Three-photon States Research Articles

Photonic Source of Heralded Greenberger-Horne-Zeilinger States.

Generating large multiphoton entangled states is of main interest due to enabling universal photonic quantum computing and all-optical quantum repeater nodes. These applications exploit measurement-based quantum computation using cluster states. Remarkably, it was shown that photonic cluster states of arbitrary size can be generated by using feasible heralded linear optics fusion gates that act on heralded three-photon Greenberger-Horne-Zeilinger (GHZ) states as the initial resource state. Thus, the capability of generating heralded GHZ states is of great importance for scaling up photonic quantum computing. Here, we experimentally demonstrate this required building block by reporting a polarisation-encoded heralded GHZ state of three photons, for which we build a high-rate six-photon source (547±2 Hz) from a solid-state quantum emitter and a stable polarization-based interferometer. The detection of three ancillary photons heralds the generation of three-photon GHZ states among the remaining particles with fidelities up to F=0.7278±0.0106. Our results initiate a path for scalable entangling operations using heralded linear-optics implementations.

Generation of five-photon hyperentangled cluster state with three-photon GHZ state and Bell state via weak cross-Kerr nonlinearity

Generation of five-photon hyperentangled cluster state with three-photon GHZ state and Bell state via weak cross-Kerr nonlinearity

Complete conversion of KLM entanglement to GHZ entanglement with error-detected quantum devices

Quantum entanglement plays a crucial role in quantum information technologies. In the paper, we propose two schemes to convert from two-photon Knill–Laflamme–Milburn (KLM) entangled states to Bell states and three-photon KLM state to Greenberger–Horne–Zeilinger states based on error-detected quantum devices (EDQDs), which employ the interaction between a quantum-dot-cavity system and a photon. Moreover, the quantum circuits of EDQDs applied in the conversion processes make our schemes carry out faithfully, as the practical photon-scattering deviations are changed into heralded-failure detections. Analyses show that conversion cases have unity fidelities and high efficiencies, which encourage us to appreciate deeply fundamental properties of entanglement.

Proposal for the complete high-dimensional Greenberger–Horne–Zeilinger state measurement

Abstract A theoretical proposal for the complete analysis of high-dimensional Greenberger–Horne–Zeilinger (GHZ) state is presented in this Letter. We first demonstrate the approach for the complete three-photon GHZ state measurement in three dimensions, and then generalize it to the situation of N-photon system in d dimensions. In our approach, the photonic hyperentanglement and quantum Fourier transform are both utilized. The presented proposal will be useful for the high-dimensional multi-photon quantum computation and quantum communication.

Resource-saving quantum key distribution based on three-photon matrix product states

Resource-saving quantum key distribution based on three-photon matrix product states

Amplification of cascaded down-conversion by reusing photons with a switchable cavity

The ability to efficiently produce and manipulate nonclassical states of light is a critical requirement for the development of quantum optical technologies. In recent years, experiments have demonstrated that cascaded spontaneous parametric down-conversion is a promising approach to implement photon precertification, providing a way to overcome photon transmission losses for quantum communication, as well as to directly produce entangled three-photon states and heralded Bell pairs. However, the low efficiency of this process has so far limited its applicability beyond basic experiments. Here, we propose a scheme to amplify triplet production rates by using a fast switch and a delay loop to reuse photons that fail to convert on the first pass through the cascade's second nonlinear crystal. We construct a theoretical model to predict amplification rates and verify them in an experimental implementation. Our proof-of-concept device increases the rate of detected photon triplets as predicted, demonstrating that the method has the potential to dramatically improve the usefulness of cascaded down-conversion for device-independent quantum communication and entangled state generation.

Demonstrating quantum properties of triple photons generated by chi ^3 processes

Triple-photon generation (TPG) is based on a third-order nonlinear optical interaction, which is the most direct way to produce pure quantum three-photon states. These states can exhibit three-body quantum correlations, and their statistics cannot be reproduced by any Gaussian statistics of coherent sources or optical parametric twin-photon generator, making them potentially useful for quantum information processing tasks such as quantum state distillation, quantum error-correction and universal quantum computing. Furthermore, the generation of entangled photon pairs heralded by the detection of a third photon can be used in advanced quantum communication protocols. We made the first experimental demonstration of TPG in 2004 using a bi-stimulation scheme in a bulk KTP crystal, followed by the quantum theory. The new challenges are now to achieve a spontaneous TPG and the corresponding quantum experiments and protocols using oriented ridge KTP waveguides, which ensures both birefringence phase-matching and light confinement. The waveguides are cut by a precision dicing saw. We recently performed their characterization using third-harmonic generation measurements, which showed their good quality. A rate of about 5 triplets per second is expected when pumping a 5-cm-long waveguide with a 5-W 532 nm beam in the CW regime. Such a spontaneous TPG exhibits low rate of triple photons, which makes the certification of quantum features hard. In this article, we review our theoretical and experimental work on TPG and the associated quantum modeling. We also develop theoretical tools for the certification of quantum features of spontaneous triple-photon states.Graphic abstract

Joint remote implementation of operators

We propose a deterministic protocol for three distant parties to cooperate so that two parties can implement their secret unitary operators on the third party’s secret quantum state via shared quantum channel assisted by cross-Kerr nonlinearities. The operators are of general form while the state may be encoded either in spatial degree of freedom or polarization degree of freedom. The quantum channel is served by a three-photon hyperentangled state establishing the minimum of consumed photon number for this type of task. This protocol can be named joint remote implementation of operators which is necessary for distributed quantum tasks throughout a quantum network.

All-Photonic Architecture for Scalable Quantum Computing with Greenberger-Horne-Zeilinger States

Linear optical quantum computing is beset by the lack of deterministic entangling operations besides photon loss. Motivated by advancements at the experimental front in deterministic generation of various kinds of multiphoton entangled states, we propose an architecture for linear-optical quantum computing that harnesses the availability of three-photon Greenberger-Horne-Zeilinger (GHZ) states. Our architecture and its subvariants use polarized photons in GHZ states, polarization beam splitters, delay lines, optical switches and on-off detectors. We concatenate topological quantum error correction code with three-qubit repetition codes and estimate that our architecture can tolerate remarkably high photon-loss rate of $11.5 \%$; this makes a drastic change that is at least an order higher than those of known proposals. Further, considering three-photon GHZ states as resources, we estimate the resource overheads to perform gate operations with an accuracy of $10^{-6}~(10^{-15})$ to be $2.0\times10^6~(5.6\times10^7)$. Compared to other all-photonic schemes, our architecture is also resource-efficient. In addition, the resource overhead can be even further improved if larger GHZ states are available. Given its striking enhancement in the photon loss threshold and the recent progress in generating multiphoton entanglement, our scheme will make scalable photonic quantum computing a step closer to reality.

Entangled photons from composite cascade emitters.

One of the most versatile sources for entangled photons are emitters that interact via more than one tunable mechanism. Here, we demonstrate how hybridization and dipole-dipole interactions-potentially simultaneously available in colloidal quantum dots and molecular aggregates-leveraged in conjunction can couple simple, well understood emitters into composite emitters with flexible control over the level structure. We show that cascade decay through carefully designed level structures can result in emission of frequency-entangled photons with Bell states and three-photon GHZ states as example cases. These results pave the way toward rational design of quantum optical emitters of entangled photons.

Classification of three-photon states in waveguide quantum electrodynamics

We provide the first classification of three-photon eigenstates in a finite periodic array of two-level atoms coupled to a waveguide. We focus on the strongly subwavelength limit and show the hierarchical structure of the eigenstates in the complex plane. The main characteristic eigenstates are explored using entanglement entropy as a distinguishing feature. We show that the rich interplay of effects from order, chaos to localisation found in two-photon systems extends naturally to three-photon systems. There also exist interaction-induced localised states unique to three-photon systems such as bound trimers, corner states and trimer edge states.

Joint remote preparation of single-photon three-qubit state with hyperentangled state via linear-optical elements

Transmitting quantum states securely and efficiently is an important task in quantum communication. In this article, we investigate the protocols for joint remote preparation of arbitrary three-qubit states with three-photon hyperentangled states simultaneously entangled in three degrees of freedom. First, we propose a protocol for deterministic joint remote preparation of a three-qubit state via a hyperentangled state simultaneously entangled in three degrees of freedom based on quantum state initialization. Second, we present a scheme for recursive joint remote preparation of the state via partially hyperentangled state, resorting to linear-optical elements only. The protocol has the advantage of having high channel capacity for joint remote preparing an arbitrary three-qubit state via hyperentangled state. Moreover, it is more convenient in application since it only requires linear-optical elements for joint remote preparation of arbitrary three-qubit state.

Entanglement teleportation with photons from quantum dots: towards a solid-state based quantum network

Semiconductor quantum dots are currently emerging as one of the most promising sources of non-classical light on which to base future quantum networks. They can generate single photons as well as pairs of entangled photons with unprecedented brightness, indistinguishability, and degree of entanglement. These features have very recently opened up the possibility to perform advanced quantum optics protocols that were previously inaccessible to single quantum emitters. In this work, we report on two experiments that use the non-local properties of entanglement to teleport quantum states: three-photon state teleportation and four-photon entanglement teleportation. We discuss all the experimental results in light of a theoretical model that we develop to account for the non-idealities of the quantum source. The excellent agreement between theory and experiment enables a deep understanding of how each parameter of the source affects the teleportation fidelities and it pinpoints the requirements needed to overcome the classical limits. Finally, our model suggests how to further improve quantum-dot entangled-photon sources for practical quantum networks.

Time-dependent spectral properties of a photoexcited one-dimensional ionic Hubbard model: an exact diagonalization study

Motivated by the recent progress in time-resolved nonequilibrium spectroscopy in condensed matter, we study an optically excited one-dimensional ionic Hubbard model by exact diagonalization. The model is relevant to organic crystals, transition metal oxides, or ultracold atoms in optical lattices. We implement numerical pump-probe measurements to calculate time-dependent conductivity and single-particle spectral functions. In general, short optical excitation induces a metallic behavior imprinted as a Drude peak in conductivity or an in-gap density of states. In a Mott insulator, we find that the induced Drude peak oscillates at the pump frequency and its second harmonic. The former comes from the oscillation of currents, and the latter from the interference of single- and three-photon excited states. In a band insulator, the Drude peak oscillates only at the pump frequency, and quantities such as the double occupancy do not oscillate. The absence of the second harmonic oscillation is due to the degeneracy of multi-photon excited states. The in-gap density of states in both insulators correlates with the Drude weight and the energy absorption for weak pumping. Strong pumping leads to saturation of the in-gap density of states and to suppression of the Drude weight in the Mott regime. We have also checked that the above features are robust for insulators in the intermediate parameter range. Our study demonstrates the distinct natures of the multi-photon excited states in two different insulators.

Witnessing Entanglement In Compton Scattering Processes Via Mutually Unbiased Bases

We present a quantum information theoretic version of the Klein-Nishina formula. This formulation singles out the quantity, the a priori visibility, that quantifies the ability to deduce the polarisation property of single photons. The Kraus-type structure allows a straightforward generalisation to the multiphoton cases, relevant in the decay of positronium which is utilized e.g. for metabolic PET-imaging (Positron- Emission- Tomograph). Predicted by theory but never experimentally proven, the two- or three-photon states should be entangled. We provide an experimentally feasible method to witness entanglement for these processes via MUBs (Mutually Unbiased Bases), exploiting Bohr’s complementarity. Last but not least we present explicit cases exemplifying the interrelation of geometry and entanglement including relations to its potentiality for teleportation schemes or Bell inequality violations or in future for detecting cancer in human beings.

Scheme for encoding single logical qubit information into three-photon decoherence-free states assisted by quantum dots

We propose an optical scheme to encode quantum information into three-photon decoherence-free states (single logical qubit information) and thereby acquire immunity from collective decoherence. Our scheme consists of quantum dots (QDs) within single-sided optical cavities and linearly optical devices for generation of three-photon decoherence-free states (logical qubits) and for encoding arbitrary quantum information. In our proposition, the interaction between photons and electron spin in the QD-cavity system is the critical component and plays the role of a quantum controlled operation to perform the processing of single logical qubit information with immunity against collective decoherence. Thus, we also analyze the performance of interaction between a photon and an electron in a QD. Consequently, for generating three-photon decoherence-free state encoded arbitrary quantum information, our scheme using QD-cavity systems is feasible. In practice, it could be implemented experimentally with current technologies.

Deterministic state analysis for polarization-spatial-time-bin hyperentanglement with nonlinear optics

We present two deterministic hyperentangled state analysis protocols for photons entangled in polarization, spatial-mode and time-bin degrees of freedom (DOFs). The first protocol is a hyperentangled Bell state analyzer, and the second is a hyperentangled Greenberger–Horne–Zeilinger (GHZ) state analyzer for three photons. In the first scheme, we construct a polarization parity-check quantum nondemolition detector (P-QND) and a spatial-mode parity-check quantum nondemolition detector (S-QND) based on cross-Kerr nonlinearities. With these P-QND and S-QND, we design the setup of Bell state analyzer in polarization and spatial-mode DOFs. While time-bin entanglement is discriminated with the help of the polarization entanglement. We generalize the idea to analyze the three-photon hyperentangled GHZ states. In each scheme, a set of mutually orthogonal hyperentangled basis states are completely discriminated via three steps. These two state analysis schemes are expected to provide practical applications for high-capacity and long-distance quantum communication.

Preparation of quantum information encoded on three-photon decoherence-free states via cross-Kerr nonlinearities

We present a scheme to encode quantum information (single logical qubit information) into three-photon decoherence-free states, which can conserve quantum information from collective decoherence, via nonlinearly optical gates (using cross-Kerr nonlinearities: XKNLs) and linearly optical devices. For the preparation of the decoherence-free state, the nonlinearly optical gates (multi-photon gates) consist of weak XKNLs, quantum bus (qubus) beams, and photon-number-resolving (PNR) measurement. Then, by using a linearly optical device, quantum information can be encoded on three-photon decoherence-free state prepared. Subsequently, by our analysis, we show that the nonlinearly optical gates using XKNLs, qubus beams, and PNR measurement are robust against the decoherence effect (photon loss and dephasing) in optical fibers. Consequently, our scheme can be experimentally implemented to efficiently generate three-photon decoherence-free state encoded quantum information, in practice.

Self-assisted complete analysis of three-photon hyperentangled Greenberger–Horne–Zeilinger states with nitrogen-vacancy centers in microcavities

We propose a self-assisted complete analysis scheme of three-photon hyperentangled Greenberger–Horne–Zeilinger (GHZ) states with nitrogen-vacancy (NV) centers in microcavities (NV center-cavity systems), which is used to distinguish 64 three-photon hyperentangled GHZ states entangled in polarization and spatial-mode degrees of freedom. In our scheme, only three NV center-cavity systems are required for distinguishing the 64 three-photon hyperentangled GHZ states, which is much simpler than the previous schemes. Moreover, the three-photon spatial-mode GHZ states are distinguished with the three NV center-cavity systems without affecting the hyperentangled state of three-photon system, so the three-photon polarization GHZ states can be distinguished with linear optical elements assisted by the spatial-mode entangled state of three-photon system. With our scheme, the difficulty in the experimental realization of complete analysis of hyperentangled GHZ states may be largely decreased, which could potentially improve the performance of high-capacity multi-party quantum communication.

Dispersion tuning in sub-micron tapers for third-harmonic and photon triplet generation.

Precise control of the dispersion landscape is of crucial importance if optical fibers are to be successfully used for the generation of three-photon states of light-the inverse of third-harmonic generation (THG). Here we report gas-tuning of intermodal phase-matched THG in sub-micron-diameter tapered optical fiber. By adjusting the pressure of the surrounding argon gas up to 50bars, intermodally phase-matched third-harmonic light can be generated for pump wavelengths within a 15nm range around 1.38μm. We also measure the infrared fluorescence generated in the fiber when pumped in the visible and estimate that the accidental coincidence rate in this signal is lower than the predicted detection rate of photon triplets.