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-based QKD protocol, using photons simultaneously entangled in polarization and time-bin, leading to significantly higher secure key rates, at the cost of increased technical complexity and system size. We show that our protocol is suitable for a space-to-ground link, after incorporating Doppler shift compensation, and verify its security using a rigorous finite-key analysis. Additionally, We discuss system engineering considerations relevant to those and other quantum communication protocols, and their dependence on what photonic degrees of freedom are utilized.
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…
Hyperentangled states can outperform their classical counterparts on solving certain tasks. Here we present a simplified scheme for completely distinguishing two-photon hyperentangled Bell states in polarization, spatial, and time-bin degrees of freedom (DOFs). Unity fidelity can be achieved in principle without strong couple limitation between photon and quantum dot (QD), and the incomplete and imperfect QD-cavity interactions are prevented by single-photon detectors. In addition, auxiliary photons or DOFs are not required in our scheme. The necessary linear optical elements are fewer than th…
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 …
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 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…
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 …
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…
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…
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 …
Practically Enhanced Hyperentanglement Concentration for Polarization-spatial Hyperentangled Bell States with Linear Optics and Common Single-photon Detectors
Encoding many qubits in different degrees of freedom (DOFs) of single photons is one of the routes towards enlarging the Hilbert space spanned by a photonic quantum state. Hyperentangled photon states (i.e. states showing entanglement in multiple DOFs) have demonstrated significant implications for both fundamental physics tests and quantum communication and computation. Increasing the number of qubits of photonic experiments requires miniaturization and integration of the basic elements and functions to guarantee the set-up stability. This motivates the development of technologies allowing th…
Hyperentangled Bell-state analysis (HBSA) is critical for high-capacity quantum communication. Here we design two effective schemes for error-heralded deterministic generation and self-assisted complete analysis of hyperentangled Bell states for two-photon systems in both the polarization and spatial-mode degrees of freedom, assisted by single-sided quantum-dot-cavity systems. We construct an error-heralded block with a singly charged quantum dot inside a single-sided optical microcavity, two circular polarization beam splitters, one half-wave plate, and one single-photon detector, in which th…
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…
Hyperentangled Bell states analysis (HBSA) is an essential building block for certain hyper-parallel quantum information processing. We propose a complete and deterministic HBSA scheme encoded in spatial and polarization degrees of freedom (DOFs) of two-photon system assisted by a fixed frequency-based entanglement and a time interval DOF. The parity information the spatial-based and polarization-based hyper-entanglement can be distinguished by the distinct time intervals of the photon pairs, and the phase information can be distinguished by the detection signature. Compared with previous sche…
We experimentally demonstrate the first quantum system entangled in every degree of freedom (hyperentangled). Using pairs of photons produced in spontaneous parametric downconversion, we verify entanglement by observing a Bell-type inequality violation in each degree of freedom: polarization, spatial mode and time-energy. We also produce and characterize maximally hyperentangled states and novel states simultaneously exhibiting both quantum and classical correlations. Finally, we report the tomography of a 2x2x3x3 system (36-dimensional Hilbert space), which we believe is the first reported ph…
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…
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 quant…
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 use photon pairs hyperentangled in polarization and orbital angular momentum to implement a novel entanglement-enhanced quantum state communication technique, known as SuperDense Teleportation, to communicate a specific class of single-photon ququart states between two remote parties, with an average fidelity of 87.0(1)%, almost twice the classical limit of 44%. We compare this technique with quantum teleportation and remote state preparation and show that SuperDense teleportation requires less classical information and fewer experimental resources. We discuss the information content of thi…
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…
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 contradicts to the local realism constraint.
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 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…
We propose an experimentally feasible scheme for generating a two $2\times4\times4$ dimensional photons 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 realizabl…
Six-qubit cluster states built on the simultaneous entanglement of two photons in three independent degrees of freedom, i.e. polarization and a double longitudinal momentum, have been recently demonstrated. We present here the peculiar entanglement properties of the linear cluster state $\LCtilde$ related to the three degrees of freedom. This state has been adopted to realize various kinds of Controlled NOT (CNOT) gates, obtaining in all the cases high values of the gate fidelity. Our results demonstrate that a number of qubits $\leq$10 in cluster states of two photons entangled in multiple de…
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…
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
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…
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 frequency-multiplexed entangled photon pair and a high-dimensional hyperentangled photon pair are useful to realize a high-capacity quantum communication. A biphoton frequency comb (BFC) with entanglement can be used to prepare both states. We demonstrate polarization entangled BFCs with over 1400 frequency modes, which is approximately two orders of magnitude larger than those of earlier entangled BFCs, by placing a singly resonant periodically poled LiNbO3 waveguide resonator within a Sagnac loop. The BFCs are demonstrated by measuring the joint spectral intensity, cross-correlation, and a…
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 …
Quantum key distribution (QKD) has long been a promising area for application of quantum effects toward solving real-world problems. But two major obstacles have stood in the way of widespread applications: low secure key generation rates and short achievable operating distances. In this paper, a new physical mechanism for dealing with the first of these problems is proposed: interplay between different degrees of freedom in a hyperentangled system (parametric down conversion) is used to increase the Hilbert space dimension available for key generation while maintaining security. Polarization-…
As the hyperentanglement of photon systems presents lots of unique opportunities in high-capacity quantum networking, the hyperentanglement purification protocol (hyper-EPP) becomes a vital project work and the quality of its accomplishment attracts much attention recently. Here we present the first theoretical scheme of faithful hyper-EPP for nonlocal two-photon systems in two degrees of freedom (DOFs) by constructing several fidelity-robust quantum circuits for hyper-encoded photons. With this faithful hyper-EPP, the bit-flip errors in both the polarization and spatial-mode DOFs can be effic…
We use a genetic algorithm (GA) as a design aid for determining the optimal provisioning of entangled photon spectrum in flex-grid quantum networks with arbitrary numbers of channels and users. After introducing a general model for entanglement distribution based on frequency-polarization hyperentangled biphotons, we derive upper bounds on fidelity and entangled bit rate for networks comprising one-to-one user connections. Simple conditions based on user detector quality and link efficiencies are found that determine whether entanglement is possible. We successfully apply a GA to find optimal …
High-quality long-distance entanglement is essential for both quantum communication and scalable quantum networks. Entanglement purification is to distill high-quality entanglement from low-quality entanglement in a noisy environment and it plays a key role in quantum repeaters. The previous significant entanglement purification experiments require two pairs of low-quality entangled states and were demonstrated in table-top. Here we propose and report a high-efficiency and long-distance entanglement purification using only one pair of hyperentangled states. We also demonstrate its practical ap…
Quantum entanglement is a fundamental resource in quantum information processing and its distribution between distant parties is a key challenge in quantum communications. Increasing the dimensionality of entanglement has been shown to improve robustness and channel capacities in secure quantum communications. Here we report on the distribution of genuine high-dimensional entanglement via a 1.2-km-long free-space link across Vienna. We exploit hyperentanglement, that is, simultaneous entanglement in polarization and energy-time bases, to encode quantum information, and observe high-visibility …
To build a global quantum communication network, low-transmission, fiber-based communication channels can be supplemented by using a free-space channel between a satellite and a ground station on Earth. We have constructed a system that generates hyperentangled photonic "ququarts" and measures them to execute multiple quantum communication protocols of interest. We have successfully executed and characterized superdense teleportation, a modified remote-state preparation protocol that transfers more quantum information than standard teleportation, for the same classical information cost, and mo…
We present a deterministic entanglement purification protocol (EPP) working for currently available experiment technique. In this protocol, we resort to the robust time-bin entanglement to purify the polarization entanglement determinately, which is quite different from the previous EPPs. After purification, one can obtain a completely pure maximally entangled pair with the success probability of 100%, in principle. As the maximal polarization entanglement is of vice importance in long-distance quantum communication, this protocol may have a wide application.
Design of an Electrically Tunable Microtoroid for Frequency Selection of Polarization-Entangled Photons
Wyant College of Optical Sciences, The University of Arizona（亚利桑那大学怀特光学科学学院）；Department of Biomedical Engineering, The University of Arizona（亚利桑那大学生物医学工程系）
The encoding of quantum information in photonic time-bin qubits is apt for long distance quantum communication schemes. In practice, due to technical constraints such as detector response time, or the speed with which co-polarized time-bins can be switched, other encodings, e.g. polarization, are often preferred for operations like state detection. Here, we present the conversion of qubits between polarization and time-bin encodings using a method that is based on an ultrafast optical Kerr shutter and attain efficiencies of 97% and an average fidelity of 0.827+/-0.003 with shutter speeds near …
We have generated a new type of biphoton state by cavity-enhanced down-conversion in a type-II phase-matched, periodically-poled KTiOPO_4 (PPKTP) crystal. By introducing a weak intracavity birefringence, the polarization-entangled output was modulated between the singlet and triplet states according to the arrival-time difference of the signal and idler photons. This cavity-enhanced biphoton source is spectrally bright, yielding a single-mode fiber-coupled coincidence rate of 0.7 pairs/s per mW of pump power per MHz of down-conversion bandwidth. Its novel biphoton behavior may be utilized in s…
A single photon has many physical degrees of freedom (DOF) that can carry the state of a high-dimensional quantum system. Nevertheless, only a single DOF is usually used in any specific demonstration. Furthermore, when more DOF are being used, they are analyzed and measured one at a time. We introduce a two-qubit information system, realized by two degrees of freedom of a single photon: polarization and time. The photon arrival time is divided into two time-bins representing a qubit, while its polarization state represents a second qubit. The time difference between the two time-bins is create…
Robust implementation of quantum key distribution requires precise state generation and measurements, as well as a transmission that is resistant to channel disturbances. However, the choice of the optimal encoding scheme is not trivial and depends on external factors such as the quantum channel. In fact, stable and low-error encoders are available for polarization encoding, suitable for free-space channels, whereas time-bin encoding represent a good candidate for fiber-optic channels, as birefingence does not perturb this kind of states. Here we present a cross-encoded scheme where high accur…
We describe a technique to produce narrow-band photon pairs with frequency-bin entanglement, whose relative phase can be tuned using linear polarization optics. We show that, making use of the polarization-frequency coupling effect, the phase of a complex polarizer can be transferred into the frequency entanglement.
