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.
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…
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 …
Practically Enhanced Hyperentanglement Concentration for Polarization-spatial Hyperentangled Bell States with Linear Optics and Common Single-photon Detectors
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 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 …
Hyperentanglement is a promising resource in quantum information processing with its high capacity character, defined as the entanglement in multiple degrees of freedom (DOFs) of a quantum system, such as polarization, spatial-mode, orbit-angular-momentum, time-bin and frequency DOFs of photons. Recently, hyperentanglement attracts much attention as all the multiple DOFs can be used to carry information in quantum information processing fully. In this review, we present an overview of the progress achieved so far in the field of hyperentanglement in photon systems and some of its important app…
We propose two schemes for concentration of hyperentanglement of nonlocal multipartite states which are simultaneously entangled in the polarization and spatial modes. One scheme uses an auxiliary singlephoton state prepared according to the parameters of the less-entangled states. The other scheme uses two less-entangled states with unknown parameters to distill the maximal hyperentanglement. The procrustean concentration is realized by two parity check measurements in both the two degrees of freedom. Nondestructive quantum nondemolition detectors based on cross-Kerr nonlinearity are used to …
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.
Two photons can simultaneously share entanglement between several degrees of freedom such as polarization, energy-time, spatial mode and orbital angular momentum. This resource is known as hyperentanglement, and it has been shown to be an important tool for optical quantum information processing. Here we demonstrate the quantum storage and retrieval of photonic hyperentanglement in a solid-state quantum memory. A pair of photons entangled in polarization and energy-time is generated such that one photon is stored in the quantum memory, while the other photon has a telecommunication wavelength …
We report an optical one-way quantum computing experiment with stationary quantum memory involved. First we create a hybrid four-qubit cluster state with two qubits propagating as photons and the other two stationary and stored in a laser-cooled atomic-ensemble quantum memory, and characterize it with entanglement witness and quantum state tomography. Then, by making use of this cluster state and fast operations of electro-optic modulators, we realize memory-assisted feedforward operations and demonstrate deterministic single-qubit rotation as an example.
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）
Bell state measurement is crucial to quantum information protocols, but it is impossible to unambiguously distinguish all the Bell states encoded in multi-photon using only linear optics. There is a maximum number of distinguished Bell states, i.e. distinguising limit which is very important for increasing the channel capacity of quantum communications. In this paper, we separate $n$-photon $D$-dimensional hyperentanglement into two groups. For the first group of $U$ ($G_1$), we obtain the limit ${N_1} = nD - (n - 1)$, which can be applied for both bosons' and fermions' cases. We further discu…
Recently, two-photon six-qubit hyperentangled states were produced in experiment and they can improve the channel capacity of quantum communication largely. Here we present a scheme for the hyperentanglement purification of nonlocal two-photon systems in three degrees of freedom (DOFs), including the polarization, the first-longitudinal-momentum, and the second longitudinal momentum DOFs. Our hyperentanglement purification protocol (hyper-EPP) is constructed with two steps resorting to parity-check quantum nondemolition measurement on the three DOFs and SWAP gates, respectively. With these two…
We demonstrate the generation of narrowband biphotons with polarization-frequency coupled hy- perentanglement from spontaneous four-wave mixing in cold atoms. The coupling between polariza- tion and frequency is realized through a frequency shifter and linear optics. When the polarization- frequency degrees of freedom are decoupled, it is robust to create polarization and frequency Bell states, confirmed by the polarization quantum-state tomography and the two-photon temporal quan- tum beating. Making use of the polarization-frequency coupling to transfer polarization phase retard to the entan…
In quantum illumination, the signal mode of light, entangled with an idler mode, is dispatched towards a suspected object bathed in thermal noise and the returning mode, along with the stored idler mode, is measured to determine the presence or absence of the object. In this process, entanglement is destroyed but its benefits in the form of classical correlations and enlarged Hilbert space survive. Here, we propose the use of probe state hyperentangled in two degrees of freedom - polarization and frequency, to achieve a significant 12dB performance improvement in error probability exponent ove…
Multipartite entanglement plays an important role in controlled quantum teleportation, quantum secret sharing, quantum metrology and some other important quantum information branches. However, the maximally multipartite entangled state will degrade into the mixed state because of the noise. We present an efficient multipartite entanglement purification protocol (EPP) which can distill the high quality entangled states from low quality entangled states for N-photon systems in a Greenberger-Horne-Zeilinger (GHZ) state in only linear optics. After performing the protocol, the spatial-mode entangl…
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…
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 …
Adopting quantum communication to modern networking requires transmitting quantum information through fiber-based infrastructure. We report the first demonstration of superdense coding over optical fiber links, taking advantage of a complete Bell-state measurement enabled by time-polarization hyperentanglement, linear optics, and common single-photon detectors. We demonstrate the highest single-qubit channel capacity to date utilizing linear optics, $1.665 \pm 0.018$, and we provide a full experimental implementation of a hybrid, quantum-classical communication protocol for image transfer.
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 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…
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…
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…
The concept of `flat optics' is quickly conquering different fields of photonics, but its implementation in quantum optics is still at infancy. In particular, polarization entanglement, which is central to quantum photonics due to the simplicity of polarization qubit encoding and control, is so far not realized on flat platforms. Meanwhile, relaxed phase matching of flat nonlinear optical sources enables enormous freedom in tailoring their polarization properties. Here we use this freedom to generate photon pairs with tunable polarization entanglement via spontaneous parametric down-conversion…
It is known that it is impossible to unambiguously distinguish the four Bell states encoded in pairs of photon polarizations using only linear optics. However, hyperentanglement, the simultaneous entanglement in more than one degree of freedom, has been shown to assist the complete Bell analysis of the four Bell states (given a fixed state of the other degrees of freedom). Yet introducing other degrees of freedom also enlarges the total number of Bell-like states. We investigate the limits for unambiguously distinguishing these Bell-like states. In particular, when the additional degree of fre…
We propose a scheme for concentrating nonmaximally pure and mixed polarization-entangled state of individual photon pairs. The scheme uses only simple linear optical elements and may be feasible within current optical technology.
We report a practical non-postselection entanglement concentration scheme in which a maximally entangled Bell-state photon pair is produced from two pairs of partially (or non-maximally) entangled photons. Since this scheme is built only upon linear optical elements and does not require photon-number resolving detectors, it has immediate applications in experimental implementations of various quantum information protocols which require two-photon Bell-states.
Hyperentanglement of photonic light modes is a valuable resource in quantum information processing and quantum communication. Here we propose a new protocol using the interference of two optical nonlinearities and control of the heralding (detection) basis in the orbital-angular-momentum degree of freedom. This setup is capable of generating states which are both maximally- and hyper- entangled in at least four dimensions. The resultant state in the four-dimensional case is a generalization of the so-called N00N state (a maximally path-entangled state well known in quantum optics). The product…
The concatenated Greenberger-Horne-Zeiglinger (C-GHZ) state which is a new type of logic-qubit entanglement has attracted a lot of attentions recently. We present a feasible entanglement concentration protocol (ECP) for logic-qubit entanglement. This ECP is based on the linear optics, and it does not know the initial coefficients of the less-entangled C-GHZ state. This protocol can be extended to arbitrary C-GHZ state. This protocol may be useful in future quantum information processing tasks.
We present a nonlocal entanglement concentration scheme for reconstructing some maximally entangled multipartite states from partially entangled ones by exploiting cross-Kerr nonlinearities to distinguish the parity of two polarization photons. Compared with the entanglement concentration schemes based on two-particle collective unitary evolution, this scheme does not require the parties to know accurately information about the partially entangled states--i.e., their coefficients. Moreover, it does not require the parties to possess sophisticated single-photon detectors, which makes this proto…
We present an entanglement concentration protocols (ECPs) for less-entangled W state with quantum-dot and microcavity coupled system. The present protocol uses the quantum nondemolition measurement on the spin parity to construct the parity check gate. Different from other ECPs, this less-entangled W state with quantum-dot and microcavity coupled system can be concentrated with the help of some single photons. The whole protocol can be repeated to get a higher success probability. It may be useful in current quantum information processing.
We proposed two linear optics based entanglement concentration protocols (ECPs) to obtain maximally entangled 4-mode Cluster-type entangled coherent state (ECS) from less (partially) entangled Cluster-type ECS. The first ECP is designed using a superposition of single-mode coherent state with two unknown parameters, whereas the second ECP is obtained using a superposition of single-mode coherent state and a superposition of two-mode coherent state with four unknown parameters. The success probabilities have been calculated for both the ECPs. Necessary quantum circuits enabling future experimen…
Two remote parties, Alice and Bob initially share some non-maximally entangled states. Through the entanglement concentration by local operation and classical communication(LOCC), they may obtain an outcome of maximally entangled states in the price of decreasing the number of pairs shared by them. Recently, entanglement concentration have been experimently demonstrated by post-selection (T. Yamamoto et al, Nature, 421, 343(2003) and Z. Zhao et al, quant-ph/0301118). Here we give a modified scheme which can be used for the entanglement concentration without any post selection by using only pra…
We proposed two entanglement concentration protocols (ECPs) to obtain maximally entangled Greenberger-Horne-Zeilinger (GHZ)-type entangled coherent state (ECS) from the corresponding partially entangled GHZ-type ECSs. We obtained the first ECP using a partially entangled GHZ-type ECS assisted with a superposition of single-mode coherent state, however the second ECP is designed using two copies of partially entangled GHZ-type ECSs. The success probabilities have also been calculated and discussed for both the ECPs. We have further compared the success probabilities of our first ECP for 3-mode …
A recent paper [Chuan Wang, Phys. Rev. A \textbf{86}, 012323 (2012)] discussed an entanglement concentration protocol (ECP) for partially entangled electrons using a quantum dot and microcavity coupled system. In his paper, each two-electron spin system in a partially entangled state can be concentrated with the assistance of an ancillary quantum dot and a single photon. In this paper, we will present an optimal ECP for such entangled electrons with the help of only one single photon. Compared with the protocol of Wang, the most significant advantage is that during the whole ECP, the single ph…
We present two groups of practical entanglement concentration protocols (ECPs) for optical hybrid entangled state (HES). In the first group, it contains two ECPs and both ECPs do not need to know the initial coefficients of the less-entangled state. The second group contains three ECPs and they need to know the initial coefficients. It is shown that the yield of the entanglement concentration in the second group is greater than the first group. Moreover, some protocols are based on the linear optics and can be easily realized under current experiment condition. These protocols may be useful in…
Classical simulation and model concentration in passive linear optics
School of Informatics, University of Edinburgh（爱丁堡大学信息学院）；Terra Quantum AG；Laboratoire d’Informatique de Paris 6, CNRS, Sorbonne Université（巴黎第六大学计算机实验室，法国国家科学研究中心，索邦大学）；Quandela；DIENS, École Normale Supérieure, PSL University, CNRS, INRIA（高等师范学院计算机科学系，巴黎文理研究大学，法国国家科学研究中心，法国国家信息与自动化研究所）；Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院物理研究所）；Centre for Quantum Science and Engineering, École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院量子科学与工程中心）
Optical interferometry is amongst the most sensitive techniques for precision measurement. By increasing the light intensity a more precise measurement can usually be made. However, in some applications the sample is light sensitive. By using entangled states of light the same precision can be achieved with less exposure of the sample. This concept has been demonstrated in measurements of fixed, known optical components. Here we use two-photon entangled states to measure the concentration of the blood protein bovine serum albumin (BSA) in an aqueous buffer solution. We use an opto-fluidic devi…
We present two realistic entanglement concentration protocols (ECPs) for pure partially entangled photons. A partially entangled photon pair can be concentrated to a maximally entangled pair with only an ancillary single photon in a certain probability, while the conventional ones require two copies of partially entangled pairs at least. Our first protocol is implemented with linear optics and the second one is implemented with cross-Kerr nonlinearities. Compared with other ECPs, they do not need to know the accurate coefficients of the initial state. With linear optics, it is feasible with cu…
We propose two optimal entanglement concentration protocols (ECPs) for arbitrary single-photon multi-mode W state and multi-photon polarization W state, respectively. In both ECPs, we only require one pair of partially entangled W state, and do not consume any auxiliary photon. Both ECPs are based on the linear optics which can be easily realized. On the other hand, the concentrated maximally entangled states can be remained, which are quite different from the previous ECPs. Moreover, for the concentration of the arbitrary single-photon N-mode W state or N-mode polarization W state, the total …
We present a systematic entanglement concentration protocol (ECP) for an arbitrary unknown less-entangled three-photon W state, resorting to the optical property of the quantum-dot spins inside one-sided optical microcavities. In our ECP, the parties obtain not only some three-photon systems in the partially entangled with two unknown parameters when one of the parties picks up the robust odd-parity instance with the parity-check gate (PCG) on his two photons, but also some entangled two-photon systems by keeping the even-parity instance in the first step. By exploiting the above three-photon …
The spontaneous emission of photons from optical cavities and from trapped atoms has been studied extensively in the framework of quantum optics. Theoretical predictions based on the rotating wave approximation (RWA) are in general in very good agreement with experimental findings. However, current experiments aim at combining better and better cavities with large numbers of tightly confined atoms. Here we predict an energy concentrating mechanism in the behavior of such a composite quantum system which cannot be described by the RWA. Its result is the continuous leakage of photons through the…
The concentration of a chiral solution is a key parameter in many scientific fields and industrial processes. This parameter can be estimated to high precision by exploiting circular birefringence or circular dichroism present in optically active media. Using the Quantum Fisher information formalism, we quantify the performance of Gaussian probes in estimating the concentration of chiral analytes. We find that bright-polarization squeezed state probes provide a quantum advantage over equally bright classical strategies that scales exponentially with the squeezing factor for a circularly birefr…
We provide a stochastic interpretation of non-commutative Dirichlet forms in the context of quantum filtering. For stochastic processes motivated by quantum optics experiments, we derive an optimal finite time deviation bound expressed in terms of the non-commutative Dirichlet form. Introducing and developing new non-commutative functional inequalities, we deduce concentration inequalities for these processes. Examples satisfying our bounds include tensor products of quantum Markov semigroups as well as Gibbs samplers above a threshold temperature.
