangled vibronic states in N trapped ions. Beyond their fundamental importance, these states may be of interest for quantum information processing and may be used in experimental studies on decoherence.

Generating entangled atom-photon pairs from bose-einstein condensates

We propose using spontaneous Raman scattering from an optically driven Bose-Einstein condensate as a source of atom-photon pairs whose internal states are maximally entangled. Generating entanglement between a particle which is easily transmitted (the photon) and one which is easily trapped and coherently manipulated (an ultracold atom) will prove useful for a variety of quantum-information related applications. We analyze the type of entangled states generated by spontaneous Raman scattering and construct a geometry which results in maximum entanglement.

Limitations on practical quantum cryptography

We provide limits to practical quantum key distribution, taking into account channel losses, a realistic detection process, and imperfections in the "qubits" sent from the sender to the receiver. As we show, even quantum key distribution with perfect qubits might not be achievable over long distances when the other imperfections are taken into account. Furthermore, existing experimental schemes (based on weak pulses) currently do not offer unconditional security for the reported distances and signal strength. Finally we show that parametric down-conversion offers enhanced performance compared to its weak coherent pulse counterpart.

Phase-modulation transmission system for quantum cryptography

We describe a new method for quantum key distribution that utilizes phase modulation of sidebands of modulation by use of integrated electro-optic modulators at the transmitting and receiving modules. The system is shown to produce constructive or destructive interference with unity visibility, which should allow quantum cryptography to be carried out with high flexibility by use of conventional devices.

Photon counting with passively quenched germanium avalanche

We demonstrate photon counting in germanium avalanche photodiodes biased beyond breakdown and quenched with a simple series resistance circuit. The devices show moderate (> 7%) quantum efficiency with limited afterpulsing and dark counts and subnanosecond jitter.

Quantum cryptography using optical fibers

Quantum cryptography permits the transmission of secret information whose security is guaranteed by the uncertainty principle. An experimental system for quantum crytography is implemented based on the linear polarization of single photons transmitted by an optical fiber. Polarization-preserving optical fiber and a feedback loop are employed to maintain the state of polarization. Error rates of less than 0.5% are obtained.