Entanglement Purification Protocol Research Articles

Purification for Hybrid Entanglement between Discrete‐ and Continuous‐Variable States

AbstractHybrid entangled states (HES) have attracted significant attention and been utilized in various quantum information processing applications. However, like many other entangled states, maximally entangled HES may degrade to mixed states due to environmental noise and operational imperfections. In this paper, a hybrid entanglement purification protocol (HEPP) for the HES, which consists of photon‐number state and coherent state is proposed. This HEPP is designed to effectively purify a bit‐flip error occurring in any qubit of the HES. Furthermore, HEPP is extended to a general condition, say, the multi‐party scenario, and integrates the generation of HES into the HEPP. Moreover, if different initial mixed states are chosen, then the residual entanglement can be utilized to distill high‐quality entanglement. The HEPP has important applications in the future quantum information processing field.

Universal Highly Effective Entanglement Purification with Single‐Copy Hyperentangled State

AbstractEntanglement purification is a powerful way to protect the quality of entangled system from channel noise and environment noise. A universal highly effective entanglement purification protocol with single‐copy hyperentangled state (H‐UHEPP) is proposed for distillable mixed entangled states with bilateral controlled‐not gate operations, bilateral asymmetrical rotation operations and single photon Bell‐state measurements, where all of these operations and measurements are easy to implement in polarization, spatial and time‐bin degrees of freedom (DOFs) of photon system. This H‐UHEPP, which requires only one pair of hyperentangled photons and simple unitary operations on three DOFs of a photon, can significantly enhance the fidelity of the purified state compared with the previous works. As a consequence, H‐UHEPP can speed up the entanglement purification process and reduce the resource consumption, which makes it useful in future quantum information processing.

Toward the Advantages of Quantum Trajectories on Entanglement Distribution in Quantum Networks

Quantum mechanics allows an information carrier to traverse through multiple trajectories of communication channels simultaneously, this leads us to quantum trajectories where alternative causal orders of communication channels being traversed are in a superposition, so that the relative orders of communication channels become indefinite. It has been shown that entanglement distribution process over quantum trajectory with an EPR pair being prepared by a sender enables quantum teleportation process to be heralded as a noiseless communication process with probability, the heralded result of which is unachievable in classical trajectory with a definite causal order of communication channels. In this work, we investigate the potential advantage of quantum trajectory on the generation of link-level entanglement, the basic element of quantum networks. To this aim, the performance of entanglement distribution process over multiple quantum trajectories where an EPR pair is prepared by a communication provider is analyzed. Besides, the application of entanglement purification protocol on quantum trajectory is first analyzed to reduce the effect of noise on link-level entanglement. The analysis shows that the link-level entanglement generated over quantum trajectory is more robust to long-distance quantum communication, with respect to classical trajectory, which paves the way for designing effective quantum networks.

Entanglement Purification for Logic-Qubit of Photon System Based on Parity Check Measurement Gate.

It has been found that logic-qubit entanglement has great potential for applications in quantum communication and quantum networks in recent years. However, along with the effects of noise and decoherence, the fidelity of the communication transmission can be greatly reduced. In this paper, we investigate the entanglement purification of logic bit-flip error and phase-flip error in polarization logic-qubit entanglement based on the parity-check measurement (PCM) gate, which is constructed by the cross-Kerr nonlinearity and used to distinguish the parity information of two-photon polarization states. The probability of entanglement purification is higher than the scheme using the linear optical method. Moreover, the quality of logic-qubit entangled states can be improved by a cyclic purification process. This entanglement purification protocol will be useful in the future when faced with long-distance communication with logic-qubit entanglement states.

A Survey of Quantum Entanglement Routing Protocols—Challenges for Wide‐Area Networks

AbstractIn this paper, the key challenges (loss due to distance, entanglement routing, multi‐commodities) for the coming quantum internet, relying on entanglement of quantum bits (for short, qubits) on top of an existing network, are analyzed. A unifying framework enabling to compare the various entanglement distribution, purification, and routing protocols published so far is presented. With regard to entanglement routing, the introduction of different time windows will be essential in order to cope efficiently with the main challenges like complex route calculation and fidelity estimation on the one hand, actual entanglement route selection and entangled photon generation on the other hand. For a roll‐out on top of existing transmission networks, all the research publications for the last 20 years start to cover pretty well the global scheme. Nevertheless, open questions remain, like the actual advantage of some task execution prior to the online quantum path selection, or the design of algorithms approximating the multi‐commodities flow optimization problem, or the issue of dealing with a processing time not much longer than the qubit life time.

Optimal two-qubit gates in recurrence protocols of entanglement purification

We propose and investigate a method to optimize recurrence entanglement purification protocols. The approach is based on a numerical search in the whole set of SU(4) matrices with the aid of a quasi-Newton algorithm. Our method evaluates average concurrences where the probabilistic occurrence of mixed entangled states is also taken into account. We show for certain families of states that optimal protocols are not necessarily achieved by bilaterally applied controlled-NOT gates. As we discover several optimal solutions, the proposed method offers some flexibility in experimental implementations of entanglement purification protocols and interesting perspectives in quantum information processing.

Measurement-based logical qubit entanglement purification

Entanglement purification is the distilling of high-quality entanglement from low-quality entanglement and is a key element in the quantum repeater. As a new branch of entanglement purification, the measurement-based entanglement purification protocol (MBEPP) only requires one to perform the Bell state measurement to couple resource states with noisy pairs, and it tolerates more local noise than the conventional purification protocols. Existing MBEPPs usually focus on physical qubit entanglement. In this paper, we propose a measurement-based logical qubit entanglement purification protocol (MBLEPP) with quantum nondemolition detection (QND), where the qubit is encoded in the quantum parity code. The results show that this MBLEPP can also work with photon loss under the conditions that each block of the logical Bell state measurement contains at least one physical qubit, that at least one of the blocks is intact, and that the entanglement exists between all blocks. Moreover, we also consider the MBLEPP with imperfect QND. We show that below a certain QND error threshold, this MBLEPP can still work. In this way, this MBLEPP not only obtains high-fidelity entanglement but also tolerates photon loss and the error from imperfect QND. This MBLEPP combines the benefits of the MBEPP and quantum error correction code and may have potential application in long-distance quantum communication.

Remotely Establishing Polarization Entanglement Over Noisy Polarization Channels

The faithful distribution of entanglement over noisy channels is a vital prerequisite for many quantum technological applications. Quantum information can be encoded in different degrees of freedom (DOF) of photons, where each encoding comes with its own advantages and disadvantages with respect to noise resilience and practicality in manipulation. In this work, we experimentally implement a deterministic entanglement purification protocol that allows us to faithfully distribute entanglement in one DOF over a noisy channel and then remotely transfer it to another DOF for manipulation. In particular, we distribute robust energy-time entanglement and transfer it to polarization entanglement at the communicating parties. The remotely obtained polarization state is independent of the polarization noise during distribution and reaches fidelities to a Bell state of up to 97.6%. Our scheme enables robust and efficient polarization entanglement distribution in the presence of arbitrary polarization noise, which is relevant for future large-scale quantum networks.

Experimental one-step deterministic polarization entanglement purification

Entanglement purification is to distill high-quality entangled states from low-quality entangled states. It is a key step in quantum repeaters, determines the efficiency and communication rates of quantum communication protocols, and is hence of central importance in long-distance communications and quantum networks. In this work, we report the first experimental demonstration of deterministic entanglement purification using polarization and spatial mode hyperentanglement. After purification, the fidelity of polarization entanglement arises from 0.268±0.002 to 0.989±0.001. Assisted with robust spatial mode entanglement, the total purification efficiency can be estimated as 109 times that of the entanglement purification protocols using two copies of entangled states when one uses the spontaneous parametric down-conversion sources. Our work may have the potential to be implemented as a part of full repeater protocols.

Self-error-rejecting multipartite entanglement purification for electron systems assisted by quantum-dot spins in optical microcavities

We present a self-error-rejecting multipartite entanglement purification protocol (MEPP) for N-electron-spin entangled states, resorting to the single-side cavity-spin-coupling system. Our MEPP has a high efficiency containing two steps. One is to obtain high-fidelity N-electron-spin entangled systems with error-heralded parity-check devices (PCDs) in the same parity-mode outcome of three electron-spin pairs, as well as M-electron-spin entangled subsystems (2 ≤ M < N) in the different parity-mode outcomes of those. The other is to regain the N-electron-spin entangled systems from M-electron-spin entangled states utilizing entanglement link. Moreover, the quantum circuits of PCDs make our MEPP works faithfully, due to the practical photon-scattering deviations from the finite side leakage of the microcavity, and the limited coupling between a quantum dot and a cavity mode, converted into a failed detection in a heralded way.

Entanglement-Assisted Entanglement Purification.

The efficient generation of high-fidelity entangled states is the key element for long-distance quantum communication, quantum computation, and other quantum technologies, and at the same time the most resource-consuming part in many schemes. We present a class of entanglement-assisted entanglement purification protocols that can generate high-fidelity entanglement from noisy, finite-size ensembles with improved yield and fidelity as compared to previous approaches. The scheme utilizes high-dimensional auxiliary entanglement to perform entangling nonlocal measurements and determine the number and positions of errors in an ensemble in a controlled and efficient way, without disturbing the entanglement of good pairs. Our protocols can deal with arbitrary errors, but are best suited for few errors, and work particularly well for decay noise. Our methods are applicable to moderately sized ensembles, as will be important for near term quantum devices.

Entanglement purification by counting and locating errors with entangling measurements

We consider entanglement purification protocols for multiple copies of qubit states. We use high-dimensional auxiliary entangled systems to learn about the number and positions of errors in the noisy ensemble in an explicit and controlled way, thereby reducing the amount of noise in the ensemble and purifying the remaining states. This allows us to design entanglement purification protocols for any number of copies that work particularly well for a small number of expected errors, i.e., high fidelity of initial states. The main tool is a counter gate with which the required nonlocal information can be transferred into the high-dimensional entangled qudit auxiliary states. We compare our schemes to standard recurrence protocols that operate on pairs of copies, and hashing and breeding protocols that operate on a (asymptotically) large number of copies. Our protocols interpolate between these two regimes, leading to higher achievable fidelity and yield. We illustrate our approach for bipartite qubit states and generalize it to purify multiparty GHZ states.

Multipartite entanglement purification using time-bin entanglement

Multipartite entanglement has been widely employed in quantum information processing. However, the unavoidable noise in quantum channels causes the maximally multipartite entangled state to degrade to the mixed state. In this paper, we propose a highly efficient multipartite entanglement purification protocol (MEPP) for the polarization Greenberger–Horne–Zeilinger state. Unlike conventional MEPPs, where two pairs of polluted entanglement are usually required, our protocol only requires one noisy copy of polarization-time-bin hyperentanglement and exploits the time-bin entanglement to purify the polarization entanglement. This feature increases the efficiency of our MEPP. Our MEPP may have potential applications in long-distance quantum communication.

Feasible measurement-based entanglement purification in linear optics.

Entanglement purification is used to distill high quality entangled states from several noisy low quality entangled states, and it plays a key role in quantum repeater. The measurement-based entanglement purification protocol (MB-EPP) does not require local two-qubit gates or single-particle measurements on the noisy pairs and may offer significant advantages compared with the gate-based EPPs. We present an alternative MB-EPP in linear optics. Subsequently, we provide a detailed analysis on the realization of this MB-EPP using spontaneous parametric down conversion (SPDC) sources. By delicately designing the optical circuits, the double-pair emission noise caused by SPDC sources can be eliminated automatically. Combined with suitable quantum memory and entanglement swapping, this MB-EPP may have application potential in the implementation of a practical measurement-based quantum repeater.

Feasible time-bin entanglement purification based on sum-frequency generation.

High quality time-bin entanglement is widely exploited to achieve the purposes of fundamental tests of physics and the implementation of quantum communication protocols both in free space and optical fiber propagation. However, the imperfect approaches of generating time-bin entangled state will degrade its quality and limit its practical application. Entanglement purification is to distill high quality entangled states from low quality entangled states. In this paper, we present the first entanglement purification protocol (EPP) for time-bin entanglement. We first explain this EPP for two-photon time-bin entangled state and then extend it to the system of multi-photon time-bin entangled state. We also design a possible realization of this EPP with practical spontaneous parametric down conversion (SPDC) source. Differ from the conventional EPPs, this EPP does not require the sophisticated controlled-not (CNOT) gate or similar operations, and it uses the feasible sum-frequency generation (SFG) to perform the purification. Moreover, the double-pair noise emitted from the SPDC source can be eliminated automatically which is the other advantage of this EPP. If we combine with the faithful entanglement swapping, this EPP may have potential to be a part of full quantum repeaters.

General Quantum Entanglement Purification Protocol using a Controlled‐Phase‐Flip Gate

AbstractEntanglement purification is an important method to guarantee the fidelity of long‐distance quantum communication. Here, a general entanglement purification protocol (EPP) for mixed state with bit‐flip error and phase‐flip error is proposed, resorting to unilateral operations and a controlled‐phase‐flip (CPF) gate. The CPF gate is working with a high fidelity under balance condition of quantum dot embedded in a double‐sided optical cavity. This general EPP scheme can purify the mixed state with both bit‐flip error and phase‐flip error to a high fidelity entangled state relatively fast in some regimes, owing to the unilateral operations and high‐fidelity CPF gate, which can largely decrease the resource consumption. This general EPP provides a convenient way for increasing the entanglement of different quantum systems, which has great potential for guaranteeing the fidelity of long‐distance quantum communication in the future.

Purification of the residual entanglement.

Entanglement purification is an indispensable ingredient in extended quantum communication networks and usually determines the efficiency and communication rate of quantum communication protocols. Different from all existing entanglement purification protocols (EPPs) where two or more copies of low quality mixed entangled states are selected from the same ensemble, here we describe a general and optimal EPP for arbitrary initial mixed states from different ensembles. We show that the successful operation of EPP may not obtain a higher fidelity mixed state, while the discarded source pair, which is usually regarded as a failure in existing EPPs, may have residual entanglement and can be reused to increase the yield of entanglement purification. We give the criterions of both the successful purification to obtain a higher fidelity mixed state and the existence of residual entanglement. Moreover, we reveal that entanglement purification procedure causes some entanglement loss. Finally, we provide an optimal approach to reduce the entanglement loss. This approach can also be used to increase the yield of entanglement purification. Our EPP may have potential application in long-distance quantum communications.

Multi-copy nested entanglement purification for quantum repeaters

Photon decoherence is one of the main obstacles in global-scale quantum communication. Entanglement purification is a powerful approach to distill high quality entanglement ensembles from low quality entanglement ensembles. In this paper, we propose a multi-copy nested entanglement purification protocol (EPP). After performing the entanglement purification, we can distill a high fidelity entangled photon pair from multiple copies of low fidelity photon pairs. This protocol has several advantages. First, the double-pair noise components generated from the spontaneous parametric down conversion (SPDC) source can be automatically eliminated. Second, with the help of entanglement swapping, the distance of purified entangled state can be extended. Third, this EPP is based on current available technology. Fourth, we can obtain high fidelity by performing this EPP only once. This EPP may have potential application in future long-distance quantum communication.

Heralded entanglement purification protocol using high-fidelity parity-check gate based on nitrogen-vacancy center in optical cavity**Project supported by the National Natural Science Foundation of China (Grants Nos. 11674033, 11474026, 11604226, and 11475021) and Science and Technology Program Foundation of the Beijing Municipal Commission of Education of China (Grant Nos. KM201710028005 and CIT&TCD201904080).

The decoherence of entangled states caused by the noisy channel is a salient problem for reducing the fidelity of quantum communication. Here we present a heralded two-photon entanglement purification protocol (EPP) using heralded high-fidelity parity-check gate (HH-PCG), which can increase the entanglement of nonlocal two-photon polarization mixed state. The HH-PCG is constructed by the input-output process of nitrogen-vacancy (NV) center in diamond embedded in a single-sided optical cavity, where the errors caused by the imperfect interaction between the NV center-cavity system and the photon can be heralded by the photon detector. As the unwanted components can be filtrated due to the heralded function, the fidelity of the EPP scheme can be enhanced considerably, which will increase the fidelity of quantum communication processing.

Device-independent quantum secure direct communication against collective attacks

“Device-independent” not only represents a relaxation of the security assumptions about the internal working of the quantum devices, but also can enhance the security of the quantum communication. In the paper, we put forward the first device-independent quantum secure direct communication (DI-QSDC) protocol and analyze its security and communication efficiency against collective attacks. Under practical noisy quantum channel condition, the photon transmission loss and photon state decoherence would reduce DI-QSDC’s communication quality and threaten its absolute security. For solving the photon transmission loss and decoherence problems, we adopt noiseless linear amplification (NLA) protocol and entanglement purification protocol (EPP) to modify the DI-QSDC protocol. With the help of the NLA and EPP, we can guarantee DI-QSDC’s absolute security and effectively improve its communication quality.