Long distance quantum teleportation in a quantum relay configuration

Telecom-band quantum dot technologies for long-distance quantum networks

A future quantum internet is expected to generate, distribute, store and process quantum bits (qubits) over the world by linking different quantum nodes via quantum states of light. To facilitate long-haul operations, quantum repeaters must operate at telecom wavelengths to take advantage of both the low-loss optical fibre network and the established technologies of modern optical communications. Semiconductor quantum dots have thus far shown exceptional performance as key elements for quantum repeaters, such as quantum light sources and spin-photon interfaces, but only in the near-infrared regime. Therefore, the development of high-performance telecom-band quantum dot devices is highly desirable for a future solid-state quantum internet based on fibre networks. In this Review, we present the physics and technological developments towards epitaxial quantum dot devices emitting in the telecom O- and C-bands for quantum networks, considering both advanced epitaxial growth for direct telecom emission and quantum frequency conversion for telecom-band down-conversion of near-infrared quantum dot devices. We also discuss the challenges and opportunities for future realization of telecom quantum dot devices with improved performance and expanded functionality through hybrid integration.

Culling a Self-Assembled Quantum Dot as a Single-Photon Source Using X-ray Microscopy

Epitaxially grown self-assembled semiconductor quantum dots (QDs) with atom-like optical properties have emerged as the best choice for single-photon sources required for the development of quantum technology and quantum networks. Nondestructive selection of a single QD having desired structural, compositional, and optical characteristics is essential to obtain noise-free, fully indistinguishable single or entangled photons from single-photon emitters. Here, we show that the structural orientations and local compositional inhomogeneities within a single QD and the surrounding wet layer can be probed in a screening fashion by scanning X-ray diffraction microscopy and X-ray fluorescence with a few tens of nanometers-sized synchrotron radiation beam. The presented measurement protocol can be used to cull the best single QD from the enormous number of self-assembled dots grown simultaneously. The obtained results show that the elemental composition and resultant strain profiles of a QD are sensitive to in-plane crystallographic directions. We also observe that lattice expansion after a certain composition-limit introduces shear strain within a QD, enabling the possibility of controlled chiral-QD formation. Nanoscale chirality and compositional anisotropy, contradictory to common assumptions, need to be incorporated into existing theoretical models to predict the optical properties of single-photon sources and to further tune the epitaxial growth process of self-assembled quantum structures.

Hertz-rate metropolitan quantum teleportation

Quantum teleportation can transfer an unknown quantum state between distant quantum nodes, which holds great promise in enabling large-scale quantum networks. To advance the full potential of quantum teleportation, quantum states must be faithfully transferred at a high rate over long distance. Despite recent impressive advances, a high-rate quantum teleportation system across metropolitan fiber networks is extremely desired. Here, we demonstrate a quantum teleportation system which transfers quantum states carried by independent photons at a rate of 7.1 ± 0.4 Hz over 64-km-long fiber channel. An average single-photon fidelity of ≥90.6 ± 2.6% is achieved, which exceeds the maximum fidelity of 2/3 in classical regime. Our result marks an important milestone towards quantum networks and opens the door to exploring quantum entanglement based informatic applications for the future quantum internet.

Long distance multiplexed quantum teleportation from a telecom photon to a solid-state qubit

Quantum teleportation is an essential capability for quantum networks, allowing the transmission of quantum bits (qubits) without a direct exchange of quantum information. Its implementation between distant parties requires teleportation of the quantum information to matter qubits that store it for long enough to allow users to perform further processing. Here we demonstrate long distance quantum teleportation from a photonic qubit at telecom wavelength to a matter qubit, stored as a collective excitation in a solid-state quantum memory. Our system encompasses an active feed-forward scheme, implementing a conditional phase shift on the qubit retrieved from the memory, as required by the protocol. Moreover, our approach is time-multiplexed, allowing for an increase in the teleportation rate, and is directly compatible with the deployed telecommunication networks, two key features for its scalability and practical implementation, that will play a pivotal role in the development of long-distance quantum communication.

Quantum State Transfer over 1200 km Assisted by Prior Distributed Entanglement

Long-distance quantum state transfer (QST), which can be achieved with the help of quantum teleportation, is a core element of important quantum protocols. A typical situation for QST based on teleportation is one in which two remote communication partners (Alice and Bob) are far from the entanglement source (Charlie). Because of the atmospheric turbulence, it is challenging to implement the Bell-state measurement after photons propagate in atmospheric channels. In previous long-distance free-space experiments, Alice and Charlie always perform local Bell-state measurement before the entanglement distribution process is completed. Here, by developing a highly stable interferometer to project the photon into a hybrid path-polarization dimension and utilizing the satellite-borne entangled photon source, we demonstrate proof-of-principle QST at the distance of over 1200 km assisted by prior quantum entanglement shared between two distant ground stations with the satellite Micius. The average fidelity of transferred six distinct quantum states is 0.82±0.01, exceeding the classical limit of 2/3 on a single copy of a qubit.

Shared Quantum Key Distribution Based on Asymmetric Double Quantum Teleportation

Quantum cryptography is a well-stated field within quantum applications where quantum information is used to set secure communications, authentication, and secret keys. Now used in quantum devices with those purposes, particularly Quantum Key Distribution (QKD), which proposes a secret key between two parties free of effective eavesdropping, at least at a higher level than classical cryptography. The best-known quantum protocol to securely share a secret key is the BB84 one. Other protocols have been proposed as adaptations of it. Most of them are based on the quantum indeterminacy for non-orthogonal quantum states. Their security is commonly based on the large length of the key. In the current work, a BB84-like procedure for QKD based on double quantum teleportation allows the sharing of the key statement using several parties. Thus, the quantum bits of information are assembled among three parties via entanglement, instead of travelling through a unique quantum channel as in the traditional protocol. Asymmetry in the double teleportation plus post-measurement retains the secrecy in the process. Despite requiring more complex control and resources, the procedure dramatically reduces the probability of success for an eavesdropper under individual attacks, because of the ignorance of the processing times in the procedure. Quantum Bit Error Rate remains in the acceptable threshold and it becomes configurable. The article depicts the double quantum teleportation procedure, the associated control to introduce the QKD scheme, the analysis of individual attacks performed by an eavesdropper, and a brief comparison with other protocols.

Near perfect two-photon interference out of a down-converter on a silicon photonic chip

Integrated entangled photon-pair sources are key elements for enabling large-scale quantum photonic solutions and address the challenges of both scaling-up and stability. Here we report the first demonstration of an energy-time entangled photon-pair source based on spontaneous parametric down-conversion in silicon-based platform-stoichiometric silicon nitride (Si₃N₄)-through an optically induced second-order (χ⁽²⁾) nonlinearity, ensuring type-0 quasi-phase-matching of fundamental harmonic and its second-harmonic inside the waveguide. The developed source shows a coincidence-to-accidental ratio of 1635 for 8 µW pump power. We report two-photon interference with remarkable near-perfect visibility of 99.36±1.94%, showing high-quality photonic entanglement without excess background noise. This opens a new horizon for quantum technologies requiring the integration of a large variety of building functionalities on a single chip.

Catalytic Quantum Teleportation

In this work, we address fundamental limitations of quantum teleportation-the process of transferring quantum information using classical communication and preshared entanglement. We develop a new teleportation protocol based upon the idea of using ancillary entanglement catalytically, i.e., without depleting it. This protocol is then used to show that catalytic entanglement allows for a noiseless quantum channel to be simulated with a quality that could never be achieved using only entanglement from the shared state, even for catalysts with a small dimension. On the one hand, this allows for a more faithful transmission of quantum information using generic states and fixed amount of consumed entanglement. On the other hand, this shows, for the first time, that entanglement catalysis provides a genuine advantage in a generic quantum-information processing task. Finally, we show that similar ideas can be directly applied to study quantum catalysis for more general problems in quantum mechanics. As an application, we show that catalysts can activate so-called passive states, a concept that finds widespread application, e.g., in quantum thermodynamics.

Coherent Dynamics in Quantum Emitters under Dichromatic Excitation

We characterize the coherent dynamics of a two-level quantum emitter driven by a pair of symmetrically detuned phase-locked pulses. The promise of dichromatic excitation is to spectrally isolate the excitation laser from the quantum emission, enabling background-free photon extraction from the emitter. While excitation is not possible without spectral overlap between the exciting pulse and the quantum emitter transition for ideal two-level systems due to cancellation of the accumulated pulse area, we find that any additional interactions that interfere with cancellation of the accumulated pulse area may lead to a finite stationary population inversion. Our spectroscopic results of a solid-state two-level system show that, while coupling to lattice vibrations helps to improve the inversion efficiency up to 50% under symmetric driving, coherent population control and a larger amount of inversion are possible using asymmetric dichromatic excitation, which we achieve by adjusting the ratio of the intensities between the red- and blue-detuned pulses. Our measured results, supported by simulations using a real-time path-integral method, offer a new perspective toward realizing efficient, background-free photon generation and extraction.

1GHz clocked distribution of electrically generated entangled photon pairs

Quantum networks are essential for realising distributed quantum computation and quantum communication. Entangled photons are a key resource, with applications such as quantum key distribution, quantum relays, and quantum repeaters. All components integrated in a quantum network must be synchronised and therefore comply with a certain clock frequency. In quantum key distribution, the most mature technology, clock rates have reached and exceeded 1GHz. Here we show the first electrically pulsed sub-Poissonian entangled photon source compatible with existing fiber networks operating at this clock rate. The entangled LED is based on InAs/InP quantum dots emitting in the main telecom window, with a multi-photon probability of less than 10% per emission cycle and a maximum entanglement fidelity of 89%. We use this device to demonstrate GHz clocked distribution of entangled qubits over an installed fiber network between two points 4.6km apart.

Twenty Years of Quantum State Teleportation at the Sapienza University in Rome

Quantum teleportation is one of the most striking consequence of quantum mechanics and is defined as the transmission and reconstruction of an unknown quantum state over arbitrary distances. This concept was introduced for the first time in 1993 by Charles Bennett and coworkers, it has then been experimentally demonstrated by several groups under different conditions of distance, amount of particles and even with feed forward. After 20 years from its first realization, this contribution reviews the experimental implementations realized at the Quantum Optics Group of the University of Rome La Sapienza.

Photonic quantum information processing: a review

Photonic quantum technologies represent a promising platform for several applications, ranging from long-distance communications to the simulation of complex phenomena. Indeed, the advantages offered by single photons do make them the candidate of choice for carrying quantum information in a broad variety of areas with a versatile approach. Furthermore, recent technological advances are now enabling first concrete applications of photonic quantum information processing. The goal of this manuscript is to provide the reader with a comprehensive review of the state of the art in this active field, with a due balance between theoretical, experimental and technological results. When more convenient, we will present significant achievements in tables or in schematic figures, in order to convey a global perspective of the several horizons that fall under the name of photonic quantum information.

All-photonic quantum teleportation using on-demand solid-state quantum emitters

All-optical quantum teleportation lies at the heart of quantum communication science and technology. This quantum phenomenon is built up around the nonlocal properties of entangled states of light that, in the perspective of real-life applications, should be encoded on photon pairs generated on demand. Despite recent advances, however, the exploitation of deterministic quantum light sources in push-button quantum teleportation schemes remains a major open challenge. Here, we perform an important step toward this goal and show that photon pairs generated on demand by a GaAs quantum dot can be used to implement a teleportation protocol whose fidelity violates the classical limit (by more than 5 SDs) for arbitrary input states. Moreover, we develop a theoretical framework that matches the experimental observations and that defines the degree of entanglement and indistinguishability needed to overcome the classical limit independently of the input state. Our results emphasize that on-demand solid-state quantum emitters are one of the most promising candidates to realize deterministic quantum teleportation in practical quantum networks.

Experimental Study of Nonclassical Teleportation Beyond Average Fidelity

Quantum teleportation establishes a correspondence between an entangled state shared by two separate parties that can communicate classically and the presence of a quantum channel connecting the two parties. The standard benchmark for quantum teleportation, based on the average fidelity between the input and output states, indicates that some entangled states do not lead to channels which can be certified to be quantum. It was recently shown that if one considers a finer-grained witness, then all entangled states can be certified to produce a nonclassical teleportation channel. Here we experimentally demonstrate a complete characterization of a new family of such witnesses, of the type proposed in Phys. Rev. Lett. 119, 110501 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.110501 under different conditions of noise. We report nonclassical teleportation using quantum states that cannot achieve average fidelity of teleportation above the classical limit. We further use the violation of these witnesses to estimate the negativity of the shared state. Our results have fundamental implications in quantum information protocols and may also lead to new applications and quality certification of quantum technologies.

Electric-Field-Induced Energy Tuning of On-Demand Entangled-Photon Emission from Self-Assembled Quantum Dots

We explore a method to achieve electrical control over the energy of on-demand entangled-photon emission from self-assembled quantum dots (QDs). The device used in our work consists of an electrically tunable diode-like membrane integrated onto a piezoactuator, which is capable of exerting a uniaxial stress on QDs. We theoretically reveal that, through application of the quantum-confined Stark effect to QDs by a vertical electric field, the critical uniaxial stress used to eliminate the fine structure splitting of QDs can be linearly tuned. This feature allows experimental realization of a triggered source of energy-tunable entangled-photon emission. Our demonstration represents an important step toward realization of a solid-state quantum repeater using indistinguishable entangled photons in Bell state measurements.

Subnatural-linewidth biphotons from a Doppler-broadened hot atomic vapour cell

Entangled photon pairs, termed as biphotons, have been the benchmark tool for experimental quantum optics. The quantum-network protocols based on photon-atom interfaces have stimulated a great demand for single photons with bandwidth comparable to or narrower than the atomic natural linewidth. In the past decade, laser-cooled atoms have often been used for producing such biphotons, but the apparatus is too large and complicated for engineering. Here we report the generation of subnatural-linewidth (<6 MHz) biphotons from a Doppler-broadened (530 MHz) hot atomic vapour cell. We use on-resonance spontaneous four-wave mixing in a hot paraffin-coated ⁸⁷Rb vapour cell at 63 °C to produce biphotons with controllable bandwidth (1.9-3.2 MHz) and coherence time (47-94 ns). Our backward phase-matching scheme with spatially separated optical pumping is the key to suppress uncorrelated photons from resonance fluorescence. The result may lead towards miniature narrowband biphoton sources.

Active stabilization of a fiber-optic two-photon interferometer using continuous optical length control

The practical realization of long-distance entanglement-based quantum communication systems strongly rely on the observation of highly stable quantum interference between correlated single photons. This task must accompany active stabilization of the optical path lengths within the single-photon coherence length. Here, we provide two-step interferometer stabilization methods employing continuous optical length control and experimentally demonstrate two-photon quantum interference using an actively stabilized 6-km-long fiber-optic Hong-Ou-Mandel interferometer. The two-step active control techniques are applied for measuring highly stable two-photon interference fringes by scanning the optical path-length difference. The obtained two-photon interference visibilities with and without accidental subtraction are found to be approximately 90.7% and 65.4%, respectively.

Energy-tunable sources of entangled photons: a viable concept for solid-state-based quantum relays

We propose a new method of generating triggered entangled photon pairs with wavelength on demand. The method uses a microstructured semiconductor-piezoelectric device capable of dynamically reshaping the electronic properties of self-assembled quantum dots (QDs) via anisotropic strain engineering. Theoretical models based on k·p theory in combination with finite-element calculations show that the energy of the polarization-entangled photons emitted by QDs can be tuned in a range larger than 100 meV without affecting the degree of entanglement of the quantum source. These results pave the way towards the deterministic implementation of QD entanglement resources in all-electrically-controlled solid-state-based quantum relays.

All-photonic quantum repeaters

Quantum communication holds promise for unconditionally secure transmission of secret messages and faithful transfer of unknown quantum states. Photons appear to be the medium of choice for quantum communication. Owing to photon losses, robust quantum communication over long lossy channels requires quantum repeaters. It is widely believed that a necessary and highly demanding requirement for quantum repeaters is the existence of matter quantum memories. Here we show that such a requirement is, in fact, unnecessary by introducing the concept of all-photonic quantum repeaters based on flying qubits. In particular, we present a protocol based on photonic cluster-state machine guns and a loss-tolerant measurement equipped with local high-speed active feedforwards. We show that, with such all-photonic quantum repeaters, the communication efficiency scales polynomially with the channel distance. Our result paves a new route towards quantum repeaters with efficient single-photon sources rather than matter quantum memories.

Quantum repeaters are needed for long-distance quantum communication but it is thought that they require matter quantum memories. Azuma et al. introduce an all-photonic quantum repeater based on flying qubits that scales polynomially with the channel distance without the need for matter quantum memories.

Coherent dynamics of a telecom-wavelength entangled photon source

Quantum networks can interconnect remote quantum information processors, allowing interaction between different architectures and increasing net computational power. Fibre-optic telecommunications technology offers a practical platform for routing weakly interacting photonic qubits, allowing quantum correlations and entanglement to be established between distant nodes. Although entangled photons have been produced at telecommunications wavelengths using spontaneous parametric downconversion in nonlinear media, as system complexity increases their inherent excess photon generation will become limiting. Here we demonstrate entangled photon pair generation from a semiconductor quantum dot at a telecommunications wavelength. Emitted photons are intrinsically anti-bunched and violate Bell's inequality by 17 standard deviations High-visibility oscillations of the biphoton polarization reveal the time evolution of the emitted state with exceptional clarity, exposing long coherence times. Furthermore, we introduce a method to evaluate the fidelity to a time-evolving Bell state, revealing entanglement between photons emitted up to 5 ns apart, exceeding the exciton lifetime.

Time-bin entangled photons from a quantum dot

Long-distance quantum communication is one of the prime goals in the field of quantum information science. With information encoded in the quantum state of photons, existing telecommunication fibre networks can be effectively used as a transport medium. To achieve this goal, a source of robust entangled single-photon pairs is required. Here we report the realization of a source of time-bin entangled photon pairs utilizing the biexciton-exciton cascade in a III/V self-assembled quantum dot. We analyse the generated photon pairs by an inherently phase-stable interferometry technique, facilitating uninterrupted long integration times. We confirm the entanglement by performing quantum state tomography of the emitted photons, which yields a fidelity of 0.69(3) and a concurrence of 0.41(6) for our realization of time-energy entanglement from a single quantum emitter.

Long-distance practical quantum key distribution by entanglement swapping

We develop a model for practical, entanglement-based long-distance quantum key distribution employing entanglement swapping as a key building block. Relying only on existing off-the-shelf technology, we show how to optimize resources so as to maximize secret key distribution rates. The tools comprise lossy transmission links, such as telecom optical fibers or free space, parametric down-conversion sources of entangled photon pairs, and threshold detectors that are inefficient and have dark counts. Our analysis provides the optimal trade-off between detector efficiency and dark counts, which are usually competing, as well as the optimal source brightness that maximizes the secret key rate for specified distances (i.e. loss) between sender and receiver.

Hong-Ou-Mandel dip measurements of polarization-entangled photon pairs at 1550 nm

We performed a quantum interference experiment using two polarization-entangled photon pairs at 1550 nm, created in periodically poled lithium niobate waveguides. Using four-fold coincidences, a Hong-Ou-Mandel dip at diagonal polarization was observed with a visibility of 74.5% before subtracting accidental coincidences. This experiment lays a foundation for demonstrating polarization-based entanglement swapping and for realizing a quantum relay.

Stabilization of a long-armed fiber-optic single-photon interferometer

We report on single-photon interference experiments in a Michelson-type interferometer built with two 6-km-long fiber spools, as well as on the active stabilization of the interferometer. A weak coherent light signal was (de-) multiplexed with a strong reference light using wavelength-division multiplexing technique, and real-time feedback control technique was applied for the reference light to actively stabilize the phase fluctuation in the long-armed fiber interferometer. The stabilized interferometer showed phase stability of 0.06 rad, which corresponds to an optical path length fluctuation of 15 nm between the 6-km-long interfering arms. The raw visibility obtained without subtracting noise counts in the single-photon interference experiment was more than 98% for stabilized conditions.

Integrated optical source of polarization entangled photons at 1310 nm

We report the realization of a new polarization entangled photon-pair source based on a titanium-indiffused waveguide integrated on periodically poled lithium niobate pumped by a CW laser at 655 nm. The paired photons are emitted at the telecom wavelength of 1310 nm within a bandwidth of 0.7 nm. The quantum properties of the pairs are measured using a two-photon coalescence experiment showing a visibility of 85%. The evaluated source brightness, on the order of 10(5) pairs s(-1)GHz(-1)mW(-1), associated with its compactness and reliability, demonstrates the source's high potential for long-distance quantum communication.

Subnatural linewidth biphotons with controllable temporal length

This Letter describes the generation of biphotons with a temporal length that can be varied over the range of 50-900 ns, with an estimated subnatural linewidth as small as 0.75 MHz. We make use of electromagnetically induced transparency and slow light in a two-dimensional magneto-optical trap with an optical depth as high as 62. We report a sharp leading edge spike that is a Sommerfeld-Brillouin precursor, as observed at the biphoton level.

Quantum teleportation between light and matter

Quantum teleportation is an important ingredient in distributed quantum networks, and can also serve as an elementary operation in quantum computers. Teleportation was first demonstrated as a transfer of a quantum state of light onto another light beam; later developments used optical relays and demonstrated entanglement swapping for continuous variables. The teleportation of a quantum state between two single material particles (trapped ions) has now also been achieved. Here we demonstrate teleportation between objects of a different nature--light and matter, which respectively represent 'flying' and 'stationary' media. A quantum state encoded in a light pulse is teleported onto a macroscopic object (an atomic ensemble containing 10 caesium atoms). Deterministic teleportation is achieved for sets of coherent states with mean photon number (n) up to a few hundred. The fidelities are 0.58 +/- 0.02 for n = 20 and 0.60 +/- 0.02 for n = 5--higher than any classical state transfer can possibly achieve. Besides being of fundamental interest, teleportation using a macroscopic atomic ensemble is relevant for the practical implementation of a quantum repeater. An important factor for the implementation of quantum networks is the teleportation distance between transmitter and receiver; this is 0.5 metres in the present experiment. As our experiment uses propagating light to achieve the entanglement of light and atoms required for teleportation, the present approach should be scalable to longer distances.

Synchronization of mode-locked femtosecond lasers through a fiber link

Two mode-locked femtosecond fiber lasers, connected via a 7 km fiber link, are synchronized to an rms timing jitter of 19 fs, observed over the entire Nyquist bandwidth (half of the 93 MHz repetition frequency). This result is achieved in two steps. First, active cancellation of the fiber-transmission noise reduces timing jitter caused by path length fluctuations to a record level of 16 fs. Second, using a wide bandwidth interactivity actuator, the slave laser is synchronized to the incoming stable pulse train from the reference laser to within 10 fs. These results are confirmed by an optical cross-correlation measurement performed independently of the feedback loop operated in the microwave domain.

Experimental quantum error rejection for quantum communication

We report an experimental demonstration of a bit-flip error-rejection protocol for error-reduced transfer of quantum information through a noisy quantum channel. In the experiment, an unknown state to be transmitted is encoded into a two-photon entangled state, which is then sent through an engineered noisy quantum channel. At the final stage, the unknown state is decoded by a parity measurement, successfully rejecting the erroneous transmission over the noisy quantum channel.

Remote preparation of arbitrary time-encoded single-photon ebits

We propose and experimentally verify a novel method for the remote preparation of entangled bits (ebits) made of a single photon coherently delocalized in two well-separated temporal modes. The proposed scheme represents a remotely tunable source for tailoring arbitrary ebits, whether maximally or nonmaximally entangled, which is highly desirable for applications in quantum information technology. The remotely prepared ebit is studied by performing homodyne tomography with an ultrafast balanced homodyne detection scheme recently developed in our laboratory.

Experimental free-space distribution of entangled photon pairs over 13 km: towards satellite-based global quantum communication

We report free-space distribution of entangled photon pairs over a noisy ground atmosphere of 13 km. It is shown that the desired entanglement can still survive after both entangled photons have passed through the noisy ground atmosphere with a distance beyond the effective thickness of the aerosphere. This is confirmed by observing a spacelike separated violation of Bell inequality of 2.45+/-0.09. On this basis, we exploit the distributed entangled photon source to demonstrate the Bennett-Brassard 1984 quantum cryptography scheme. The distribution distance of entangled photon pairs achieved in the experiment is for the first time well beyond the effective thickness of the aerosphere, hence presenting a significant step towards satellite-based global quantum communication.

Creating single time-bin-entangled photon pairs

When a single emitter is excited by two phase-coherent pulses with a time delay, each of the pulses can lead to the emission of a photon pair, thus creating a "time-bin-entangled" state. Double pair emission can be avoided by initially preparing the emitter in a metastable state. We show how photons from separate emissions can be made indistinguishable, permitting their use for multiphoton interference. Possible realizations are discussed. The method might also allow the direct creation of n-photon entangled states (n > 2).