Hyperentangled States Research Articles

Complete hyperentangled state analysis and generation of multi-particle entanglement based on charge detection

We propose the schemes for implementing hyperentangled state analysis and generating four-electron high entangled states (including cluster state, |χ〉 state, and symmetric Dicke state) based on the charge detection of free electrons. These schemes are deterministic and rely only on charge detection and single-spin rotations. This method, which uses noninteracting electrons, is not only efficient but also saves on quantum resources.

General hyperentanglement concentration for photon systems assisted by quantum-dot spins inside optical microcavities

Hyperentanglement is a promising resource in quantum information processing, especially for increasing the channel capacity of long-distance quantum communication. Here we present a general hyper-entanglement concentration protocol (hyper-ECP) for nonlocal partially hyperentangled Bell states that decay with the interrelationship between the polarization and the spatial-mode degrees of freedom of two-photon systems, which is not taken into account in other hyper-ECPs, resorting to the optical property of the quantum-dot spins inside one-side optical microcavities. We show that the success probability of our hyper-ECP is largely increased by iteration of the hyper-ECP process. Our hyper-ECP can be straightforwardly generalized to distill nonlocal maximally hyperentangled N-photon Greenberger-Horne-Zeilinger (GHZ) states from arbitrary partially hyperentangled GHZ-class states.

Hyperconcentration Based on Projection Measurements

We propose an efficient hyperconcentration protocol for distilling maximally hyperentangled state from partially entangled pure state, resorting to the projection measurement on an auxiliary photon. In our scheme, two photons simultaneously entangled in polarization states and spatial modes are considered. One party performs quantum nondemolition detections on his photon and an additional photon to produce three photon hyperentangled state, then he projects the assistant photon into an orthogonal basis composed of both the polarization and spatial degree of freedom. Then the state of the left two photons collapses into maximally hyperentangled state with a certain probability. In the rest cases, some less-entangled states are obtained, which can be used as resource for the next round concentration. By repeating the concentration process for several rounds, a higher success probability can be obtained, which makes our scheme useful in practical quantum information applications.

Experimental Detection of Quantum Channels

We demonstrate experimentally the possibility of efficiently detecting properties of quantum channels and quantum gates. The experimentally realized quantum channel detection method has been recently proposed theoretically, and allows us to characterize the properties of quantum channels with a much smaller experimental effort than quantum process tomography. Here, the optimal detection scheme is first achieved for nonentanglement breaking channels of the depolarizing form and is based on the generation and detection of polarized entangled photons. We then demonstrate channel detection for nonseparable maps by considering the CNOT gate and employing two-photon hyperentangled states.

Hyperentanglement purification and concentration assisted by diamond NV centers inside photonic crystal cavities

Hyperentanglement has attracted much attention due to its fascinating applications in quantum communication. However, it is impossible to purify a pair of photon systems in a mixed hyperentangled state with errors in two degrees of freedom using linear optical elements only, far different from all the existing entanglement purification protocols in a degree of freedom (DOF) for quantum systems. Here, we investigate the possibility of purifying a spatial-polarization mixed hyperentangled Bell state with the errors in both the spatial-mode and polarization DOFs, resorting to the nonlinear optics of a nitrogen-vacancy (NV) center in a diamond embedded in a photonic crystal cavity coupled to a waveguide. We present the first hyperentanglement purification protocol for purifying a pair of two-photon systems in a mixed hyperentangled Bell state with the errors in two DOFs. We also propose an efficient hyperentanglement concentration protocol for a partially hyperentangled Bell pure state, which has the maximal success probability in principle. These two protocols are useful in long-distance quantum communication with hyperentanglement.

Hyperconcentration for entanglement in two degrees of freedom

We present two hyperconcentration protocols for hyperentangled states, in which entanglement occurs simultaneously in the polarization and the spatial degrees of freedom. One uses an auxiliary single photon prepared in a fixed state. The other uses two less-entangled photon pairs. In both schemes, a two photon maximally hyperentangled state can be obtained from the nonmaximally entangled states with a certain success probability. The procrustean concentration is realized by polarizing beam splitters and nondestructive quantum nondemolition detection. In both protocols the unsuccessful instances can be reconcentrated repeatedly to get a higher success probability, which makes our schemes efficient and useful in quantum information processing.

Generation and analysis of hyperentangled multiqubit states for photons using quantum-dot spins in optical microcavities

We propose a scheme for the generation of hyperentangled multiqubit cluster states and Greenberger–Horne–Zeilinger states in both polarization and spatial mode degrees of freedom using the quantum-dot cavity system. This device can be used as the complete analyzer of hyperentangled multiphoton states. This proposed hyperentanglement generation and analyzer device can serve as a crucial component of high capacity, long-distance quantum communication. Using existing experimental data, it is demonstrated that the present scheme may be feasible in strong-coupling regimes with current techniques.

Hyperentanglement concentration for two-photon four-qubit systems with linear optics

Hyperentanglement, defined as the entanglement in several degrees of freedom (DOFs) of a quantum system, has attracted much attention recently. Here we investigate the possibility of concentrating the two-photon four-qubit systems in partially hyperentangled states in both the spatial mode and the polarization DOFs with linear optics. We first introduce our parameter-splitting method to concentrate the systems in the partially hyperentangled states with known parameters, including partially hyperentangled Bell states and cluster states. Subsequently, we present another two nonlocal hyperentanglement concentration protocols (hyper-ECPs) for the systems in partially hyperentangled unknown states, resorting to the Schmidt projection method. It will be shown that our parameter-splitting method is very efficient for the concentration of the quantum systems in partially entangled states with known parameters, resorting to linear-optical elements only. All these four hyper-ECPs are feasible with current technology and they may be useful in long-distance quantum communication based on hyperentanglement as they require only linear optical elements.

Three-photon energy–time entanglement

Entangled quantum particles have correlations stronger than those allowed by classical physics. These correlations are the focus of of the deepest issues in quantum mechanics [1-3] and are the basis of many quantum technologies. The entanglement of discrete particle properties has been studied extensively in the context of quantum computing [4], cryptography [5], and quantum repeaters [6] while entanglement between the continuous properties of particles may play a critical role in improving the sensitivity of gravitational wave detectors [7,8], atomic clocks [9], and other high precision instruments. The attributes of three or more entangled particles are fundamentally different from those of two entangled particles [10-14]. While the discrete variables of up to 14 ions [15] and the continuous variables between three intense optical beams [16, 17] have been entangled, it has remained an open challenge to entangle the continuous properties of more than two individual particles. Here we experimentally demonstrate genuine tripartite continuous-variable entanglement between three separated particles. In our setup the three particles are photons created directly from a single input photon; the creation process leads to quantum correlations between the colours, or energies, and emission times of the photons. The entanglement between our three photons is the three-party generalization of the Einstein-Podolsky-Rosen (EPR) [1] correlations for continuous variables, and allows for new fundamental tests of quantum mechanics to be carried out. Our scheme can be extended to carry out multi-particle Franson interferometry [18,19], and opens the possibility of using additional degrees of freedom in our photons to simultaneously engineer discrete and continuous-variable hyper-entangled states that could serve as a valuable resource in a wide variety of quantum information tasks.

Experimental Quantum Networking Protocols via Four-Qubit Hyperentangled Dicke States

We report the experimental demonstration of two quantum networking protocols, namely quantum 1→3 telecloning and open-destination teleportation, implemented using a four-qubit register whose state is encoded in a high-quality two-photon hyperentangled Dicke state. The state resource is characterized using criteria based on multipartite entanglement witnesses. We explore the characteristic entanglement-sharing structure of a Dicke state by implementing high-fidelity projections of the four-qubit resource onto lower-dimensional states. Our work demonstrates for the first time the usefulness of Dicke states for quantum information processing.

Complete hyperentangled-Bell-state analysis for photon systems assisted by quantum-dot spins in optical microcavities

Bell-state analysis (BSA) is essential in quantum communication, but it is impossible to distinguish unambiguously the four Bell states in the polarization degree of freedom (DOF) of two-photon systems with only linear optical elements, except for the case in which the BSA is assisted with hyperentangled states, the simultaneous entanglement in more than one DOF. Here, we propose a scheme to distinguish completely the 16 hyperentangled Bell states in both the polarization and the spatial-mode DOFs of two-photon systems, by using the giant nonlinear optics in quantum dot-cavity systems. This scheme can be applied to increase the channel capacity of long-distance quantum communication based on hyperentanglement, such as entanglement swapping, teleportation, and superdense coding. We use hyperentanglement swapping as an example to show the application of this HBSA.

Compact generation of polarization-frequency hyperentangled photon pairs by using quasi-phase-matched lithium niobate

We propose a compact generation of polarization-frequency hyperentangled photon-pair source emitting at a telecom wavelength by engineering a multi-stripe lithium niobate bulk crystal. Each stripe is designed to be poled following a dual-periodic structure and serves for a nondegenerate cross-polarization-entanglement generation. The frequency of photon pair from each stripe differs, thus resulting in a high-dimensional frequency-entanglement. The degree of entanglement and temperature-detuning character of the hyperentangled state are analyzed. Furthermore, another feasible experiment realization of such a photon source is proposed based on guided-wave optics which improves the performance with high brightness, miniaturization and stabilization. Such high-dimensional frequency and cross-polarization hyperentangled photon pairs will have potential applications in quantum communication networks.

Proposal for a new scheme for producing a two-photon, high dimensional hyperentangled state

We propose an experimentally feasible scheme for generating a two 2 × 4 × 4 dimensional photon hyperentangled state, entangled in polarization, frequency and spatial mode. This scheme is mainly based on a parametric down-conversion source and cross-Kerr nonlinearities, which avoids the complicated uncertain post-selection. Our method can be easily expanded to the production of hyperentangled states with more photons in multidimensions. Hence the expectation for vast quantities of information in quantum information processing will possibly come true. Finally, we put forward a realizable quantum key distribution (QKD) protocol based on the high dimensional hyperentangled state.

Efficient hyperentangled Greenberger–Horne–Zeilinger states analysis with cross-Kerr nonlinearity

The entangled states analysis is a very important element for quantum information. It is impossible to unambiguously distinguish the three-photon Greenberger–Horne–Zeilinger (GHZ) states in polarization, resorting to linear optical elements only. Here, we propose an efficient scheme to complete three-photon hyperentangled GHZ states analysis (HGSA) with the help of the cross-Kerr nonlinearity. The three-photon HGSA scheme can also be generalized to N-photon hyperentangled GHZ states analysis. We discuss the application of the HGSA in the quantum secure direct communication (QSDC) with polarization and spatial-mode degrees of freedom. The results show that the HGSA not only increase the channel capacity but also ensure the unconditional security in long-distance quantum communication.

Scalable generation and characterization of a four-photon twelve-qubit hyperentangled state

An experimentally feasible scheme for generating a 12-qubit hyperentangled state via four photons, entangled in polarization, frequency and spatial mode, is proposed. We study the nature of quantum non-locality of this hyperentangled state by evaluating its violation degree to a Bell-type inequality, and find that the result agrees well with quantum mechanics prediction while extremely contradicting the local realism constraint.

Complete Greenberger–Horne–Zeilinger state analyzer using hyperentanglement

In this paper, a scheme for N-photon Greenberger---Horne---Zeilinger (GHZ) state analysis using hyperentangled states in multiple degrees of freedom with only linear optics and single photon detectors is proposed. The photons are separated and processed in different processing units. All the eight GHZ-states in either the polarization or the momentum degree of freedom can be completely distinguished. The scheme is implementable using present-day technology.

Quantum Secure Direct Communication by Using Three-Dimensional Hyperentanglement

We propose two schemes for realizing quantum secure direct communication (QSDC) by using a set of ordered two-photon three-dimensional hyperentangled states entangled in two degrees of freedom (DOFs) as quantum information channels. In the first scheme, the photons from Bob to Alice are transmitted only once. After insuring the security of the quantum channels, Bob encodes the secret message on his photons. Then Alice performs single-photon two-DOF Bell bases measurements on her photons. This scheme has better security than former QSDC protocols. In the second scheme, Bob transmits photons to Alice twice. After insuring the security of the quantum channels, Bob encodes the secret message on his photons. Then Alice performs two-photon Bell bases measurements on each DOF. The scheme has more information capacity than former QSDC protocols.

Generation of modal- and path-entangled photons using a domain-engineered integrated optical waveguide device

Integrated optical devices are expected to play a promising role in the field of quantum information science and technology. In this paper, we propose a scheme for the generation of nondegenerate, copolarised, modal, and path- entangled photons using a directional coupler and an asymmetric Y-coupler geometry in type 0 phase-matched domain engineered lithium niobate(LN) waveguide. The nonlinearity in LN is tailored in such a way that quasi phase matching conditions for two different spontaneous parametric down conversion processes are obeyed simultaneously, leading to a modal and path-entangled state at the output. Assuming typical values of various parameters, we show, through numerical simulations, that an almost maximally entangled state is achievable over a wide range of waveguide parameters. For the degenerate case, the scheme gives a NOON state for N = 2. The generated entangled photon pairs should have potential applications in quantum information schemes and also in quantum metrology. By appropriate domain engineering and component designing, the idea can be further extended to generate hyperentangled and two-photon multipath-entangled states, which may have further applications in quantum computation protocols.

Generation of hyperentangled states between remote noninteracting atomic ions

We propose a scheme of generating four-qubit hyperentangled states between a pair of remote noninteracting atomic ions with a $\ensuremath{\Lambda}$ configuration that are confined in Paul traps. These hyperentangled states, different from the normal entangled states that are entangled in a single degree of freedom, are entangled in both spin and motion degrees of freedom. In our proposal, the entanglement is first generated in spin degrees of freedom using linear optics and then transferred to the motion degree of freedom using a sequence of laser pluses, including the stimulated Raman carrier transitions and sideband transitions. The proposal is completed with regenerating entanglement in spin degrees of freedom using linear optics.

Complete hyperentangled-Bell-state analysis for quantum communication

It is impossible to unambiguously distinguish the four Bell states in polarization, resorting to linear optical elements only. Recently, the hyperentangled Bell state, the simultaneous entanglement in more than one degree of freedom, has been used to assist in the complete Bell-state analysis of the four Bell states. However, if the additional degree of freedom is qubitlike, one can only distinguish 7 from the group of 16 states. Here we present a way to distinguish the hyperentangled Bell states completely with the help of cross-Kerr nonlinearity. Also, we discuss its application in the quantum teleportation of a particle in an unknown state in two different degrees of freedom and in the entanglement swapping of hyperentangled states. These applications will increase the channel capacity of long-distance quantum communication.