Entanglement Concentration Protocol Research Articles

A Two‐Step Entanglement Concentration for the Less‐Entangled Four‐Photon Cluster States

AbstractEntanglement concentration serves as an essential tool to obtain the maximally entangled states from the less‐entangled states in quantum information processing tasks. An efficient two‐step entanglement concentration protocol (ECP) is proposed to concentrate the less‐entangled four‐photon cluster states with four unknown coefficients into the maximally entangled states in this paper. The protocol utilizes parity‐check gate and photon‐polarized controlled‐Z gate, constructed with a single semiconductor quantum dot in a single optical microcavity (quantum dot‐cavity coupled system) and several linear optical elements. The discarded quantum states can be recycled in the next round concentration to achieve a higher success probability. Under conditions of strong coupling and weak side leakage rate, the ECP can tend toward ideal fidelity and efficiency. Compared to the previously proposed ECPs that utilize various auxiliary tools such as additional entangled states and complex quantum logic gates, the ECP significantly simplifies the analysis process and enables efficient implementation. Thus, the ECP is more economical and feasible in future optical systems.

Compact entanglement concentration for three-electron-spin W states with error-detected parity-check gates

We present a compact entanglement concentration protocol (ECP) for unknown less-entangled three-electron-spin W states, resorting to the interaction rules between the circularly polarized photon and cavity-quantum-dot (QD) system. In the first step of our ECP, the parties utilize two less-entangled three-electron-spin systems not only to obtain one partially entangled three-electron-spin system with two unknown parameters if the odd-parity occurs with the parity-check gate (PCG) but also to get one entangled two-electron-spin system if the even-parity occurs. By exploiting the above three-electron-spin and two-electron-spin systems as the resource for the second step of our ECP, the parties can obtain a standard three-electron-spin W state if the odd parity occurs. Meanwhile, the systems in the even-parity instance can be used as the resource in the next round of our ECP. As the imperfect performances originated from the side leakage and the limited coupling strength of the cavity-QD system can be reflected by clicking the single-photon detectors, the fidelity of the PCG is unit, in principle, immune to strong coupling-strength restriction. Moreover, the success of our ECP not only is heralded by the detectors but also its efficiency further is improved by repeating the operation processes. Therefore, our ECP is useful in the quantum communication network.

Deterministic entanglement distribution on series-parallel quantum networks

The performance of distributing entanglement between two distant nodes in a large-scale quantum network (QN) of partially entangled bipartite pure states is generally benchmarked against the classical entanglement percolation (CEP) scheme. Improvements beyond CEP were only achieved by nonscalable strategies for restricted QN topologies. This paper explores and amplifies a new and more effective mapping of a QN, referred to as concurrence percolation theory (ConPT), that suggests using deterministic rather than probabilistic protocols for scalably improving on CEP across arbitrary QN topology. More precisely, we implement ConPT via a deterministic entanglement transmission (DET) scheme that is fully analogous to resistor network analysis, with the corresponding series and parallel rules represented by deterministic entanglement swapping and concentration protocols, respectively. The main contribution of this paper is to establish a powerful mathematical framework, which is applicable to arbitrary $d$-dimensional information carriers (qudits), that provides different natural optimality metrics in terms of generalized $k$-concurrences (a family of fundamental entanglement measures) for different QN topologies. In particular, we conclude that the introduced DET scheme (a) is optimal over the well-known nested repeater protocol for distilling entanglement from partially entangled qubits and (b) leads to higher success probabilities of obtaining a maximally entangled state than using CEP. The implementation of the DET scheme is experimentally feasible as tested on IBM's quantum computation platform.

Heralded and high-efficient entanglement concentrations based on linear optics assisted by time-delay degree of freedom.

Entanglement concentration is a critical technique to prevent degraded fidelity and security in long-distance quantum communication. We propose novel practical entanglement concentration protocols (ECPs) for less-entangled Bell and Greenberger-Horne-Zeilinger states with unknown parameters by solely using simple linear optics. We avoid the need for the post-selection principles or photon-number-resolving detectors to identify the parity-check measurement completely by orchestrating auxiliary time degree of freedom, and the success of ECPs is exactly heralded by the detection signatures without destroying the incident qubits. Additionally, the outting incident photons kept are in the maximally entangled or the less-entangled state, and the success probability can be increased by recycling the latter. The heralded and the basic linear optical elements make our practical ECPs are accessible to experimental investigation with current technology.

Logic W‐state concentration with parity check

Logic W state, which replaces each physical qubit in a W state with a Greenberger–Horne–Zeilinger state is robust against photon transmission loss in long-distance quantum communication. In practical application, the environmental noise may make maximally entangled logic W state degrade to less entangled state, which largely limits its application. In this article, we propose an efficient entanglement concentration protocol (ECP) for logic W state, which can recover the less entangled logic W state into the maximally entangled logic W state. Our ECP relies on the nondemolition polarization parity check (PPC) gate constructed with cross-Kerr nonlinearity. The distilled maximally entangled logic W state can be preserved for other application. Moreover, when the ECP fails, we can repeat the ECP to further concentrate the distilled less entangled logic W state. By repeating the ECP, the total success probability can be effectively increased. Based on above features, this ECP may be useful in quantum communication field.

Entanglement Concentration Protocols for GHZ-type Entangled Coherent State Based on Linear Optics

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 GHZ-type ECS with an ECP of 3-mode W-type ECS and found that our ECP is more efficient (maximal success probabilities) for larger value (\beta=0.7) of state parameter. For the physical realization, two optical circuits (for two ECPs) using linear optical elements, viz 50:50 beam splitter, phase shifter, and photon detectors are provided, which support the future experimental implementation possible with the present technology.

Hierarchical Quantum Network using Hybrid Entanglement

The advent of a new kind of entangled state known as hybrid entangled state, i.e., entanglement between different degrees of freedom, makes it possible to perform various quantum computational and communication tasks with lesser amount of resources. Here, we aim to exploit the advantage of these entangled states in communication over quantum networks. Unfortunately, the entanglement shared over the network deteriorates due to its unavoidable interaction with surroundings. Thus, an entanglement concentration protocol is proposed to obtain a maximally entangled hybrid Omega-type state from the corresponding non-maximally entangled states. The advantage of the proposed entanglement concentration protocol is that it is feasible to implement this protocol with linear optical components and present technology. The corresponding linear optical quantum circuit is provided for experimental realizations, while the success probability of the concentration protocol is also reported. Thereafter, we propose an application of maximally entangled hybrid state in the hierarchical quantum teleportation network by performing information splitting using Omega-type state, which is also the first hierarchical quantum communication scheme in the hybrid domain so far. The present hybrid entangled state has advantage in circumventing Pauli operations on the coherent state by polarization rotation of single qubit, which can be performed with lesser errors.

Concentration of entanglement in collective-rotating decoherence-free subspace

An entanglement concentration protocol in photonic collective-rotating decoherence-free subspace (CRDFS) is proposed. To accomplish the scheme, two methods to construct parity measurement devices in CRDFS are presented by exploiting the cross-Kerr nonlinearity, through which partially entangled states are converted to maximally entangled states. The performance of the protocol can be improved by iteration method. Fidelity in consideration of dissipation is discussed, which demonstrates good robustness. In contrast to the conventional protocols, the present one has distinctive feature since it can not only get maximally entangled state from less entangled state, but also maintain the maximal entanglement in collective-rotating noise environment.

Linear optics-based entanglement concentration protocols for cluster-type entangled coherent state

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. The necessary quantum circuits enabling future experimental realizations of the proposed ECPs are provided using linear optical elements. Further, the benefit of the proposed schemes is established in the context of long-distance quantum communication where photon loss is an obstruction.

Heralded entanglement concentration of nonlocal photons assisted by doublesided optical microcavities

Assisted by a system with quantum dot (QD) embedded in doublesided microcavity, we present an entanglement concentration protocol (ECP) for two nonlocal photons with a heralded pattern, which makes this protocol intrinsically robust to the unexpected experimental detrimental effects. In addition, by using a pair of entangled QD spins, the ECP works in a parallel style but a cascade one. We assess the success probability and feasibility of this scheme and show it can be implemented with current technology.

Entanglement purification and concentration based on hybrid spin entangled states of separate nitrogen-vacancy centers

We present a hybrid entanglement purification and concentration protocol for nuclear spin entangled states of nitrogen-vacancy (N-V) centers resorting to the ancillary photons and electrons. In the entanglement purification protocol, the mixed entangled states of the N-V centers can be purified with high fidelity using two pairs of entangled photons to interact with each electron in N-V centers. By performing local measurement on the electrons, the original entangled state can be obtained between the two remote parities. In the entanglement concentration protocol, the partially entangled states of the nuclear spin in N-V centers can be concentrated to the maximally entangled state by using an ancillary photon on one local user. The fidelity of the entangled state with different excited state decay rate and the relation between the yield and different decay rate are numerically simulated.

Generation of two-photon orbital-angular-momentum entanglement with a high degree of entanglement

An important problem in the practical application of high-dimensional two-photon orbital angular momentum (OAM) entanglement generated by spontaneous down conversion is a lower degree of entanglement, where the amplitudes of modes are not uniformly distributed. In contrast to the previously raised entanglement concentration protocol, we here report on an experimental scheme that addresses this problem by tuning the two-photon quantum angular position correlation. An opaque mask with N evenly distributed angular slits having a radius r is inserted in the two-photon down-conversion light path. The number N should be such that the separation of adjacent angular slits is larger than the scale of the two-photon angular position correlation. The OAM entanglement for the two-photon state after the opaque mask is cast into a set of folded subbands with a dimension of N, owing to the reduction of rotational symmetry from continuous invariance to discrete invariance. Almost maximum OAM entanglement can be realized by properly setting the width of the angular slits.

Logic Bell state concentration with parity check measurement

Logic qubit plays an important role in current quantum communication. In this paper, we propose an efficient entanglement concentration protocol (ECP) for a new kind of logic Bell state, where the logic qubit is the concatenated Greenber–Horne–Zeilinger (C-GHZ) state. Our ECP relies on the nondemolition polarization parity check (PPC) gates constructed with cross-Kerr nonlinearity, and can distill one pair of maximally entangled logic Bell state from two same pairs of less-entangled logic Bell states. Benefit from the nondemolition PPC gates, the concentrated maximally entangled logic Bell state can be remained for further application. Moreover, our ECP can be repeated to further concentrate the less-entangled logic Bell state. By repeating the ECP, the total success probability can be effectively increased. Based on above features, this ECP may be useful in future long-distance quantum communication.

Universal and distortion-free entanglement concentration of multiqubit quantum states in the W class

We propose a multipartite extension of Matsumoto and Hayashi's distortion-free entanglement concentration protocol, which takes $n$ copies of a general multipartite state and, via local measurements, produces a maximally-entangled multipartite state between local spaces of dimensions $\sim 2^{n E_i}$, where $E_i$ are the local entropies of the input state. However, the extended protocol is generally not universal in the sense that for the same measurement outcomes, the output state will still depend on the input state. Our main result is that when specialized to any state in the multiqubit W class, the protocol is also universal, so that as in the biparatite version, the output is a unique, maximally-entangled state for each given set of measurement outcomes. Our analysis brings to the forefront a new and interesting family of maximally-entangled multipartite states, which we term Kronecker states. A recurrence relation to obtain the coefficients of the W-class Kronecker states is also given.

Entanglement concentration for photon systems assisted with single photons

The entanglement concentration protocols (ECPs) are presented for concentrating arbitrary partially entangled Bell-like state, N-photon GHZ state and N-photon W state, respectively, and the corresponding maximally entangled state can be obtained finally with a certain probability. Besides, compared with other ECPs, the accurate coefficients of the initial partially entangled state in our ECPs do not need to know in advance. Moreover, current ECPs can be repeated to acquire a higher success probability. The devices used in the schemes are linear which leads to flexible operations and improves the performance greatly in the present experiment and our ECPs may be useful in the long-distance quantum information processing.

Entanglement concentration and purification of two-mode squeezed microwave photons in circuit QED

We present a theoretical proposal for a physical implementation of entanglement concentration and purification protocols for two-mode squeezed microwave photons in circuit quantum electrodynamics (QED). First, we give the description of the cross-Kerr effect induced between two resonators in circuit QED. Then we use the cross-Kerr media to design the effective quantum nondemolition (QND) measurement on microwave-photon number. By using the QND measurement, the parties in quantum communication can accomplish the entanglement concentration and purification of nonlocal two-mode squeezed microwave photons. We discuss the feasibility of our schemes by giving the detailed parameters which can be realized with current experimental technology. Our work can improve some practical applications in continuous-variable microwave-based quantum information processing.

Entanglement concentration for arbitrary four-particle linear cluster states

Cluster states, whose model are a remarkably rich structure in measurement-based quantum computation, hold high degree of entanglement, while entanglement is very fragile during the process of transmission because of the inevitable interaction with the environment. We propose two entanglement concentration protocols for four-particle linear cluster states which and are susceptible to the decoherence and the imperfect communication setups. In the first protocol, POVM operators are introduced to maximize the success probability, and the second protocol is based on cross-Kerr nonlinearity which is utilized to check the parity between the original particle and the ancillary particle. Both of the protocols have their own advantages. The first one can be easily realized in experiment by linear optics, while the one with cross-Kerr nonlinearity reach more than 90% success probability by iteration. Since the wide application of cluster states, the two protocols are efficient and valuable to different fields of quantum communication.

Entanglement concentration of unknown states on separate nitrogen-vacancy centers via error-detected entanglement swapping

Here we propose a new entanglement concentration protocol (ECP) for unknown less-entangled states on separate nitrogen-vacancy (NV) centers. The protocol exploits the error-detected entanglement swapping based on cavity quantum electrodynamics, which is more robust and practical than previous ECPs for NV centers. We present in detail the principle and the advantages of the ECP. Also, the performance of the protocol with current experimental parameters is discussed. We believe that the ECP could provide a promising building block for solid-state quantum repeaters and quantum networks in the future.

Electronic Entanglement Concentration for the Concatenated Greenberger-Horne-Zeilinger State

Concatenated Greenberger-Horne-Zeilinger (C-GHZ) state, which encodes many physical qubits in a logic qubit will have important applications in both quantum communication and computation. In this paper, we will describe an entanglement concentration protocol (ECP) for electronic C-GHZ state, by exploiting the electronic polarization beam splitters (PBSs) and charge detection. This protocol has several advantages. First, the parties do not need to know the exact coefficients of the initial less-entangled C-GHZ state, which makes this protocol feasible. Second, with the help of charge detection, the distilled maximally entangled C-GHZ state can be remained for future application. Third, this protocol can be repeated to obtain a higher success probability. We hope that this protocol can be useful in future quantum computation based on electrons.

Efficient Concentration Protocols for the Single-Photon Entanglement State with Polarization Feature

We propose two efficient entanglement concentration protocols (ECPs) for arbitrary less-entangled single-photon entanglement state, in which the photon qubit has the polarization feature. The first ECP is in linear optics, and the second ECP is in nonlinear optics. The two ECPs have some attractive advantages. First, they can preserve the polarization feature of the photon qubit, while all the other existing ECPs for single photon state cannot achieve this goal. Second, they only require one pair of less-entangled single-photon entanglement state and some auxiliary single photons. Third, they only require local operations. Especially, the second ECP can be used repeatedly, which can increase its success probability largely. Based on above properties, our two ECPs, especially the second one may be useful in current and future quantum communication.