Entanglement Concentration Research Articles

The distillability of entanglement of bipartite reduced density matrices of a tripartite state

The relation between the distillability of entanglement of three bipartite reduced density matrices from a tripartite pure state has been studied in Hayashi and Chen [2011 Phys. Rev. A 84 012325]. We extend this result to the tripartite mixed state of rank at most three. In particular we show that if the state has two bipartite reduced density operators with rank two, then the third bipartite reduced density operator additionally having non positive partial transpose (non-PPT) is distillable. In contrast, we show that the tripartite PPT state with two reduced density operators of rank two is a three-qubit fully separable state. We obtain these facts by proving a conjectured matrix inequality for the bipartite matrix M with Schmidt rank at most three. This is one of the main results of this paper. We also prove it for some M with arbitrary Schmidt rank.

Effects of Polymer Entanglement in Sodium Hyaluronate Solution on Elastic Instability in Abrupt Contraction-Expansion Micro Channels

In this study, the effects of polymer flexibility and entanglement on elastic instability were investigated by observing sodium hyaluronate (Hyaluronic Acid Sodium salt, Na-HA) solution in planar abrupt contraction-expansion microchannels. The rigidity of Na-HA in a solution is affected by ion concentration in the solution. Therefore, we prepared Na-HA water solution and Na-HA PBS solution with concentrations from 0.15 wt% to 0.45 wt%. The rheological properties were measured and analyzed to detect the Na-HA overlap and entanglement concentrations. The flow regimes of the Na-HA solutions in several planar abrupt contraction-expansion channels were characterized in terms of rheological properties, polymer flexibility and polymer entanglement.

Key rates for quantum key distribution protocols with asymmetric noise

We consider the asymptotic key rates achieved in the simplest quantum key distribution protocols, namely the BB84 and the six-state protocols, when non-uniform noise is present in the system. We first observe that higher qubit error rates do not necessarily imply lower key rates. Secondly, we consider protocols with advantage distillation and show that it can be advantageous to use the basis with higher quantum bit error rate for the key generation. We then discuss the relation between advantage distillation and entanglement distillation protocols. We show that applying advantage distillation to a string of bits formed by the outcomes of measurements in the basis with higher quantum bit error rate is closely connected to the two-to-one entanglement distillation protocol DEJMPS. Finally, we discuss the implications of these results for implementations of quantum key distribution.

Imperfect-interaction-free entanglement purification on stationary systems for solid quantum repeaters.

Solid quantum repeater is a core part in a large-scale quantum network. Entanglement purification, the key technique in a quantum repeater, is used to distill high-quality nonlocal entanglement from an ensemble in a mixed entangled state and to depress the vicious influence on quantum information carriers caused by noise. Here, we present an imperfect-interaction-free entanglement purification on nonlocal electron spins in quantum dots for solid quantum repeaters, using faithful parity check on electron spins. The faithful parity check can make correct judgement on the parity mode without destructing the nonlocal solid entanglement even with the imperfect interaction between a QD embedded inside a microcavity and a circularly polarized photon in the nearly realistic condition. Therefore, the imperfect-interaction-free entanglement purification can prevent the maximally entangled states from being changed into partially entangled ones and guarantee the fidelity of the nonlocal mixed state to a desired one after purification. As this scheme is feasible in the nearly realistic condition with imperfect interaction, the requirements for experimental implementation will be relaxed. These distinctive features make this imperfect-interaction-free entanglement purification have more practical applications in solid quantum repeaters for a large-scale quantum network.

Entanglement purification of two-photon systems in multiple degrees of freedom

Hyperentanglement purification is a very important element for high-capacity long-distance quantum communication. We present an efficient hyperentanglement purification protocol (hyper-EPP) for nonlocal two-photon systems in three degrees of freedom (DoFs), including the polarization, the time-bin, and the spatial-mode DoFs. Our hyper-EPP is constructed with two steps resorting to polarization–time–spatial parity-check operation using the quantum nondemolition detector and SWAP gates, respectively. With this hyper-EPP, the bit-flip errors in the three DoFs can be corrected with high efficiency. The implementation of our hyper-EPP is contributed by a cross-Kerr nonlinearity between the signal photons and a coherent state via Kerr media, which could be achieved with current techniques. Moreover, some currently available optical elements are applied in the purification process, which offer facilities for the practical implementation. It is useful for long-distance high-capacity quantum communication with hyperentanglement in multiple DoFs.

Spin-controlled generation of indistinguishable and distinguishable photons from silicon vacancy centres in silicon carbide

Quantum systems combining indistinguishable photon generation and spin-based quantum information processing are essential for remote quantum applications and networking. However, identification of suitable systems in scalable platforms remains a challenge. Here, we investigate the silicon vacancy centre in silicon carbide and demonstrate controlled emission of indistinguishable and distinguishable photons via coherent spin manipulation. Using strong off-resonant excitation and collecting zero-phonon line photons, we show a two-photon interference contrast close to 90% in Hong-Ou-Mandel type experiments. Further, we exploit the system’s intimate spin-photon relation to spin-control the colour and indistinguishability of consecutively emitted photons. Our results provide a deep insight into the system’s spin-phonon-photon physics and underline the potential of the industrially compatible silicon carbide platform for measurement-based entanglement distribution and photonic cluster state generation. Additional coupling to quantum registers based on individual nuclear spins would further allow for high-level network-relevant quantum information processing, such as error correction and entanglement purification.

Study on the formation and structural evolution of bead‐on‐string in electrospun polysulfone mats

Bead‐on‐string is a desirable morphology for some emerging applications of electrospun mats such as superhydrophobic surfaces. In this study, the bead‐on‐string morphology in electrospun polysulfone (PSU) mats was investigated and correlated with the solution concentration, voltage and feed rate. PSU/dimethylformamide solutions with different concentrations (4, 5.5, 7, 15, 18 and 20 wt% PSU) were electrospun at a constant feed rate (3.5 mL h–1) and voltage (15 kV). Critical chain overlap and entanglement concentrations were found to be 3.65 and 7.12 wt% PSU, respectively. The bead‐on‐string morphology was detected in the concentration range 7–18 wt% PSU, in close agreement with theoretical estimations. The evolution of the bead‐on‐string morphology in mats prepared from 15 wt% PSU solution and electrospun at three feed rates (i.e. 1.5, 2.5 and 3.5 mL h–1) and voltages (i.e. 12.5, 15 and 18 kV) were also studied. The results showed that the beads appear less in number as either the feed rate or the voltage increases. In addition, the morphology of the beads revealed a transition from a spherical to a spindle‐like appearance with an increase in voltage. The effect of feed rate on bead geometry, however, was revealed to depend on the applied voltage. © 2020 Society of Chemical Industry

Rheological aspects in fabricating pullulan-whey protein isolate emulsion suitable for electrospraying: Application in improving β-carotene stability

Beta-carotene has been used as a food colorant and functional ingredient, but these applications are limited due to its poor stability. The aim of this work was to improve the stability of β-carotene by encapsulating it in electrosprayed particles. The electrohydrodynamic behavior of pullulan solution was studied and the influence of encapsulation and core-to-wall ratio on the stability of β-carotene at different temperatures and relative humidity were investigated. The specific viscosity of the polymer solution increased linearly with the concentration until 5% w/w concentration. The critical entanglement concentration of the pullulan was found to be 4.58% wt. Among the various concentrations of pullulan studied, 3% w/w pullulan solution yielded spherical, monodisperse nanoparticles. Electrosprayed particles with 1:50 core-to-wall ratio had highest encapsulation efficiency. The rate of β-carotene loss displayed first order reaction kinetic within 14 days, while displayed diffusion limited mode after 14 days storage. The retention of β-carotene from the electrosprayed particles accelerated markedly with decreasing temperatures and relative humidity. This study provides a strategy for the preparation of promising electrosprayed particles to improve the stability of β-carotene.

Orbital-angular-momentum-based experimental test of Hardy's paradox for multisetting and multidimensional systems

Characterizing high-dimensional entangled states is of crucial importance in quantum information science and technology. Recent theoretical progress has been made to extend Hardy's paradox into a general scenario with multisetting and multidimensional systems, which enables the maximum probability of nonlocal events to surpass the bound that was limited in Hardy's original test. Hitherto, no experimental verification has been conducted to verify Hardy's paradox, as most of the previous experimental efforts were restricted to two-dimensional systems. Here, based on two-photon high-dimensional orbital angular momentum (OAM) entanglement, we report an experiment to demonstrate Hardy's paradox for multiple settings and multiple outcomes. We demonstrate the paradox for two-setting higher-dimensional OAM subspaces up to $d=7$, which reveals that the nonlocal events increase with dimension. Furthermore, we showcase the nonlocality with an experimentally recorded probability of 36.77% for a five-setting three-dimensional OAM subspace via entanglement concentration, thus showing a sharper contradiction between quantum mechanics and classical theory.

Intense circularly polarized attosecond pulse generation from solid targets irradiated with a two-color linearly polarized laser

Characterizing high-dimensional entangled states is of crucial importance in quantum information science and technology. Recent theoretical progress has been made to extend the Hardy's paradox into a general scenario with multisetting multidimensional systems, which can surpass the bound limited by the original version. Hitherto, no experimental verification has been conducted to verify such a Hardy's paradox, as most of previous experimental efforts were restricted to two-dimensional systems. Here, based on two-photon high-dimensional orbital angular momentum (OAM) entanglement, we report the first experiment to demonstrate the Hardy's paradox for multiple settings and multiple outcomes. We demonstrate the paradox for two-setting higher-dimensional OAM subspaces up to d = 7, which reveals that the nonlocal events increase with the dimension. Furthermore, we showcase the nonlocality with an experimentally recording probability of 36.77% for five-setting three-dimensional OAM subspace via entanglement concentration, and thus showing a sharper contradiction between quantum mechanics and classical theory.

Assisted concentration of Gaussian resources

In spite of their outstanding experimental relevance, Gaussian operations in continuous-variable quantum systems are subjected to fundamental limitations, as it is known that general resources cannot be distilled within the Gaussian paradigm. We show that these limitations can be overcome by considering a collaborative setting where one party increases the amount of local resource with the aid of another party, whose operations are assumed to be Gaussian but are otherwise unrestricted; the two parties can only communicate classically. We show that in single-shot scenarios, unlike in the well-known case of entanglement theory, two-way classical communication does not lead to any improvement over one-way classical communication from the aiding party to the aided party. We then provide a concise general expression for the Gaussian resource of assistance, i.e., the maximum amount of resource that can be obtained when the aiding party holds a purification of the aided party's state, as measured by a general monotone. To demonstrate its usefulness, we apply our result to two important kinds of resources, squeezing and entanglement, and find some simple analytic solutions. In the case of entanglement theory, we are able to find general upper bounds on the regularized Gaussian entanglement of assistance, and to establish additivity for tensor powers of thermal states. This allows us to draw a quantitative and enlightening comparison with the performance of assisted entanglement distillation in the non-Gaussian setting. On the technical side, we develop some variational expressions to handle functions of symplectic eigenvalues that may be of independent interest. Our results suggest further potential for Gaussian operations to play a major role in practical quantum information processing protocols.

Experimental random-party entanglement distillation via weak measurement

This work shows a proof-of-principle demonstration of the random entanglement distillation of Einstein-Podolsky-Rosen pairs from tripartite W states via weak measurements. The experimental distillation rate between two random parties appears larger than the theoretical limit of any distillation scheme between two specified parties.

Entanglement manipulation beyond local operations and classical communication

When a quantum system is distributed to spatially separated parties, it is natural to consider how the system evolves when the parties perform local quantum operations with classical communication (LOCC). However, the structure of LOCC channels is exceedingly complex, leaving many important physical problems unsolved. In this paper, we consider generalized resource theories of entanglement based on different relaxations to the class of LOCC. The behavior of various entanglement measures is studied under non-entangling channels, as well as the newly introduced classes of dually non-entangling and positive partial transpose (PPT)-preserving channels. In an effort to better understand the nature of LOCC bound entanglement, we study the problem of entanglement distillation in these generalized resource theories. We first show that unlike LOCC, general non-entangling maps can be superactivated, in the sense that two copies of the same non-entangling map can, nevertheless, be entangling. On the single-copy level, we demonstrate that every NPT entangled state can be converted into an LOCC-distillable state using channels that are both dually non-entangling and having a PPT Choi representation and that every state can be converted into an LOCC-distillable state using operations belonging to any family of polytopes that approximate LOCC. We then turn to the stochastic convertibility of multipartite pure states and show that any two states can be interconverted by any polytope approximation to the set of separable channels. Finally, as an analog to k-positive maps, we introduce and analyze the set of k-non-entangling channels.

Characterizing multipartite entanglement by violation of CHSH inequalities

Entanglement of high-dimensional and multipartite quantum systems offer promising perspectives in quantum information processing. However, the characterization and measure of such kind of entanglement is of great challenge. Here we consider the overlaps between the maximal quantum mean values and the classical bound of the CHSH inequalities for pairwise-qubit states in two-dimensional subspaces. We show that the concurrence of a pure state in any high-dimensional multipartite system can be equivalently represented by these overlaps. Here we consider the projections of an arbitrary high-dimensional multipartite state to two-qubit states. We investigate the non-localities of these projected two-qubit sub-states by their violations of CHSH inequalities. From these violations, the overlaps between the maximal quantum mean values and the classical bound of the CHSH inequality, we show that the concurrence of a high-dimensional multipartite pure state can be exactly expressed by these overlaps. We further derive a lower bound of the concurrence for any quantum states, which is tight for pure states. The lower bound not only imposes restriction on the non-locality distributions among the pairwise qubit states, but also supplies a sufficient condition for distillation of bipartite entanglement. Effective criteria for detecting genuine tripartite entanglement and the lower bound of concurrence for genuine tripartite entanglement are also presented based on such non-localities.

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.

Continuous-variable quantum repeater based on quantum scissors and mode multiplexing

Quantum repeaters are indispensable for high-rate, long-distance quantum communications. The vision of a future quantum internet strongly hinges on realizing quantum repeaters in practice. Numerous repeaters have been proposed for discrete-variable (DV) single-photon-based quantum communications. Continuous variable (CV) encodings over the quadrature degrees of freedom of the electromagnetic field mode offer an attractive alternative. For example, CV transmission systems are easier to integrate with existing optical telecom systems compared to their DV counterparts. Yet, repeaters for CV have remained elusive. We present a novel quantum repeater scheme for CV entanglement distribution over a lossy bosonic channel that beats the direct transmission exponential rate-loss tradeoff. The scheme involves repeater nodes consisting of a) two-mode squeezed vacuum (TMSV) CV entanglement sources, b) the quantum scissors operation to perform nondeterministic noiseless linear amplification of lossy TMSV states, c) a layer of switched, mode multiplexing inspired by second-generation DV repeaters, which is the key ingredient apart from probabilistic entanglement purification that makes DV repeaters work, and d) a non-Gaussian entanglement swap operation. We report our exact results on the rate-loss envelope achieved by the scheme.

Approximate Quantum Error Correction Revisited: Introducing the Alpha-Bit

We establish that, in an appropriate limit, qubits of communication should be regarded as composite resources, decomposing cleanly into independent correlation and transmission components. Because qubits of communication can establish ebits of entanglement, qubits are more powerful resources than ebits. We identify a new communications resource, the zero-bit, which is precisely half the gap between them, replacing classical bits by zero-bits makes teleportation asymptotically reversible. The decomposition of a qubit into an ebit and two zero-bits has wide-ranging consequences including applications to state merging, the quantum channel capacity, entanglement distillation, quantum identification and remote state preparation. The source of these results is the theory of approximate quantum error correction. The action of a quantum channel is reversible if and only if no information is leaked to the environment, a characterization that is useful even in approximate form. However, different notions of approximation lead to qualitatively different forms of quantum error correction in the limit of large dimension. We study the effect of a constraint on the dimension of the reference system when considering information leakage. While the resulting condition fails to ensure that the entire input can be corrected, it does ensure that all subspaces of dimension matching that of the reference are correctable. The size of the reference can be characterized by a parameter $\alpha$, we call the associated resource an $\alpha$-bit. Changing $\alpha$ interpolates between standard quantum error correction and quantum identification, a form of equality testing for quantum states. We develop the theory of $\alpha$-bits, including the applications above, and determine the $\alpha$-bit capacity of general quantum channels, finding single-letter formulas for the entanglement-assisted and amortised variants.

Activation of Nonlocality in Bound Entanglement.

We discuss the relation between entanglement and nonlocality in the hidden nonlocality scenario. Hidden nonlocality signifies nonlocality that can be activated by applying local filters to a particular state that admits a local hidden-variable model in the Bell scenario. We present a fully biseparable three-qubit bound entangled state with a local model for the most general (nonsequential) measurements. This proves for the first time that bound entangled states can admit a local model for general measurements. We furthermore show that the local model breaks down when suitable local filters are applied. Our results demonstrate the first example of activation of nonlocality in bound entanglement. Hence, we show that genuine hidden nonlocality does not imply entanglement distillability.

Scaling laws of entangled polysaccharides

We study the dilute solution properties and entangled dynamics of hydroxypropyl cellulose (HPC), a semiflexible polymer, in aqueous solution. Intrinsic viscosity data are consistent with a polymer in θ solvent with a Kuhn length ≃22 nm. The overlap concentration, estimated as the reciprocal of the intrinsic viscosity scales with the degree of polymerisation as c* ∝ N−0.9. We evaluate different methods for estimating the entanglement cross-over, following the de Gennes scaling and hydrodynamic scaling models, and show that these lead to similar results. Above the entanglement concentration, the specific viscosity, longest relaxation time and plateau modulus scale as ηsp ≃ N3.9c4.2, τ ≃ N3.9c2.4 and GP ≃ N0c1.9. A comparison with other polymers suggests that the rheological properties displayed by HPC are common to many polysaccharide systems of varying backbone composition, stiffness and solvent quality, as long as the effect of hyper-entanglements can be neglected. On the other hand, the observed scaling laws differ appreciably from those of synthetic flexible polymers in good or θ-solvent.

$O(\sqrt\eta)$ efficiency entanglement distillation with one-time photon subtraction over near-zero transmittance bosonic channel

Entanglement distillation is an efficient method to retrieve high-quality entanglement from a large number of noise-damped entanglement states. Many investigations on continuous variable entanglement distillation have focused on low-loss or medium-loss channels. Herein, we primarily study entanglement distillation in extremely lossy (total channel transmittance η ≪ 1 ) or even near-zero transmittance ( η ≈ 0 ) channels. In particular, we analyze the manner in which entanglement and success probability decrease as η → 0 . The performances of conventional biside photon subtraction and one-time photon subtraction on two optical modes separated by L km are investigated. The motivation for our study includes the recent advancements in twin-field quantum key distribution, wherein single-photon detection is sufficient to provide a useful private key. In the same vein, we propose an entanglement distillation scheme with an efficiency of O ( η ) using one-time photon subtraction and weak coherent state injection. Thus, our proposed scheme provides a method for distilling extremely damped entanglement states for continuous variable quantum information processing.