We present an efficient scheme for the complete analysis of hyperentangled Greenberger-Horne-Zeilinger (GHZ) state in polarization and time-bin degrees of freedom with two steps. First, the polarization GHZ state is distinguished completely and nondestructively, resorting to the controlled phase flip (CPF) gate constructed by the cavity-assisted interaction. Subsequently, the time-bin GHZ state is analyzed by using the preserved polarization entanglement. With the help of CPF gate and self-assisted mechanism, our scheme can be directly generalized to the complete N-photon hyperentangled GHZ state analysis, and it may have potential applications in the hyperentanglement-based quantum communication.
We present a complete hyperentangled Bell state analysis protocol for two-photon four-qubit states which are simultaneously entangled in the polarization and time-bin degrees of freedom. The 16 hyperentangled states can be unambiguously distinguished via two steps. In the first step, the polarization entangled state is distinguished deterministically and nondestructively with the help of the cross-Kerr nonlinearity. Then, in the second step, the time-bin state is analyzed with the aid of the polarization entanglement. We also discuss the applications of our protocol for quantum information pro…
We present two hyperentanglement concentration schemes for two-photon states that are partially entangled in the polarization and time-bin degrees of freedom. The first scheme distills a maximally hyperentangled state from two identical less-entangled states with unknown parameters via the Schmidt projection method. The other scheme can be used to concentrate an initial state with known parameters, and requires only one copy of the initial state for the concentration process. Both these two protocols can be generalized to concentrate N-photon hyperentangled Greenberger- Horne-Zeilinger states …
We present two efficient schemes which can simultaneously accomplish hyperentanglement concentration and purification for two-photon four-qubit systems in an unknown partially hyperentangled mixed states. The first can correct errors in the polarization entanglement and extract maximal hyperentanglement in polarization and spatial mode with additional partial frequency entanglement. The second uses additional maximal frequency entanglement to purify and concentrate hyperentanglement in polarization and spatial mode deterministically. Both of the two schemes are only based on existing optical d…
Practically Enhanced Hyperentanglement Concentration for Polarization-spatial Hyperentangled Bell States with Linear Optics and Common Single-photon Detectors
Hyperentanglement has attracted much attention for 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…
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 hyperentang…
Hyperentanglement is a promising resource in quantum information processing, especially for increasing the channel capacity of long-distance quantum communication. Hyperentanglement purification is an important method to obtain high-fidelity nonlocal hyperentangled states from mixed hyperentangled states in a long-distance quantum communication process with noisy channels. Here, we present a two-step hyperentanglement purification protocol for nonlocal mixed hyperentangled states with polarization bit-flip errors and spatial-mode phase-flip errors, resorting to polarization-spatial phase-check…
A 6-qubit hyperentangled state has been realized by entangling two photons in three degrees of freedom. These correspond to the polarization, the longitudinal momentum and the indistinguishable emission produced by a 2-crystal system operating with Type I phase matching in the spontaneous parametric down conversion regime. The state has been characterized by a chained interferometric apparatus and its complete entangled nature has been tested by a novel witness criterium specifically introduced for hyperentangled states. The experiment represents the first realization of a genuine hyperentangl…
We report the experimental realization and the characterization of polarization and momentum hyperentangled two photon states, generated by a new parametric source of correlated photon pairs. By adoption of these states an "all versus nothing" test of quantum mechanics was performed. The two photon hyperentangled states are expected to find at an increasing rate a widespread application in state engineering and quantum information. PACS: 03.65.Ud, 03.67.Mn, 42.65. Lm
We propose a scheme for the complete differentiation of 64 three-photon hyperentangled GHZ states in both polarization and spatial-mode degrees of freedoms using the quantum-dot cavity system. The three-photon hyperentangled-GHZ-state-analysis scheme can also be used to generate 3-photon hyperentangled GHZ states. This proposed hyperentangled analysis and generation device can serve as crucial components of the high-capacity, long-distance quantum communication. We use quantum swapping as an example to show the application of this device in quantum communication with polarization and spatial-m…
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 sc…
We propose a simple scheme for complete Bell-state measurement of photons using hyperentangled states - entangled in multiple degrees of freedom. In addition to hyperentanglement, our scheme requires only linear optics and single photon detectors, and is realizable with current technology. At the cost of additional classical communication, our Bell-state measurement can be implemented non-locally. We discuss the possible application of these results to quantum dense coding and quantum teleportation.
We present two efficient schemes for the deterministic generation and the complete nondestructive analysis of hyperentangled Bell states in both the polarization and spatial-mode degrees of freedom (DOFs) of two-photon systems, assisted by the nitrogen-vacancy (NV) centers in diamonds coupled to microtoroidal resonators as a result of cavity quantum electrodynamics (QED). With the input-output process of photons, two-photon polarization-spatial hyperentangled Bell states can be generated in a deterministic way and their complete nondestructive analysis can be achieved. These schemes can be gen…
Entanglement is a key resource in quantum information science and associated emerging technologies. Photonic systems offer a large range of exploitable entanglement degrees of freedom such as frequency, time, polarization, and spatial modes. Hyperentangled photons exploit multiple degrees of freedom simultaneously to enhance the performance of quantum information protocols. Here, we report a fully guided-wave approach for generating polarization and energy-time hyperentangled photons at telecom wavelengths. Moreover, by demultiplexing the broadband emission spectrum of the source into five sta…
Hyperentanglement, the simultaneous and independent entanglement of quantum particles in multiple degrees of freedom, is a powerful resource that can be harnessed for efficient quantum information processing. In photonic systems, the two degrees of freedom (DoF) often used to carry quantum and classical information are polarization and frequency, thanks to their robustness in transmission, both in free space and in optical fibers. Telecom-band hyperentangled photons generated in optical fibers are of particular interest because they are compatible with existing fiber-optic infrastructure, and …
We present a simple method for the complete analysis of maximally hyperentangled state in polarization and spatial-mode degrees of freedom assisted by the weak cross-Kerr nonlinearity. Our method not only can be used for two-photon hyperentangled Bell state analysis and three-photon hyperentangled Greenberger-Horne-Zeilinger (GHZ) state analysis, but also is suitable for N-photon hyperentangled GHZ state analysis. In our protocols, the bit information of hyperentanglement is read out via the nonlinear interaction, and the phase information is obtained by using linear optical element and single…
We describe an efficient way for measuring the concurrence of the hyperentanglement. In this protocol, the hyperentangled state is encoded in both polarization and momentum degrees of freedom. We show that the concurrences of both polarization and momentum entanglement can be conversed into the total success probability of picking up the odd-parity state and can be measured directly. This protocol requires the weak cross-Kerr nonlinearity to construct the quantum nondemolition measurement and does not resort to the sophisticated controlled-not gate operation. It is feasible in current experime…
By exploiting the hyperentanglement, we propose a new concrete scheme to realize weak value amplification, which can be implemented by N hyperentangled photons along with coincidence detection. Our scheme can optimally increase the amplification factor by a factor of N compared to the usage of N uncorrelated photons, and achieve the Heisenberg limit for the purpose of parameter estimation. We expect our study can inspire a further investigation on the usage of hyperentanglement in weak measurement and quantum metrology.
A new criterium to detect the entanglement present in a {\it hyperentangled state}, based on the evaluation of an entanglement witness, is presented. We show how some witnesses recently introduced for graph states, measured by only two local settings, can be used in this case. We also define a new witness $W_3$ that improves the resistance to noise by increasing the number of local measurements.
High fidelity preservation of photonic hyperentanglement in a free-space optical delay line
Centre for Quantum Technologies, National University of Singapore（新加坡国立大学量子技术中心）；Department of Physics, National University of Singapore（新加坡国立大学物理系）；Thales Research and Technology（泰雷兹研究技术）
A single photon can be made to entangle simultaneously in its different internal degrees of freedom (DoF) -- polarization, orbital angular momentum (OAM), and frequency -- as well as in its external DoF -- path. Such entanglement in multiple DoF is known as hyperentanglement and provide additional advantage for quantum information processing. We propose a passive optical setup using $q$-plates and polarization beamsplitters to hyperentangle an incoming single photon in polarization, OAM, and path DoF. By mapping polarization DoF to a two-dimensional coin state, and path and OAM DoF to two spat…
We propose a linear-optical implementation of a hyperentanglement-assisted quantum error-correcting code. The code is hyperentanglement-assisted because the shared entanglement resource is a photonic state hyperentangled in polarization and orbital angular momentum. It is possible to encode, decode, and diagnose channel errors using linear-optical techniques. The code corrects for polarization "flip" errors and is thus suitable only for a proof-of-principle experiment. The encoding and decoding circuits use a Knill-Laflamme-Milburn-like scheme for transforming polarization and orbital angular …
We construct an error-detected block, assisted by the quantum-dot spins in double-sided optical microcavities. With this block, we propose three error-detected schemes for the deterministic generation, the complete analysis, and the complete nondestructive analysis of hyperentangled Bell states in both the polarization and spatial-mode degrees of freedom of two-photon systems. In these schemes, the errors can be detected, which can improve their fidelities largely, far different from other previous schemes assisted by the interaction between the photon and the quantum-dot-cavity system. Our sc…
Hyperentanglement, the entanglement in several degrees of freedom (DOFs) of a quantum system, has attracted much attention as it can be used to increase both the channel capacity of quantum communication and its security largely. Here, we present the first scheme to completely distinguish the hyperentangled Bell states of two-photon systems in three DOFs with the help of cross-Kerr nonlinearity without destruction, including two longitudinal momentum DOFs and the polarization DOF. We use cross-Kerr nonlinearity to construct quantum nondemolition detectors which can be used to make a parity-che…
Most quantum systems that are used for generating entanglement and for practical applications are not isolated from the environment, and are hence susceptible to noise. Entanglement in more than one degree of freedom between two systems, known as hyperentanglement, is known to have certain advantages, including robustness against noise over conventional entangled states. Quantum illumination, imaging and communication schemes that involve sending one photon from a pair of entangled photons and retaining the other photon usually involve exposing only the signal photon to environmental noise. Th…
We present two complete maximally hyperentangled state analysis protocols for photons entangled in the polarization and spatial-mode degrees of freedom. The first protocol is a hyperentangled Bell state analysis scheme for two photons and the second is a hyperentangled Greenberger-Horne- Zeilinger (GHZ) state analysis scheme for three photons. In each scheme, a set of mutually orthogonal hyperentangled basis states are completely and deterministically discriminated with the aid of cross-Kerr nonlinearities and linear optics. We also generalize the schemes to unambiguously analyze the N-photon …
Fiber-based quantum communication networks are currently limited without quantum repeaters. Satellite-based quantum links have been proposed to extend the network domain. We have developed a quantum communication system, suitable for realistic satellite-to-ground communication. With this system, we have executed an entanglement-based quantum key distribution (QKD) protocol developed by Bennett, Brassard, and Mermin in 1992 (BBM92), achieving quantum bit error rates (QBER) below 2$\%$ in all bases. More importantly, we demonstrate low QBER execution of a higher dimensional hyperentanglement-bas…
We present a hyperconcentration scheme for nonlocal $N$-photon hyperentangled Greenberger-Horne-Zeilinger states. The maximally hyperentangled state, in which $N$ particles are entangled simultaneously in the polarization and the spatial mode, can be obtained with a certain probability from two partially hyperentangled states. The hyperconcentration scheme is based on one polarization parity check measurement, one spatial mode parity check measurement and N-2 single-photon two-qubit measurements. The concentration only requires linear optical elements, which makes it feasible and practical wit…
Entanglement purification is a powerful method to distill the high-quality entanglement from low-quality entanglement. In the paper, we propose an efficient two-step entanglement purification protocol (EPP) for the polarization entanglement by using only one copy of two-photon hyperentangled state in polarization, spatial-mode, and time-bin DOFs. We suppose that the entanglement in all DOFs suffer from channel noise. In two purification steps, the parties can reduce the bit-flip error and phase-flip error in polarization DOF by consuming the imperfect entanglement in the spatial-mode and time-…
A complete and deterministic Bell state measurement was realized by a simple linear optics experimental scheme which adopts 2-photon polarization-momentum hyperentanglement. The scheme, which is based on the discrimination among the single photon Bell states of the hyperentangled state, requires the adoption of standard single photon detectors. The four polarization Bell states have been measured with average fidelity $F=0.889\pm0.010$ by using the linear momentum degree of freedom as the ancilla. The feasibility of the scheme has been characterized as a function of the purity of momentum enta…
