Polarization-entangled States Research Articles

Frequency-induced phase-tunable polarization-entangled narrowband biphotons

Manipulating polarization entanglement of paired photons is always of great interest for understanding the quantum nature of photons and exploring their applications in quantum information processing and quantum communication. Narrowband biphotons with polarization entanglement are especially important for a quantum network based on efficient photon–atom interactions. In most demonstrated cases, the polarization-entangled states are manipulated through the birefringent effect. In this Letter, we produce narrowband polarization-entangled biphotons from spontaneous four-wave mixing in cold atoms and demonstrate a new method to tune the phase of the polarization entanglement by varying the frequency of one of the classical driving lasers. This is achieved through two-photon interference with a path-exchange symmetry. Our result represents a precision control of polarization entanglement from the frequency domain, and may have promising applications in quantum information and precision measurement.

Transmission of photonic quantum polarization entanglement in a nanoscale hybrid plasmonic waveguide.

Photonic quantum technologies have been extensively studied in quantum information science, owing to the high-speed transmission and outstanding low-noise properties of photons. However, applications based on photonic entanglement are restricted due to the diffraction limit. In this work, we demonstrate for the first time the maintaining of quantum polarization entanglement in a nanoscale hybrid plasmonic waveguide composed of a fiber taper and a silver nanowire. The transmitted state throughout the waveguide has a fidelity of 0.932 with the maximally polarization entangled state Φ(+). Furthermore, the Clauser, Horne, Shimony, and Holt (CHSH) inequality test performed, resulting in value of 2.495 ± 0.147 > 2, demonstrates the violation of the hidden variable model. Because the plasmonic waveguide confines the effective mode area to subwavelength scale, it can bridge nanophotonics and quantum optics and may be used as near-field quantum probe in a quantum near-field micro/nanoscope, which can realize high spatial resolution, ultrasensitive, fiber-integrated, and plasmon-enhanced detection.

Preparation of Six-photon Cluster State and Quantum State Sharing of Unknown Two-photon State Based on Weak Cross-Kerr Nonlinearity

We propose a nearly deterministic scheme for generating a six-photon polarization-entangled cluster state via the weak cross-Kerr nonlinearity combined with linear optics elements such as polarization beam splitters (PBSs), beam splitters, etc. Besides, by using the six-photon cluster state as the quantum channel, we propose a scheme for quantum state sharing (QSTS) of an unknown two-photon polarization state based on the weak cross-Kerr medias and linear optics elements. With the help of X quadrature homodyne measurements, our two schemes can be realized in an almost deterministic way.

Preparation and purification of four-photon Greenberger–Horne–Zeilinger state

We present an efficient scheme for the preparing and purifying of the four-photon Greenberger–Horne–Zeilinger (GHZ) state based on linear optics and postselection. First, we describe how to create a four-photon GHZ state in both polarization and spatial degrees of freedom from two pairs. Moreover, in the presence of depolarization noise our scheme is capable of purifying the desired state. In the regime of weak nonlinearity we design an indirect photon number-resolving detection to distinguish two states of the two pairs. At last, a fourfold coincidence detector click indicates the creation of a polarization-entangled four-photon GHZ state.

Distributing a multi-photon polarization-entangled state with unitary fidelity via arbitrary collective noise channels

Taking collective noise into account, a feasible protocol for distributing a multi-photon polarization-entangled state is presented assisted with spatial degree of freedom. The compositions of polarization beam splitters and half-wave plates with tilted $$\pi /4$$�/4 functioning as NOT gates convert the entanglement modes between the polarization and spatial degree of freedom. The appropriate and available optical elements are applied, by which the protocol can be feasibly implemented without the influence resulting from arbitrary collective noise. Furthermore, the successful probability of the entangled state distribution equals to unity for unitary collective noise model.

Near-deterministic Preparation for Multi-photon GHZ State Based on Quantum Non-demolition Measurement

This study presents an efficient scheme to generate an arbitrary multi-photon polarization-entangled GHZ state with quantum non-demolition measurement based on weak cross-Kerr nonlinearity. The distinct feature of the present scheme is that it works in a near-deterministic way in principle. Compared with the previous protocols, our scheme consumes less weak cross-Kerr nonlinear resources and there is no need for minus conditional phase shifts, which make us more confident in the experimental feasibility of the proposed scheme.

Tailoring entanglement through domain engineering in a lithium niobate waveguide.

We propose to integrate the electro-optic (EO) tuning function into on-chip domain engineered lithium niobate (LN) waveguide. Due to the versatility of LN, both the spontaneously parametric down conversion (SPDC) and EO interaction could be realized simultaneously. Photon pairs are generated through SPDC, and the formation of entangled state is modulated by EO processes. An EO tunable polarization-entangled photon state is proposed. Orthogonally-polarized and parallel-polarized entanglements of photon pairs are instantly switchable by tuning the applied field. The characteristics of the source are theoretically investigated showing adjustable bandwidths and high entanglement degrees. Moreover, other kinds of reconfigurable entanglement are also achievable based on suitable domain-design. We believe tailoring entanglement based on domain engineering is a very promising solution for next generation function-integrated quantum circuits.

Polarization entangled photon-pair source based on quantum nonlinear photonics and interferometry

We present a versatile, high-brightness, guided-wave source of polarization entangled photons, emitted at a telecom wavelength. Photon-pairs are generated using an integrated type-0 nonlinear waveguide, and subsequently prepared in a polarization entangled state via a stabilized fiber interferometer. We show that the single photon emission wavelength can be tuned over more than 50nm, whereas the single photon spectral bandwidth can be chosen at will over more than five orders of magnitude (from 25MHz to 4THz). Moreover, by performing entanglement analysis, we demonstrate a high degree of control of the quantum state via the violation of the Bell inequalities by more than 40 standard deviations. This makes this scheme suitable for a wide range of quantum optics experiments, ranging from fundamental research to quantum information applications.We report on details of the setup, as well as on the characterization of all included components, previously outlined in Kaiser et al. (Laser Phys. Lett. 10 (2013) 045202).

Adjustable electromagnetically induced transparency and absorption, optical controlled-phase gate in semiconductor quantum wells

We investigate theoretically both the linear and nonlinear properties of the probe and signal optical pulsed fields in a system of four-level coupled GaAs/AlGaAs quantum wells with spontaneous decay of the longitudinal optical phonons (SDLOP) between the lower excited state and the ground state levels. In the linear range, we predict the existence of electromagnetically induced absorption (EIA), and that it is possible to mutually convert from electromagnetically induced transparency to EIA by adjusting the coherent control of the control optical field and the SDLOP. In the nonlinear range, it is shown that by taking into account the influence of the SDLOP, the cross-Kerr nonlinearity of the probe and signal optical fields can be tremendously enhanced. Simultaneously, we obtain the presence of the suppression of self-Kerr optical absorption of the probe field. These characteristics are advantageous to enable the realization of efficient photon-photon entanglement, and generate conditional nonlinear phase shifts of order π. Thereafter, we present a feasible scheme to carry out a two-qubit optical controlled-phase gate by encoding the polarization state of the probe and signal optical fields. Utilizing the linear optics components, we can discriminate the maximal polarization-entangled state of such a two-qubit system. This proposal is potentially applicable to facilitate the realization of solid states mediated all-optical quantum computation and information processing.

Two-party quantum privacy comparison with polarization-entangled bell states and the coherent states

We propose a protocol of quantum privacy comparison with polarization-entangled Bell states and the coherent states. One of two legitimate participants, Alice, prepares polarization-entangled Bell states and keeps one photon of each photon pair and sends the other photons to the third party, Charlie. Receiving the photons, Charlie performs single-photon transformation operations on them and then sends them to the other legitimate participant, Bob. Three participants adopt parity analysis method to check the distribution security of Bell states. Exploiting polarization beam splitters and non-linear interactions mediated by the probe coherent states in Kerr media, Alice and Bob check the parities of their photons using the bases of {|H〉, |V〉} or {|+〉, |-〉}. On the basis of the parity analysis outcomes and Charlie's publicized information, they can analyze the security of the distributed quantum channel. Confirming secure distribution of the shared Bell states, two participants perform respective parity measurements on the privacy photons and own photons of Bell states, and then send the results to Charlie. According to information provided by two legitimate participants and his single-qubit transformation operations, Charlie compares the privacy information of Alice and Bob and publicizes the conclusion.

Generation of four-photon polarization entangled state based on Einstein-Podolsky-Rosen entanglers

We show how to prepare four-photon polarization entangled states based on some Einstein-Podolsky-Rosen (EPR) entanglers. An EPR entangler consists of two single photons, linear optics elements, quantum non-demolition measurement using a weak cross-Kerr nonlinearity, and classical feed forward. This entangler which acts as the most primary part in the construction of our scheme allows us to make two separable polarization qubits entangled near deterministically. Therefore, the efficiency of the present device completely depends on that of EPR entanglers, and it has a high success probability.

Polarization-entangled photon-pair generation in commercial-grade polarization-maintaining fiber

We demonstrate a fiber-based source of polarization-entangled photon pairs at visible wavelengths suitable for integration with local quantum processing schemes. The photons are created through birefringent phase-matching in spontaneous four-wave mixing inside a Sagnac interferometer. We address entanglement degradation due to temporal distinguishability of the photons to enable the generation of a spectrally unfiltered polarization-entangled photon-pair state with $95.86\pm0.10%$ fidelity to a maximally entangled Bell state, evaluated with a tomographic state reconstruction without applying any corrections or background subtractions. Owing to the large birefringence of the fiber, photons are created far detuned from the pump, where Raman contamination is negligible. This source's spatial mode and ability to produce spectrally uncorrelated photons make it suitable for implementing quantum information protocols over free-space and fiber-based networks.

Direct measurement of the concurrence of two-photon polarization-entangled states

We present three protocols for directly measuring the concurrence of two-photon polarization-entangled states, including pure states and mixed states. Two signal photon pairs in the same polarization-entangled states are needed in each detection round, and the signal photons will pass through polarization-independent beam splitters simultaneously. The concurrence of the photon pairs will be encoded in the total probability of picking up the balanced states in the two output modes of the beam splitter, which can be directly measured by single-photon detectors. The photon detection efficiency can be further enhanced with the help of the weak cross-Kerr nonlinearity, and the signal photons will not be absorbed. The third scheme using the bilateral nondemolition measurements can measure the concurrence of both pure and mixed states with high efficiency and high fidelity and is robust against the copy error of the state to be measured. The sophisticated controlled-not operation of the previous schemes is not required here, so our protocols are more feasible within the current experimental technology.

Generation of three-photon polarization-entangled GHZ state via linear optics and weak cross-Kerr nonlinearity

We propose a simple scheme for generating three-photon polarization-entangled GHZ state via cross-Kerr medium, linear optical elements and P homodyne measurement. In our protocol, the two-photon interference is used rather than the single-photon interference, which decreases the difficulty in experimental realization. Besides, the generation scheme proposed doubles the phase shift θ, which will result in lower error probability and decoherence effect. These advantages make our scheme more feasible in the regime of weak cross-Kerr nonlinearity with current experimental technologies. In addition, we give two efficient schemes for the generation of arbitrary multi-photon GHZ state, which is significant to large-scale quantum information processing (QIP).

A GENERATION SCHEME OF THE DISTRIBUTED FOUR-PHOTON CLUSTER-TYPE POLARIZATION-ENTANGLED STATES EXPLOITING THE INTEGRATION OF ENTANGLEMENT GATES AND THE CONTROLLED PHASE GATE

We propose a scheme for preparing the distributed four-photon cluster-type polarization-entangled states associated with the integration of the controlled phase gate and two kinds of entanglement gates. Employing weak cross-Kerr nonlinear interactions and Homodyne measurement, two individual photons entangle together based on the bus function of coherent states. Assisted by optical elements mainly including polarization beam splitters, the entanglement of the signal photons is converted from the spatial mode to the polarization mode. The application of classical feed forward provides the high-efficiency to the preparation of Einstein–Podolsky–Rosen (EPR) states, Greenberger–Horne–Zeilinger (GHZ) states, and four-photon cluster-type polarization-entangled states. With regard to the four-photon cluster-type state, it can be generated in two distributed nodes with less experimental requirements, integrating the features of three logical gates.

Preparing, linking, and unlinking cluster-type polarization-entangled states by integrating modules

Preparing, linking, and unlinking cluster-type polarization-entangled states by integrating modules Xiao-Ming Xiu1,2,∗, Li Dong1,2,∗, Hong-Zhi Shen2, Ya-Jun Gao1, and X. X. Yi2 1College of Mathematics and Physics, Bohai University, Jinzhou 121013, P. R. China 2School of Physics and Optoelectronic Technology, Dalian University of Technology, Dalian 116024, P. R. China ∗E-mail: xiuxiaomingdl@126.com (X.-M. X.); donglixm@163.com (L. D.)

Efficient nonlocal entangled state distribution over the collective-noise channel

We propose an efficient nonlocal entanglement distribution protocol (EDP) to purify the two-photon polarization-entangled state, resorting to the projection measurement on the additional photons. With the help of the cross-Kerr nonlinearity, two remote parties can share two-photon maximally entangled polarization state from the arbitrary two-photon states with a certain success probability by iterating the entanglement purification process 6 times. Compared with conventional EDPs, the present one can obtain maximally entangled polarization state over an collective-noise channel with deterministic success probability. That is, the EDP is an optimal one.

Perfect distribution of four-photon [formula omitted] entangled states over an arbitrary collective noise channel by spatial degree of freedom

A quantum entanglement distribution protocol of a four-photon χ-type polarization-entangled state is presented by exploiting spatial degree of freedom, which is immune to an arbitrary collective noise. This protocol can be fulfilled with nearly unitary probability by the assistance of Homodyne measurement (Y quadrature measurement) that determines the polarization part of the four photons in the transmitted process. Transforming the polarization entanglement mode to spatial entanglement mode and back, the distribution of this entangled state can overcome the influence of collective noise. Moreover, the combination of currently available optical elements is exploited in this protocol, which includes polarization beam splitters, reflection mirrors, optical detectors, and half wave plates functioning as the NOT gates, etc.

15 μm polarization entanglement generation based on birefringence in silicon wire waveguides

In this Letter, the 1.5 μm polarization entanglement generation is realized in a silicon wire waveguide utilizing its birefringence. In this scheme, two orthogonal polarized correlated states are generated by scalar processes of spontaneous four-wave mixing (SFWM) in the quasi-transverse electrical and quasi-transverse magnetic modes, respectively. Meanwhile, the vector processes of SFWM are suppressed by the group birefringence in the waveguide. The maximum polarization entangled state is generated by optimizing the pump polarization, which is demonstrated by the experiments of two-photon interference and polarization indistinguishability at one side. The fringe visibilities of two-photon interferences are 96.8±4.7% and 86.0±3.7% under two nonorthogonal polarization detection settings, respectively. This scheme provides a simple way to realize silicon integrated sources for 1.5 μm polarization entanglement generation.

A versatile source of polarization entangled photons for quantum network applications

We report a versatile and practical approach for the generation of high-quality polarization entanglement in a fully guided-wave fashion. Our setup relies on a high-brilliance type-0 waveguide generator producing paired photons at a telecom wavelength associated with an advanced energy-time to polarization transcriber. The latter is capable of creating any pure polarization entangled state, and allows manipulation of single-photon bandwidths that can be chosen at will over five orders of magnitude, ranging from tens of MHz to several THz. We achieve excellent entanglement fidelities for particular spectral bandwidths, i.e. 25 MHz, 540 MHz and 80 GHz, proving the relevance of our approach. Our scheme stands as an ideal candidate for a wide range of network applications, ranging from dense division multiplexing quantum key distribution to heralded optical quantum memories and repeaters.