Linear Optical Elements Research Articles

Concentrating partially entangled W-class states on nonlocal atoms using low-Q optical cavity and linear optical elements

Entanglement plays an important role in quantum information science, especially in quantum communications. Here we present an efficient entanglement concentration protocol (ECP) for nonlocal atom systems in the partially entangled W-class states, using the single-photon input-output process regarding low-$Q$ cavity and linear optical elements. Compared with previously published ECPs for the concentration of non-maximally entangled atomic states, our protocol is much simpler and more efficient as it employs the Faraday rotation in cavity quantum electrodynamics (QED) and the parameter-splitting method. The Faraday rotation requires the cavity with low-$Q$ factor and weak coupling to the atom, which makes the requirement for entanglement concentration much less stringent than the previous methods, and achievable with current cavity QED techniques. The parameter-splitting method resorts to linear-optical elements only. This ECP has high efficiency and fidelity in realistic experiments, and some imperfections during the experiment can be avoided efficiently with currently available techniques.

Perfect entanglement concentration of an arbitrary four-photon polarization entangled state via quantum nondemolition detectors

We show how to concentrate an arbitrary four-photon polarization entangled state into a maximally entangled state based on some quantum nondemolition detectors. The entanglement concentration protocol (ECP) resorts to an ancillary single-photon resource and the conventional projection measurement on photons to assist the concentration, which makes it more economical. Our ECP involves weak cross-Kerr nonlinearities, X homodyne measurement and basic linear-optical elements, which make it feasible in the current experimental technology. Moreover, the ECP considers cyclic utilization to enhance a higher success probability. Thus, our scheme is meaningful in practical applications in quantum communication.

Deterministic conversion of a four-photon GHZ state to a W state via homodyne measurement.

We propose a specific method for converting a four-photon Greenberger-Horne-Zeilinger (GHZ) state to a W state in a deterministic way by using linear optical elements, cross-Kerr nonlinearities, and homodyne measurement. We consider the effects of the quadrature homodyne measurements on the fidelity of the W state and the experimental feasibility of the proposed scheme. This might provide great prospects for converting multipartite entangled states into each other for future optical quantum information processing (QIP).

Practical single-photon-assisted remote state preparation with non-maximally entanglement

Remote state preparation (RSP) and joint remote state preparation (JRSP) protocols for single-photon states are investigated via linear optical elements with partially entangled states. In our scheme, by choosing two-mode instances from a polarizing beam splitter, only the sender in the communication protocol needs to prepare an ancillary single-photon and operate the entanglement preparation process in order to retrieve an arbitrary single-photon state from a photon pair in partially entangled state. In the case of JRSP, i.e., a canonical model of RSP with multi-party, we consider that the information of the desired state is split into many subsets and in prior maintained by spatially separate parties. Specifically, with the assistance of a single-photon state and a three-photon entangled state, it turns out that an arbitrary single-photon state can be jointly and remotely prepared with certain probability, which is characterized by the coefficients of both the employed entangled state and the target state. Remarkably, our protocol is readily to extend to the case for RSP and JRSP of mixed states with the all optical means. Therefore, our protocol is promising for communicating among optics-based multi-node quantum networks.

Generation of three-photon polarization-entangled decoherence-free states

We present a generation proposal of three-photon polarization-entangled decoherence-free states, which are immune to the collective decoherence. Based on weak cross-Kerr nonlinearities, the polarization and spacial entanglement gates are realized, and thus three-photon polarization-entangled decoherence-free states can be produced. According to the outcomes of Homodyne measurement performed in the spacial entanglement gate, one Swap gate is inserted into two paths of the photon 1 to swap its spacial modes, by means of classical feed forward. In addition, in the process for realizing two entanglement gates, unitary transformation operations are performed on the appropriate photons conditioned on the different phase shifts occurred on the coherent states, aiming to obtain the same state under two scenarios of the different path compositions of photons. At the output ports of the circuit, three-photon polarization-entangled decoherence-free states which can be utilized to represent two logical qubits, |0〉L and |1〉L are achieved. Apart from Kerr media, only simple linear optical elements and the classical feed forward techniques are necessary in this proposal, facilitating its practical implementation.

Single logical qubit information encoding scheme with the minimal optical decoherence-free subsystem.

We present a scheme for encoding single logical qubit information, which is immune to collective decoherence acting on Hilbert space spanned by the corresponding states. The scheme needs a spatial entanglement gate and a polarization entanglement gate, which are realized with the assistance of weak cross-Kerr nonlinear interaction between photons and coherent states via Kerr media. Under the condition of sufficient large phase shifts, single logical qubit information can be encoded into this minimal optical decoherence-free subsystem with near-unity fidelity. Together with the mature techniques of measurement and classical feed forward, simple linear optical elements are applied to complete the encoding task, which offers the feasibility of this scheme for protecting quantum information against decoherence.

Effective preparation of the N-dimension spin Greenberger–Horne–Zeilinger state with quantum dots embedded in microcavities

We propose a scheme for preparation of the N-dimension spin Greenberger–Horne–Zeilinger state by exploiting quantum dots (QDs) embedded in microcavities. Numerically analysed results show that with the spin-selective photon reflection from the cavity, we can complete the scheme assisted by one polarized photon with high fidelity and 100% successful probability in principle. Furthermore, the set-up is just composed of simple linear optical elements, delay lines and conventional photon detectors, which are feasible with existing experimental technology. Moreover, QDs have numerous admirable features in weak-coupling regime, which are practicable in realistic cavity quantum electrodynamics system shown by previous numerical simulations and experiments. Therefore, our scheme might be realized in near future.

Complete and nondestructive polarization-entangled cluster state analysis assisted by a cavity input–output process

We present two schemes to realize four- and five-photon polarization-entangled cluster state analysis. For four- and five-photon polarization cluster states, the complete bases are composed of 16 and 32 orthogonal state vectors, respectively. To distinguish all of these orthogonal bases completely and nondestructively, a parity analyzer, a polarization analyzer, and two cluster state phase analyzers are designed with some simple linear optical elements and auxiliary atoms trapped in cavities. After implementing the nondestructive cluster analysis process, the cluster states are preserved and thus could be used again in other schemes. The investigations of the fidelities show that our schemes are feasible under the current experimental technology. Our proposed schemes may be useful in multiparticle teleportation, quantum dense coding, and other quantum information processing tasks.

Nonlinear Stokes-Mueller polarimetry

The Stokes Mueller polarimetry is generalized to include nonlinear optical processes such as second- and third-harmonic generation, sum- and difference-frequency generations. The overall algebraic form of the polarimetry is preserved, where the incoming and outgoing radiations are represented by column vectors and the intervening medium is represented by a matrix. Expressions for the generalized nonlinear Stokes vector and the Mueller matrix are provided in terms of coherency and correlation matrices, expanded by higher-dimensional analogues of Pauli matrices. In all cases, the outgoing radiation is represented by the conventional $4\times 1$ Stokes vector, while dimensions of the incoming radiation Stokes vector and Mueller matrix depend on the order of the process being examined. In addition, relation between nonlinear susceptibilities and the measured Mueller matrices are explicitly provided. Finally, the approach of combining linear and nonlinear optical elements is discussed within the context of polarimetry.

Deterministic mediated superdense coding with linear optics

We present a scheme of deterministic mediated superdense coding of entangled photon states employing only linear-optics elements. Ideally, we are able to deterministically transfer four messages by manipulating just one of the photons. Two degrees of freedom, polarization and spatial, are used. A new kind of source of heralded down-converted photon pairs conditioned on detection of another pair with an efficiency of 92% is proposed. Realistic probabilistic experimental verification of the scheme with such a source of preselected pairs is feasible with today's technology. We obtain the channel capacity of 1.78 bits for a full-fledged implementation.

Generation of multi-photon entangled states based on weak measurement and linear optical elements

Abstract This paper presents a scheme which generates multi-photon entangled states based on Mach–Zehnder interferometer and is mainly composed of a photon source with weak measurement, two beam splitters and two orthogonal polarizers. This method can obtain higher efficiency and flexibility compared to previously proposed methods. Furthermore, a practical protocol of the fiber-based setup is proposed. It consists of the photons generation and the entangled states production. Moreover, the mitigation of the decoherence existing in the quantum channels between the proposed entanglement source and its users is provided. The proposed protocol can be exploited in experiments in quantum cryptography and quantum computing.

Entangling the Whole by Beam Splitting a Part

A beam splitter is a basic linear optical element appearing in many optics experiments and is frequently used as a continuous-variable entangler transforming a pair of input modes from a separable Gaussian state into an entangled state. However, a beam splitter is a passive operation that can create entanglement from Gaussian states only under certain conditions. One such condition is that the input light is suitably squeezed. We demonstrate, experimentally, that a beam splitter can create entanglement even from modes which do not possess such a squeezing provided that they are correlated to, but not entangled with, a third mode. Specifically, we show that a beam splitter can create three-mode entanglement by acting on two modes of a three-mode fully separable Gaussian state without entangling the two modes themselves. This beam splitter property is a key mechanism behind the performance of the protocol for entanglement distribution by separable states. Moreover, the property also finds application in collaborative quantum dense coding in which decoding of transmitted information is assisted by interference with a mode of the collaborating party.

Heralded high-efficiency quantum repeater with atomic ensembles assisted by faithful single-photon transmission.

Quantum repeater is one of the important building blocks for long distance quantum communication network. The previous quantum repeaters based on atomic ensembles and linear optical elements can only be performed with a maximal success probability of 1/2 during the entanglement creation and entanglement swapping procedures. Meanwhile, the polarization noise during the entanglement distribution process is harmful to the entangled channel created. Here we introduce a general interface between a polarized photon and an atomic ensemble trapped in a single-sided optical cavity, and with which we propose a high-efficiency quantum repeater protocol in which the robust entanglement distribution is accomplished by the stable spatial-temporal entanglement and it can in principle create the deterministic entanglement between neighboring atomic ensembles in a heralded way as a result of cavity quantum electrodynamics. Meanwhile, the simplified parity-check gate makes the entanglement swapping be completed with unity efficiency, other than 1/2 with linear optics. We detail the performance of our protocol with current experimental parameters and show its robustness to the imperfections, i.e., detuning and coupling variation, involved in the reflection process. These good features make it a useful building block in long distance quantum communication.

Fast multi-copy entanglement purification with linear optics**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474168 and 61401222), the Qing Lan Project of Jiangsu Province, China, the STITP Project in Nanjing University of Posts and Telecommunications, the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20151502), the Natural Science Foundation of the Jiangsu Higher Education Institutions

We describe an entanglement purification protocol for a polarization Bell state. Different from the previous protocols, it does not require the controlled-not gate, and only uses linear optical elements to complete the task. This protocol requires multi-copy degraded mixed states, which can make this protocol obtain a high fidelity in one purification step. It can also be extended to purify the multi-photon Greenberger–Horne–Zeilinger (GHZ) state. This protocol may be useful in future long-distance communication.

Superconducting single-photon detectors integrated with diamond nanophotonic circuits

Photonic quantum technologies promise to repeat the success of integrated nanophotonic circuits in non-classical applications. Using linear optical elements, quantum optical computations can be performed with integrated optical circuits and thus allow for overcoming existing limitations in terms of scalability. Besides passive optical devices for realizing photonic quantum gates, active elements such as single photon sources and single photon detectors are essential ingredients for future optical quantum circuits. Material systems which allow for the monolithic integration of all components are particularly attractive, including III-V semiconductors, silicon and also diamond. Here we demonstrate nanophotonic integrated circuits made from high quality polycrystalline diamond thin films in combination with on-chip single photon detectors. Using superconducting nanowires coupled evanescently to travelling waves we achieve high detection efficiencies up to 66 % combined with low dark count rates and timing resolution of 190 ps. Our devices are fully scalable and hold promise for functional diamond photonic quantum devices.

Complete N-Photon Greenberger-Horne-Zeilinger State Analysis Using Hyperentanglement

We present a scheme for N-photon Greenberger-Horne-Zeilinger (GHZ) state analysis using hyperentanglement in polarization and time-bin degrees of freedom. The scheme only needs linear optics elements and single-photon detectors, which is feasible with current technology. The set of 2 N mutual orthogonal states can be unambiguously distinguished and the protocol is expected to find useful applications in quantum information processing.

Complete Analysis of Four-Photon χ-Type Entangled State via Cross-Kerr Nonlinearity**Supported by the National Natural Science Foundation of China under Grant No. 11004258, and Fundamental Research Funds for the Central Universities Project under Grant No. CQDXWL-2012-014, the Natural Science Foundation Project of CQ CSTC 2011jjA90017

We propose an efficient method to construct an optical four-photon |χ〉 state analyzer via the cross-Kerr nonlinearity combined with linear optical elements. In this protocol, two four-qubit parity-check gates and two controlled phase gates are employed. We show that all the 16 orthogonal four-qubit |χ〉 states can be completely discriminated with our apparatus. The scheme is feasible and realizable with current technology. It may have useful potential applications in quantum information processing which based on |χ〉 state.

Enhancement of the sensitivity of a temperature sensor based on fiber Bragg gratings via weak value amplification.

We present a proof-of-concept experiment aimed at increasing the sensitivity of Fiber-Bragg-gratings temperature sensors by making use of a weak-value-amplification scheme. The technique requires only linear optics elements for its implementation and appears as a promising method for increasing the sensitivity than state-of the-art sensors can currently provide. The device implemented here is able to generate a shift of the centroid of the spectrum of a pulse of ∼0.035 nm/°C, a nearly fourfold increase in sensitivity over the same fiber-Bragg-grating system interrogated using standard methods.

Perfect optics with imperfect components

Many advanced optical functions, including spatial mode converters, linear optics quantum computing gates, and arbitrary linear optical processors for communications and other applications could be implemented using meshes of Mach–Zehnder interferometers in technologies such as silicon photonics, but performance is limited by beam splitters that deviate from the ideal 50∶50 split. We propose a new architecture and a novel self-adjustment approach that automatically compensate for imperfect fabricated split ratios anywhere from 85∶15 to 15∶85. The entire mesh can be both optimized and programmed after initial fabrication, with progressive algorithms, without calculations or calibration, and even using only sources and detectors external to the mesh. Hence, one universal field-programmable linear array optical element could be mass fabricated, with broad process tolerances, and then configured automatically for a wide range of complex and precise linear optical functions.

Complete Distributed Hyper-Entangled-Bell-State Analysis and Quantum Super Dense Coding

We propose a protocol to implement the distributed hyper-entangled-Bell-state analysis (HBSA) for photonic qubits with weak cross-Kerr nonlinearities, QND photon-number-resolving detection, and some linear optical elements. The distinct feature of our scheme is that the BSA for two different degrees of freedom can be implemented deterministically and nondestructively. Based on the present HBSA, we achieve quantum super dense coding with double information capacity, which makes our scheme more significant for long-distance quantum communication.