Entanglement Concentration Research Articles

Viscoelasticity and Solution Stability of Cyanoethylcellulose with Different Molecular Weights in Aqueous Solution.

Water-soluble cellulose ethers are widely used as stabilizers, thickeners, and viscosity modifiers in many industries. Understanding rheological behavior of the polymers is of great significance to the effective control of their applications. In this work, a series of cyanoethylcellulose (CEC) samples with different molecular weights were prepared with cellulose and acrylonitrile in NaOH/urea aqueous solution under the homogeneous reaction. The rheological properties of water-soluble CECs as a function of concentration and molecular weight were investigated using shear viscosity and dynamic rheological measurements. Viscoelastic behaviors have been successfully described by the Carreau model, the Ostwald-de-Waele equation, and the Cox–Merz rule. The entanglement concentrations were determined to be 0.6, 0.85, and 1.5 wt% for CEC-11, CEC-7, and CEC-3, respectively. All of the solutions exhibited viscous behavior rather than a clear sol-gel transition in all tested concentrations. The heterogeneous nature of CEC in an aqueous solution was determined from the Cox–Merz rule due to the coexistence of single chain complexes and aggregates. In addition, the CEC aqueous solutions showed good thermal and time stability, and the transition with temperature was reversible.

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.

Bound entangled singlet-like states for quantum metrology

Bipartite entangled quantum states with a positive partial transpose (PPT), i.e., PPT entangled states, are usually considered very weakly entangled. Since no pure entanglement can be distilled from them, they are also called bound entangled. In this paper we present two classes of ($2d\times 2d$)-dimensional PPT entangled states for any $d\ge 2$ which outperform all separable states in metrology significantly. We present strong evidence that our states provide the maximal metrological gain achievable by PPT states for a given system size. When the dimension $d$ goes to infinity, the metrological gain of these states becomes maximal and equals the metrological gain of a pair of maximally entangled qubits. Thus, we argue that our states could be called "PPT singlets."

Entanglement concentration for six-particle cluster states

Multi-particle cluster states play a significant role in quantum information processing. However, due to the inevitable interaction with the environment in the transmission process, the fidelity of entanglement decreases. To distill the perfect cluster states, we present two schemes for arbitrary six-particle cluster states. POVM local unitary operators that are obtained by solving the equation according to the properties of cluster states are used in the first protocol. The second protocol is based on cross-Kerr nonlinearity which is exploited to check parity between original qubit with ancillary single qubit and it can achieve a higher probability of success through iteration. Furthermore, we can generalize the first method to concentrate entanglement on even number of particles. Our protocol will be useful in practical applications.

Activating hidden teleportation power: Theory and experiment

Ideal quantum teleportation transfers an unknown quantum state intact from one party Alice to the other Bob via the use of a maximally entangled state and the communication of classical information. If Alice and Bob do not share entanglement, the maximal average fidelity between the state to be teleported and the state received, according to a classical measure-and-prepare scheme, is upper bounded by a function $f_{\mathrm{c}}$ that is inversely proportional to the Hilbert space dimension. In fact, even if they share entanglement, the so-called teleportation fidelity may still be less than the classical threshold $f_{\mathrm{c}}$. For two-qubit entangled states, conditioned on a successful local filtering, the teleportation fidelity can always be activated, i.e., boosted beyond $f_{\mathrm{c}}$. Here, for all dimensions larger than two, we show that the teleportation power hidden in a subset of entangled two-qudit Werner states can also be activated. In addition, we show that an entire family of two-qudit rank-deficient states violates the reduction criterion of separability, and thus their teleportation power is either above the classical threshold or can be activated. Using hybrid entanglement prepared in photon pairs, we also provide the first proof-of-principle experimental demonstration of the activation of teleportation power hidden in this latter family of qubit states. The connection between the possibility of activating hidden teleportation power with the closely-related problem of entanglement distillation is discussed.

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.

Enhancement of entanglement concentration using catalysts.

Auxiliary pure quantum entangled states shared between two parties can act as catalysts in bipartite entanglement transformations. The participation of a catalyst state in the transformation can enhance its success probability. We consider transformations involving entanglement concentration of a finite number of copies of arbitrary two-qubit pure states into a single copy of a maximally entangled two-qubit pure state using bipartite local quantum operations and classical communication aided by a catalyst state. We show the enhancement of success probabilities of the catalyst-assisted procedure compared to the case where no catalysts are used. The optimal two-qubit catalyst and the maximum probability of the transformation using such catalysts can be obtained analytically. The enhancement of concentration success probability using catalysts of higher dimensions is demonstrated numerically. Finally, catalyst aided strategies for obtaining multiple maximally entangled two-qubit states are discussed.

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.

Pursuing the Fundamental Limits for Quantum Communication

The quantum capacity of a noisy quantum channel determines the maximal rate at which we can code reliably over asymptotically many uses of the channel, and it characterizes the channel's ultimate ability to transmit quantum information coherently. In this paper, we derive single-letter upper bounds on the quantum and private capacities of quantum channels. The quantum capacity of a quantum channel is always no larger than the quantum capacity of its extended channels, since the extensions of the channel can be considered as assistance from the environment. By optimizing the parametrized extended channels with specific structures such as the flag structure, we obtain new upper bounds on the quantum capacity of the original quantum channel. Furthermore, we extend our approach to estimating the fundamental limits of private communication and one-way entanglement distillation. As notable applications, we establish improved upper bounds to the quantum and private capacities for fundamental quantum channels of interest in quantum information, some of which are also the sources of noise in superconducting quantum computing. In particular, our upper bounds on the quantum capacities of the depolarizing channel and the generalized amplitude damping channel are strictly better than previously best-known bounds for certain regimes.

Efficient entanglement distillation for quantum channels with polarization mode dispersion

Quantum entanglement shared by remote network nodes serves as a valuable resource for promising applications in distributed computing, cryptography, and sensing. However, distributing high-quality entanglement via fiber-optic routes could be challenging due to the various decoherence mechanisms in fibers. In particular, one of the primary polarization decoherence mechanisms in optical fibers is polarization mode dispersion (PMD), which is the distortion of optical pulses by randomly varying birefringences. To mitigate the effect of decoherence in entangled particles, quantum entanglement distillation (QED) algorithms have been proposed. One particular class, the recurrence QED algorithms, stands out because it has relatively relaxed requirements both on the size of the quantum circuits involved and on the initial quality of entanglement between particles. However, because the number of required particles grows exponentially with the number of distillation rounds, an efficient recurrence algorithm needs to converge quickly. We present a recurrence QED algorithm designed for photonic qubit pairs affected by PMD-degraded channels. Our proposed algorithm achieves the optimal fidelity as well as the optimal success probability (conditioned on the fact that optimal fidelity is achieved) in every round of distillation. The attainment of the maximal fidelity improves the convergence speed of fidelity with respect to the number of distillation rounds from linear to quadratic and, hence, significantly reduces the number of rounds. Combined with the fact that the optimal success probability is achieved, the proposed algorithm provides an efficient method to distribute entangled states with a high fidelity via optical fibers.

Optimizing repeater schemes for the quantum internet

The rate at which quantum communication tasks can be performed using direct transmission is fundamentally hindered by the channel loss. Quantum repeaters allow, in principle, to overcome these limitations, but their introduction necessarily adds an additional layer of complexity to the distribution of entanglement. This additional complexity - along with the stochastic nature of processes such as entanglement generation, Bell swaps, and entanglement distillation - makes finding good quantum repeater schemes non-trivial. We develop an algorithm that can efficiently perform a heuristic optimisation over a subset of quantum repeater schemes for general repeater platforms. We find a strong improvement in the generation rate in comparison to an optimisation over a simpler class of repeater schemes based on BDCZ repeater schemes. We use the algorithm to study three different experimental quantum repeater implementations on their ability to distribute entanglement, which we dub \emph{information processing} implementations, \emph{multiplexed} implementations, and combinations of the two. We perform this heuristic optimisation of repeater schemes for each of these implementations for a wide range of parameters and different experimental settings. This allows us to make estimates on what are the most critical parameters to improve for entanglement generation, how many repeaters to use, and which implementations perform best in their ability to generate entanglement.

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.

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.

Resource distillation in convex Gaussian resource theories

It is known that distillation in continuous variable resource theories is impossible when restricted to Gaussian states and operations. To overcome this limitation, we enlarge the theories to include convex mixtures of Gaussian states and operations. This extension is operationally well-motivated since classical randomness is easily accessible. We find that resource distillation becomes possible for convex Gaussian resource theories-albeit in a limited fashion. We derive this limitation by studying the convex roof extension of a Gaussian resource measure and then go on to show that our bound is tight by means of example protocols for the distillation of squeezing and entanglement.

Cellulose sulfate/EMIMAc solution: rheological properties and shaping into polyelectrolyte complexes for protein adsorption

Cellulose sulfates (CS) with low degree of substitution (DS) and high degree of polymerization (DP) were prepared via a controlled sulfation modification. The obtained CS with DS 0.42 and DP 293 showed an enhanced solubility of 14.7 g/100 g in the ionic liquid 1-ethyl-3-methylimidazolium acetate (EMIMAc) compared to unmodified cellulose. The rheological study revealed that the CS/EMIMAc solution behaved as polymers in a θ solvent with the unique three-region flow curves under shear stress. It also showed a property of typical polyelectrolyte solution with the overlap concentration (c*) of 0.2 wt% and the entanglement concentration (ce) of 3.0 wt%, respectively. The CS/EMIMAc solution with a concentration of 5 wt% was selected to develop polyelectrolyte complex (PEC) with chitosan using extrusion-spherization and emulsification-solvent evaporation. The produced PEC beads and magnetic microspheres had an average size of 1.0 mm and 22.1 µm, respectively. The PEC microspheres showed greater absorption capability for bovine serum albumin than the beads with the maximum adsorption value of 780 mg/g.

Effective routing design for remote entanglement generation on quantum networks

Quantum network is a promising platform for many ground-breaking applications that lie beyond the capability of its classical counterparts. Efficient entanglement generation on quantum networks with relatively limited resources such as quantum memories is essential to fully realize the network’s capabilities, the solution to which calls for delicate network design and is currently at the primitive stage. In this study we propose an effective routing scheme to enable automatic responses for multiple requests of entanglement generation between source-terminal stations on a quantum lattice network with finite edge capacities. Multiple connection paths are exploited for each connection request while entanglement fidelity is ensured for each path by performing entanglement purification. The routing scheme is highly modularized with a flexible nature, embedding quantum operations within the algorithmic workflow, whose performance is evaluated from multiple perspectives. In particular, three algorithms are proposed and compared for the scheduling of capacity allocation on the edges of quantum network. Embodying the ideas of proportional share and progressive filling that have been well-studied in classical routing problems, we design another scheduling algorithm, the propagatory update method, which in certain aspects overrides the two algorithms based on classical heuristics in scheduling performances. The general solution scheme paves the road for effective design of efficient routing and flow control protocols on applicational quantum networks.

A matrix inequality for entanglement distillation problem

The pure entangled state is of vital importance in the field of quantum information. The process of asymptotically extracting pure entangled states from many copies of mixed states via local operations and classical communication is called entanglement distillation. The entanglement distillability problem, which is a long-standing open problem, asks whether such process exists. The 2-copy undistillability of 4×4 Werner states has been reduced to the validity of a conjecture for the following matrix inequality with d=4supX∈Xd⁡σ12(X)+σ22(X)⩽3d−4d2, where σ1(X) and σ2(X) are the largest two singular values of X, Xd is the set of all matrices X=A⊗I+I⊗B with A,B∈Cd×d(d⩾4), Tr(A)=Tr(B)=0 and ‖A‖F2+‖B‖F2=1/d. The latest progress, made by Pankowski et al. (2010) [21], shows that this conjecture holds when both matrices A and B are normal. In this paper, we prove that the conjecture holds when one of matrices A and B is normal and the other one is arbitrary via optimization techniques. Our work makes solid progress towards this conjecture and thus the distillability problem.

Noiseless linear amplifiers for multimode states

The entanglement structure between different frequency components within broadband quantum light pulses, forged at entanglement creation, represents a promising route to the practical delivery of many multipartite quantum information applications. However, the scalability of such applications is largely limited by the entanglement decoherence caused by photon loss. One promising method to combat such losses is noiseless linear amplification. However, while there have been various procedures that implement noiseless linear amplification on single-mode states, no realization has thus far been proposed for noiseless linear amplification on quantum states carrying a multimode structure. In this work we close this gap, proposing a novel Noiseless Linear Amplifier (NLA) with Photon Catalysis (PC), namely, the PC-NLA. Constructing a multimode version of an existing NLA that uses Quantum Scissors (QS), the QS-NLA, we then show how the PC-NLA is compatible with the QS-NLA, even though the former uses half the physical resources of the latter. We then apply our newly developed multimode NLA frameworks to the problem of Continuous-Variable (CV) entanglement distillation, determining how the multimode structure of the entanglement impacts the performance of the NLAs. Different from single-mode NLA analyses, we find that a multimode NLA is only effective as a CV entanglement distillation strategy when the channel loss is beyond some threshold - a threshold largely dependent on the multimode structure. The results provided here will be valuable for real-world implementations of multipartite quantum information applications that utilize complex entanglement structure within broadband light pulses.

Quantum networking with short-range entanglement assistance

We propose an approach to distribute high-fidelity long-range entanglement in a quantum network assisted by the entanglement supplied by auxiliary short-range paths between the network nodes. Entanglement assistance in the form of shared catalyst states is utilized to maximize the efficiency of entanglement concentration transformations over the edges of the network. The catalyst states are recycled for use in adaptive operations at the network nodes and replenished periodically using the auxiliary short-range paths. The rate of long-range entanglement distribution using such entanglement assistance is found to be significantly higher than possible without using entanglement assistance.

Long-Distance Entanglement Purification for Quantum Communication.

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 tabletop. Here we propose and report a high-efficiency and long-distance entanglement purification using only one pair of hyperentangled state. We also demonstrate its practical application in entanglement-based quantum key distribution (QKD). One pair of polarization spatial-mode hyperentanglement was distributed over 11km multicore fiber (noisy channel). After purification, the fidelity of polarization entanglement arises from 0.771 to 0.887 and the effective key rate in entanglement-based QKD increases from 0 to 0.332. The values of Clauser-Horne-Shimony-Holt inequality of polarization entanglement arises from 1.829 to 2.128. Moreover, by using one pair of hyperentanglement and deterministic controlled-NOT gates, the total purification efficiency can be estimated as 6.6×10^{3} times than the experiment using two pairs of entangled states with spontaneous parametric down-conversion sources. Our results offer the potential to be implemented as part of a full quantum repeater and large-scale quantum network.