Preparation of multiphoton high-dimensional GHZ states

The physics associated with multipartite high-dimensional entanglement is different from that of multipartite two-dimensional entanglement. Therefore, preparing multipartite high-dimensional entanglements with linear optics is challenging. This study proposes a preparation protocol of multiphoton GHZ state with arbitrary dimensions for optical systems. Auxiliary entanglements realize a high-dimensional entanglement gate to connect the high-dimensional entangled pairs to a multipartite high-dimensional GHZ state. Specifically, we use the path degrees of freedom of photons to prepare a four-partite, three-dimensional GHZ state. Our method can be extended to other degrees of freedom to generate arbitrary GHZ entanglements in any dimension.

Entangling single atoms over 33 km telecom fibre

Quantum networks promise to provide the infrastructure for many disruptive applications, such as efficient long-distance quantum communication and distributed quantum computing1,2. Central to these networks is the ability to distribute entanglement between distant nodes using photonic channels. Initially developed for quantum teleportation3,4 and loophole-free tests of Bell's inequality5,6, recently, entanglement distribution has also been achieved over telecom fibres and analysed retrospectively7,8. Yet, to fully use entanglement over long-distance quantum network links it is mandatory to know it is available at the nodes before the entangled state decays. Here we demonstrate heralded entanglement between two independently trapped single rubidium atoms generated over fibre links with a length up to 33 km. For this, we generate atom-photon entanglement in two nodes located in buildings 400 m line-of-sight apart and to overcome high-attenuation losses in the fibres convert the photons to telecom wavelength using polarization-preserving quantum frequency conversion9. The long fibres guide the photons to a Bell-state measurement setup in which a successful photonic projection measurement heralds the entanglement of the atoms10. Our results show the feasibility of entanglement distribution over telecom fibre links useful, for example, for device-independent quantum key distribution11-13 and quantum repeater protocols. The presented work represents an important step towards the realization of large-scale quantum network links.

Bell nonlocality in networks

Bell's theorem proves that quantum theory is inconsistent with local physical models. It has propelled research in the foundations of quantum theory and quantum information science. As a fundamental feature of quantum theory, it impacts predictions far beyond the traditional scenario of the Einstein-Podolsky-Rosen paradox. In the last decade, the investigation of nonlocality has moved beyond Bell's theorem to consider more sophisticated experiments that involve several independent sources which distribute shares of physical systems among many parties in a network. Network scenarios, and the nonlocal correlations that they give rise to, lead to phenomena that have no counterpart in traditional Bell experiments, thus presenting a formidable conceptual and practical challenge. This review discusses the main concepts, methods, results and future challenges in the emerging topic of Bell nonlocality in networks.

Experimental Hong-Ou-Mandel interference using two independent heralded single-photon sources

Hong-Ou-Mandel (HOM) interference is one of the most important experimental phenomena in quantum optics. It has drawn considerable attention with respect to quantum cryptography and quantum communication because of the advent of the measurement device independent (MDI) quantum key distribution (QKD) protocol. Here, we realize HOM interference, having a visibility of approximately 38.1%, using two independent heralded single-photon sources (HSPSs). The HOM interference between two independent HSPSs is a core technology for realizing the long-distance MDI QKD protocol, the quantum coin-tossing protocol, and other quantum cryptography protocols.

Physics and Metaphysics of Wigner's Friends: Even Performed Premeasurements Have No Results

"The unambiguous account of proper quantum phenomena must, in principle, include a description of all relevant features of experimental arrangement" (Bohr). The measurement process is composed of premeasurement (quantum correlation of the system with the pointer variable) and an irreversible decoherence via interaction with an environment. The system ends up in a probabilistic mixture of the eigenstates of the measured observable. For the premeasurement stage, any attempt to introduce an "outcome" leads, as we show, to a logical contradiction, 1=i. This nullifies claims that a modified concept of Wigner's friend, who just premeasures, can lead to valid results concerning quantum theory.

Entangled photon-pair sources based on three-wave mixing in bulk crystals

Entangled photon pairs are a critical resource in quantum communication protocols ranging from quantum key distribution to teleportation. The current workhorse technique for producing photon pairs is via spontaneous parametric down conversion (SPDC) in bulk nonlinear crystals. The increased prominence of quantum networks has led to a growing interest in deployable high performance entangled photon-pair sources. This manuscript provides a review of the state-of-the-art bulk-optics-based SPDC sources with continuous wave pump and discusses some of the main considerations when building for deployment.

Experimental long-distance quantum secure direct communication

Quantum secure direct communication (QSDC) is an important quantum communication branch, which realizes the secure information transmission directly without encryption and decryption processes. Recently, two table-top experiments have demonstrated the principle of QSDC. Here, we report the first long-distance QSDC experiment, including the security test, information encoding, fiber transmission and decoding. After the fiber transmission of 0.5 km, quantum state fidelities of the two polarization entangled Bell states are 91% and 88%, respectively, which are used for information coding. We theoretically analyze the performance of the QSDC system based on current optical communication technologies, showing that QSDC over fiber links of several tens kilometers could be expected. It demonstrates the potential of long-distance QSDC and supports its future applications on quantum communication networks.

Generation and applications of an ultrahigh-fidelity four-photon Greenberger-Horne-Zeilinger state

High-quality entangled photon pairs generated via spontaneous parametric down-conversion have made great contributions to the modern quantum information science and the fundamental tests of quantum mechanics. However, the quality of the entangled states decreases sharply when moving from biphoton to multiphoton experiments, mainly due to the lack of interactions between photons. Here, for the first time, we generate a four-photon Greenberger-Horne-Zeilinger state with a fidelity of 98%, which is even comparable to the best fidelity of biphoton entangled states. Thus, it enables us to demonstrate an ultrahigh-fidelity entanglement swapping-the key ingredient in various quantum information tasks. Our results push the fidelity of multiphoton entanglement generation to a new level and would be useful in some demanding tasks, e.g., we successfully demonstrate the genuine multipartite nonlocality of the observed state in the nonsignaling scenario by violating a novel Hardy-like inequality, which requires very high state-fidelity.

Toward optical quantum information processing with quantum dots coupled to microstructures [Invited]

Major improvements have been made on semiconductor quantum dot light sources recently and now they can be seen as a serious candidate for near-future scalable photonic quantum information processing experiments. The three key parameters of these photon sources for such applications have been pushed to extreme values: almost unity single-photon purity and photon indistinguishability, and high brightness. In this paper, we review the progress achieved recently on quantum-dot-based single-photon sources. We also review some quantum information experiments where entanglement processes are achieved using semiconductor quantum dots.

Two-photon interference between disparate sources for quantum networking

Quantum networks involve entanglement sharing between multiple users. Ideally, any two users would be able to connect regardless of the type of photon source they employ, provided they fulfill the requirements for two-photon interference. From a theoretical perspective, photons coming from different origins can interfere with a perfect visibility, provided they are made indistinguishable in all degrees of freedom. Previous experimental demonstrations of such a scenario have been limited to photon wavelengths below 900 nm, unsuitable for long distance communication, and suffered from low interference visibility. We report two-photon interference using two disparate heralded single photon sources, which involve different nonlinear effects, operating in the telecom wavelength range. The measured visibility of the two-photon interference is 80 ± 4%, which paves the way to hybrid universal quantum networks.

Entangling different-color photons via time-resolved measurement and active feed forward

Entangling independent photons is not only of fundamental interest but also of crucial importance for quantum-information science. Two-photon interference is a major method for entangling independent identical photons. If two photons are different in color, perfect two-photon coalescence can no longer happen, which makes the entangling of different-color photons difficult to realize. In this Letter, by exploring and developing time-resolved measurement and active feed forward, we have entangled two independent photons of different colors for the first time. We find that entanglement with a varying form can be identified for different two-photon temporal modes through time-resolved measurement. By using active feed forward, we are able to convert the varying entanglement into uniform entanglement. Adopting these measures, we have successfully entangled two photons with a frequency separation 16 times larger than their linewidths. In addition to its fundamental interest, our work also provides an approach for solving the frequency-mismatch problem for future quantum networks.

Highly indistinguishable heralded single-photon sources using parametric down conversion

We theoretically and experimentally investigate the conditions necessary to realize highly indistinguishable single-photon sources using parametric down conversion. The visibilities of Hong-Ou-Mandel (HOM) interference between photons in different fluorescence pairs were measured and a visibility of 95.8 ± 2% was observed using a 0.7-mm-long beta barium borate crystal and 2-nm bandpass filters, after compensating for the reflectivity of the beam splitter. A theoretical model of HOM interference visibilities is proposed that considers non-uniform down conversion process inside the nonlinear crystal. It well explains the experimental results.

Teleportation-based realization of an optical quantum two-qubit entangling gate

In recent years, there has been heightened interest in quantum teleportation, which allows for the transfer of unknown quantum states over arbitrary distances. Quantum teleportation not only serves as an essential ingredient in long-distance quantum communication, but also provides enabling technologies for practical quantum computation. Of particular interest is the scheme proposed by D. Gottesman and I. L. Chuang [(1999) Nature 402:390-393], showing that quantum gates can be implemented by teleporting qubits with the help of some special entangled states. Therefore, the construction of a quantum computer can be simply based on some multiparticle entangled states, Bell-state measurements, and single-qubit operations. The feasibility of this scheme relaxes experimental constraints on realizing universal quantum computation. Using two different methods, we demonstrate the smallest nontrivial module in such a scheme--a teleportation-based quantum entangling gate for two different photonic qubits. One uses a high-fidelity six-photon interferometer to realize controlled-NOT gates, and the other uses four-photon hyperentanglement to realize controlled-Phase gates. The results clearly demonstrate the working principles and the entangling capability of the gates. Our experiment represents an important step toward the realization of practical quantum computers and could lead to many further applications in linear optics quantum information processing.

Experimental test of fidelity limits in six-photon interferometry and of rotational invariance properties of the photonic six-qubit entanglement singlet state

Quantum multiphoton interferometry has now reached the six-photon stage. Thus far, the observed fidelities of entangled states never reached 2/3. We report a high fidelity (estimated at 88%) experiment in which six-qubit singlet correlations were observed. With such a high fidelity we are able to demonstrate the central property of these "singlet" correlations, their "rotational invariance," by performing a full set of measurements in three complementary polarization bases. The patterns are almost indistinguishable. The data reveal genuine six-photon entanglement. We also study several five-photon states, which result upon detection of one of the photons. Multiphoton singlet states survive some types of depolarization and are thus important in quantum communication schemes.

Generation of narrow-band polarization-entangled photon pairs for atomic quantum memories

We report an experimental realization of a narrow band polarization-entangled photon source with a linewidth of 9.6 MHz through cavity-enhanced spontaneous parametric down-conversion. This linewidth is comparable to the typical linewidth of atomic ensemble-based quantum memories. Single-mode output is realized by setting a reasonable cavity length difference between different polarizations, using of temperature controlled etalons and actively stabilizing the cavity. The entangled property is characterized with quantum state tomography, giving a fidelity of 94% between our state and a maximally entangled state. The coherence length is directly measured to be 32 m through two-photon interference.

Multistage entanglement swapping

We report an experimental demonstration of entanglement swapping over two quantum stages. By successful realizations of two cascaded photonic entanglement swapping processes, entanglement is generated and distributed between two photons, that originate from independent sources and do not share any common past. In the experiment we use three pairs of polarization entangled photons and conduct two Bell-state measurements: one between the first and second pair, and one between the second and third pair. This results in projecting the remaining two outgoing photons from pair 1 and 3 into an entangled state, as characterized by an entanglement witness. The experiment represents an important step towards a full quantum repeater where multiple entanglement swapping is a key ingredient.

Demonstration of a compiled version of Shor's quantum factoring algorithm using photonic qubits

We report an experimental demonstration of a complied version of Shor's algorithm using four photonic qubits. We choose the simplest instance of this algorithm, that is, factorization of N=15 in the case that the period r=2 and exploit a simplified linear optical network to coherently implement the quantum circuits of the modular exponential execution and semiclassical quantum Fourier transformation. During this computation, genuine multiparticle entanglement is observed which well supports its quantum nature. This experiment represents an essential step toward full realization of Shor's algorithm and scalable linear optics quantum computation.

Experimental interference of independent photons

Interference of photons emerging from independent sources is essential for modern quantum-information processing schemes, above all quantum repeaters and linear-optics quantum computers. We report an observation of nonclassical interference of two single photons originating from two independent, separated sources, which were actively synchronized with a rms timing jitter of 260 fs. The resulting (two-photon) interference visibility was (83+/-4)%.

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.

Experimental synchronization of independent entangled photon sources

We report the generation of independent entangled photon pairs from two synchronized but mutually incoherent laser sources. The quality of synchronization is confirmed by observing a violation of Bell's inequality with 3.2 standard deviations in an entanglement swapping experiment. The techniques developed in our experiment are not only important for realistic linear optical quantum-information processing, but also enable new tests of local realism.

Experimental realization of optimal asymmetric cloning and telecloning via partial teleportation

We report an experimental realization of both optimal asymmetric cloning and telecloning of single photons by making use of partial teleportation of an unknown state. In the experiment, we demonstrate that, conditioned on the success of partial teleportation of single photons, not only the optimal asymmetric cloning can be accomplished, but also one of two outputs can be transferred to a distant location, realizing the telecloning. The experimental results represent a novel way to achieve quantum cloning and may have potential applications in the context of quantum communication.

Experimental demonstration of a nondestructive controlled-NOT quantum gate for two independent photon qubits

Universal logic gates for two quantum bits (qubits) form an essential ingredient of quantum information processing. However, photons, one of the best candidates for qubits, suffer from a lack of strong nonlinear coupling, which is required for quantum logic operations. Here we show how this drawback can be overcome by reporting a proof-of-principle experimental demonstration of a nondestructive controlled-NOT (CNOT) gate for two independent photons using only linear optical elements in conjunction with single-photon sources and conditional dynamics. Moreover, we exploit the CNOT gate to discriminate all four Bell states in a teleportation experiment.

Experimental demonstration of five-photon entanglement and open-destination teleportation

Quantum-mechanical entanglement of three or four particles has been achieved experimentally, and has been used to demonstrate the extreme contradiction between quantum mechanics and local realism. However, the realization of five-particle entanglement remains an experimental challenge. The ability to manipulate the entanglement of five or more particles is required for universal quantum error correction. Another key process in distributed quantum information processing, similar to encoding and decoding, is a teleportation protocol that we term 'open-destination' teleportation. An unknown quantum state of a single particle is teleported onto a superposition of N particles; at a later stage, this teleported state can be read out (for further applications) at any of the N particles, by a projection measurement on the remaining particles. Here we report a proof-of-principle demonstration of five-photon entanglement and open-destination teleportation (for N = 3). In the experiment, we use two entangled photon pairs to generate a four-photon entangled state, which is then combined with a single-photon state. Our experimental methods can be used for investigations of measurement-based quantum computation and multi-party quantum communication.

Long distance quantum teleportation in a quantum relay configuration

A long distance quantum teleportation experiment with a fiber-delayed Bell state measurement (BSM) is reported. The source creating the qubits to be teleported and the source creating the necessary entangled state are connected to the beam splitter realizing the BSM by two 2 km long optical fibers. In addition, the teleported qubits are analyzed after 2.2 km of optical fiber, in another laboratory separated by 55 m. Time-bin qubits carried by photons at 1310 nm are teleported onto photons at 1550 nm. The fidelity is of 77%, above the maximal value obtainable without entanglement. This is the first realization of an elementary quantum relay over significant distances, which will allow an increase in the range of quantum communication and quantum key distribution.

Violation of Bell's inequality with photons from independent sources

We report a violation of Bell's inequality using one photon from a parametric down-conversion source and a second photon from an attenuated laser beam. The two photons were entangled at a beam splitter using the postselection technique of Shih and Alley [Phys. Rev. Lett. 61, 2921 (1988)]]. A quantum interference pattern with a visibility of 91% was obtained using the photons from these independent sources, as compared with a visibility of 99.4% using two photons from a central parametric down-conversion source.

Experimental realization of entanglement concentration and a quantum repeater

We report an experimental realization of entanglement concentration using two polarization-entangled photon pairs produced by pulsed parametric down-conversion. In the meantime, our setup also provides a proof-in-principle demonstration of a quantum repeater. The quality of our procedure is verified by observing a violation of Bell's inequality by more than 5 standard deviations. The high experimental accuracy achieved in the experiment implies that the requirement of tolerable error rate in multistage realization of quantum repeaters can be fulfilled, hence providing a useful toolbox for quantum communication over large distances.

Experimental observation of four-photon entanglement from parametric down-conversion

We observe polarization entanglement between four photons produced from a single down-conversion source. The nonclassical correlations between the measurement results violate a generalized Bell inequality for four qubits. The characteristic properties and its easy generation with high interferometric contrast make the observed four-photon state well suited for implementing advanced quantum communication schemes such as multiparty quantum key distribution, secret sharing, and telecloning.

Experimental entanglement purification of arbitrary unknown states

Distribution of entangled states between distant locations is essential for quantum communication over large distances. But owing to unavoidable decoherence in the quantum communication channel, the quality of entangled states generally decreases exponentially with the channel length. Entanglement purification--a way to extract a subset of states of high entanglement and high purity from a large set of less entangled states--is thus needed to overcome decoherence. Besides its important application in quantum communication, entanglement purification also plays a crucial role in error correction for quantum computation, because it can significantly increase the quality of logic operations between different qubits. Here we demonstrate entanglement purification for general mixed states of polarization-entangled photons using only linear optics. Typically, one photon pair of fidelity 92% could be obtained from two pairs, each of fidelity 75%. In our experiments, decoherence is overcome to the extent that the technique would achieve tolerable error rates for quantum repeaters in long-distance quantum communication. Our results also imply that the requirement of high-accuracy logic operations in fault-tolerant quantum computation can be considerably relaxed.

Experimental extraction of an entangled photon pair from two identically decohered pairs

Entanglement is considered to be one of the most important resources in quantum information processing schemes, including teleportation, dense coding and entanglement-based quantum key distribution. Because entanglement cannot be generated by classical communication between distant parties, distribution of entangled particles between them is necessary. During the distribution process, entanglement between the particles is degraded by the decoherence and dissipation processes that result from unavoidable coupling with the environment. Entanglement distillation and concentration schemes are therefore needed to extract pairs with a higher degree of entanglement from these less-entangled pairs; this is accomplished using local operations and classical communication. Here we report an experimental demonstration of extraction of a polarization-entangled photon pair from two decohered photon pairs. Two polarization-entangled photon pairs are generated by spontaneous parametric down-conversion and then distributed through a channel that induces identical phase fluctuations to both pairs; this ensures that no entanglement is available as long as each pair is manipulated individually. Then, through collective local operations and classical communication we extract from the two decohered pairs a photon pair that is observed to be polarization-entangled.

Demonstration of nondeterministic quantum logic operations using linear optical elements

Knill, Laflamme, and Milburn [Nature (London) 409, 46 (2001)] recently showed that nondeterministic quantum logic operations could be performed using linear optical elements, additional photons (ancilla), and postselection based on the output of single-photon detectors. Here we report the experimental demonstration of two logic devices of this kind, a destructive controlled-NOT (CNOT) gate and a quantum parity check. These two devices can be combined with a pair of entangled photons to implement a conventional (nondestructive) CNOT that succeeds with a probability of 1/4.

Experimental nonlocality proof of quantum teleportation and entanglement swapping

Quantum teleportation strikingly underlines the peculiar features of the quantum world. We present an experimental proof of its quantum nature, teleporting an entangled photon with such high quality that the nonlocal quantum correlations with its original partner photon are preserved. This procedure is also known as entanglement swapping. The nonlocality is confirmed by observing a violation of Bell's inequality by 4.5 standard deviations. Thus, by demonstrating quantum nonlocality for photons that never interacted, our results directly confirm the quantum nature of teleportation.

Experimental demonstration of four-photon entanglement and high-fidelity teleportation

We experimentally demonstrate observation of highly pure four-photon GHZ entanglement produced by parametric down-conversion and a projective measurement. At the same time this also demonstrates teleportation of entanglement with very high purity. Not only does the achieved high visibility enable various novel tests of quantum nonlocality, it also opens the possibility to experimentally investigate various quantum computation and communication schemes with linear optics. Our technique can, in principle, be used to produce entanglement of arbitrarily high order or, equivalently, teleportation and entanglement swapping over multiple stages.

Experimental test of quantum nonlocality in three-photon Greenberger-Horne-Zeilinger entanglement

Bell's theorem states that certain statistical correlations predicted by quantum physics for measurements on two-particle systems cannot be understood within a realistic picture based on local properties of each individual particle-even if the two particles are separated by large distances. Einstein, Podolsky and Rosen first recognized the fundamental significance of these quantum correlations (termed 'entanglement' by Schrodinger) and the two-particle quantum predictions have found ever-increasing experimental support. A more striking conflict between quantum mechanical and local realistic predictions (for perfect correlations) has been discovered; but experimental verification has been difficult, as it requires entanglement between at least three particles. Here we report experimental confirmation of this conflict, using our recently developed method to observe three-photon entanglement, or 'Greenberger-Horne-Zeilinger' (GHZ) states. The results of three specific experiments, involving measurements of polarization correlations between three photons, lead to predictions for a fourth experiment; quantum physical predictions are mutually contradictory with expectations based on local realism. We find the results of the fourth experiment to be in agreement with the quantum prediction and in striking conflict with local realism.